Package 'Rwave' reference manual

Title:	Time-Frequency analysis of 1-D signals
Description:	Rwave is a library of R functions which provide an environment for the Time-Frequency analysis of 1-D signals (and especially for the wavelet and Gabor transforms of noisy signals). It was originally written for Splus by Rene Carmona, Bruno Torresani, and Wen L. Hwang, first at the University of California at Irvine and then at Princeton University. Credit should also be given to Andrea Wang whose functions on the dyadic wavelet transform are included. Rwave is based on the book: "Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S", by Rene Carmona, Wen L. Hwang and Bruno Torresani, Academic Press, 1998. This package is no longer actively maintained. A C++ rewrite of core functionality is in progress. If you'd like to participate, please contact Christian Gunning.
Authors:	S original by Rene Carmona <[email protected]> and Bruno Torresani <[email protected]>; R port by Brandon Whitcher <[email protected]>
Maintainer:	Brandon Whitcher <[email protected]> and Christian Gunning <[email protected]>
License:	GPL (>= 2)
Version:	1.25-2
Built:	2024-11-21 05:20:11 UTC
Source:	https://github.com/r-forge/rwave

Transient Signal

Description

Transient signal.

Usage

data(A0)
data(A0)

Format

A vector containing 1024 observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Transient Signal

Description

Transient signal.

Usage

data(A4)
data(A4)

Format

A vector containing 1024 observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Zero Padding

Description

Add zeros to the end of the data if necessary so that its length is a power of 2. It returns the data with zeros added if nessary and the length of the adjusted data.

Usage

adjust.length(inputdata)
adjust.length(inputdata)

Arguments

inputdata

either a text file or an S object containing data.

Value

Zero-padded 1D array.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Pixel from Amber Camara

Description

Pixel from amber camara.

Usage

data(amber7)
data(amber7)

Format

A vector containing 7000 observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Pixel from Amber Camara

Description

Pixel from amber camara.

Usage

data(amber8)
data(amber8)

Format

A vector containing 7000 observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Pixel from Amber Camara

Description

Pixel from amber camara.

Usage

data(amber9)
data(amber9)

Format

A vector containing 7000 observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Transient Signal

Description

Transient signal.

Usage

data(B0)
data(B0)

Format

A vector containing 1024 observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Transient Signal

Description

Transient signal.

Usage

data(B4)
data(B4)

Format

A vector containing 1024 observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Acoustic Returns

Description

Acoustic returns from natural underwater clutter.

Usage

data(back1.000)
data(back1.000)

Format

A vector containing 7936 observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Acoustic Returns

Description

Acoustic returns from ...

Usage

data(back1.180)
data(back1.180)

Format

A vector containing 7936 observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Acoustic Returns

Description

Acoustic returns from an underwater metallic object.

Usage

data(back1.220)
data(back1.220)

Format

A vector containing 7936 observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Transient Signal

Description

Transient signal.

Usage

data(C0)
data(C0)

Format

A vector containing 1024 observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Transient Signal

Description

Transient signal.

Usage

data(C4)
data(C4)

Format

A vector containing 1024 observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Ridge Chaining Procedure

Description

Chains the ridge estimates produced by the function crc.

Usage

cfamily(ccridge, bstep=1, nbchain=100, ptile=0.05)
cfamily(ccridge, bstep=1, nbchain=100, ptile=0.05)

Arguments

`ccridge`	unchained ridge set as the output of the function `crc`
`bstep`	maximal length for a gap in a ridge.
`nbchain`	maximal number of chains produced by the function.
`ptile`	relative threshold for the ridges.

Details

crc returns a measure in time-frequency (or time-scale) space. cfamily turns it into a series of one-dimensional objects (ridges). The measure is first thresholded, with a relative threshold value set to the input parameter ptile. During the chaining procedure, gaps within a given ridge are allowed and filled in. The maximal length of such gaps is the input parameter bstep.

Value

Returns the results of the chaining algorithm

`ordered map`	image containing the ridges (displayed with different colors)
`chain`	2D array containing the chained ridges, according to the chain data structure chain[,1]: first point of the ridge chain[,2]: length of the chain chain[,3:(chain[,2]+2)]: values of the ridge
`nbchain`	number of chains produced by the algorithm

References

See discussion in text of “Practical Time-Frequency Analysis”.

Continuous Gabor Transform

Description

Computes the continuous Gabor transform with Gaussian window.

Usage

cgt(input, nvoice, freqstep=(1/nvoice), scale=1, plot=TRUE)
cgt(input, nvoice, freqstep=(1/nvoice), scale=1, plot=TRUE)

Arguments

`input`	input signal (possibly complex-valued).
`nvoice`	number of frequencies for which gabor transform is to be computed.
`freqstep`	Sampling rate for the frequency axis.
`scale`	Size parameter for the window.
`plot`	logical variable set to TRUE to display the modulus of the continuous gabor transform on the graphic device.

Details

The output contains the (complex) values of the gabor transform of the input signal. The format of the output is a 2D array (signal\_size x nb\_scales).

Value

continuous (complex) gabor transform (2D array).

Warning

freqstep must be less than 1/nvoice to avoid aliasing. freqstep=1/nvoice corresponds to the Nyquist limit.

References

See discussion in text of “Practical Time-Frequency Analysis”.

Chen's Chirp

Description

Chen's chirp.

Usage

data(ch)
data(ch)

Format

A vector containing 15,000 observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Verify Maximum Resolution

Description

Stop when $2^{maxresoln}$ is larger than the signal size.

Usage

check.maxresoln(maxresoln, np)
check.maxresoln(maxresoln, np)

Arguments

`maxresoln`	number of decomposition scales.
`np`	signal size.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Threshold Phase based on Modulus

Description

Sets to zero the phase of time-frequency transform when modulus is below a certain value.

Usage

cleanph(tfrep, thresh=0.01, plot=TRUE)
cleanph(tfrep, thresh=0.01, plot=TRUE)

Arguments

`tfrep`	continuous time-frequency transform (2D array)
`thresh`	(relative) threshold.
`plot`	if set to TRUE, displays the maxima of cwt on the graphic device.

Value

thresholded phase (2D array)

References

See discussion in text of “Practical Time-Frequency Analysis”.

Dolphin Click Data

Description

Dolphin click data.

Usage

data(click)
data(click)

Format

A vector containing 2499 observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Ridge Estimation by Corona Method

Description

Estimate a (single) ridge from a time-frequency representation, using the corona method.

Usage

corona(tfrep, guess, tfspec=numeric(dim(tfrep)[2]), subrate=1,
temprate=3, mu=1, lambda=2 * mu, iteration=1000000, seed=-7,
stagnant=20000, costsub=1, plot=TRUE)
corona(tfrep, guess, tfspec=numeric(dim(tfrep)[2]), subrate=1,
temprate=3, mu=1, lambda=2 * mu, iteration=1000000, seed=-7,
stagnant=20000, costsub=1, plot=TRUE)

Arguments

`tfrep`	Time-Frequency representation (real valued).
`guess`	Initial guess for the algorithm.
`tfspec`	Estimate for the contribution of the noise to modulus.
`subrate`	Subsampling rate for ridge estimation.
`temprate`	Initial value of temperature parameter.
`mu`	Coefficient of the ridge's second derivative in cost function.
`lambda`	Coefficient of the ridge's derivative in cost function.
`iteration`	Maximal number of moves.
`seed`	Initialization of random number generator.
`stagnant`	Maximum number of stationary iterations before stopping.
`costsub`	Subsampling of cost function in output.
`plot`	When set(default), some results will be shown on the display.

Details

To accelerate convergence, it is useful to preprocess modulus before running annealing method. Such a preprocessing (smoothing and subsampling of modulus) is implemented in corona. The parameter subrate specifies the subsampling rate.

Value

Returns the estimated ridge and the cost function.

`ridge`	1D array (of same length as the signal) containing the ridge.
`cost`	1D array containing the cost function.

Warning

The returned cost may be a large array, which is time consuming. The argument costsub allows subsampling the cost function.

References

See discussion in text of “Practical Time-Frequency Analysis”.

Ridge Estimation by Modified Corona Method

Description

Estimate a ridge using the modified corona method (modified cost function).

Usage

coronoid(tfrep, guess, tfspec=numeric(dim(tfrep)[2]), subrate=1,
temprate=3, mu=1, lambda=2 * mu, iteration=1000000, seed=-7,
stagnant=20000, costsub=1, plot=TRUE)
coronoid(tfrep, guess, tfspec=numeric(dim(tfrep)[2]), subrate=1,
temprate=3, mu=1, lambda=2 * mu, iteration=1000000, seed=-7,
stagnant=20000, costsub=1, plot=TRUE)

Arguments

`tfrep`	Estimate for the contribution of the noise to modulus.
`guess`	Initial guess for the algorithm.
`tfspec`	Estimate for the contribution of the noise to modulus.
`subrate`	Subsampling rate for ridge estimation.
`temprate`	Initial value of temperature parameter.
`mu`	Coefficient of the ridge's derivative in cost function.
`lambda`	Coefficient of the ridge's second derivative in cost function.
`iteration`	Maximal number of moves.
`seed`	Initialization of random number generator.
`stagnant`	Maximum number of stationary iterations before stopping.
`costsub`	Subsampling of cost function in output.
`plot`	When set(default), some results will be shown on the display.

Details

To accelerate convergence, it is useful to preprocess modulus before running annealing method. Such a preprocessing (smoothing and subsampling of modulus) is implemented in coronoid. The parameter subrate specifies the subsampling rate.

Value

Returns the estimated ridge and the cost function.

`ridge`	1D array (of same length as the signal) containing the ridge.
`cost`	1D array containing the cost function.

Warning

The returned cost may be a large array. The argument costsub allows subsampling the cost function.

References

See discussion in text of “Practical Time-Frequency Analysis”.

Ridge Extraction by Crazy Climbers

Description

Uses the "crazy climber algorithm" to detect ridges in the modulus of a continuous wavelet or a Gabor transform.

Usage

crc(tfrep, tfspec=numeric(dim(tfrep)[2]), bstep=3, iteration=10000,
rate=0.001, seed=-7, nbclimb=10, flag.int=TRUE, chain=TRUE,
flag.temp=FALSE)
crc(tfrep, tfspec=numeric(dim(tfrep)[2]), bstep=3, iteration=10000,
rate=0.001, seed=-7, nbclimb=10, flag.int=TRUE, chain=TRUE,
flag.temp=FALSE)

Arguments

`tfrep`	modulus of the (wavelet or Gabor) transform.
`tfspec`	numeric vector which gives, for each value of the scale or frequency the expected size of the noise contribution.
`bstep`	stepsize for random walk of the climbers.
`iteration`	number of iterations.
`rate`	initial value of the temperature.
`seed`	initial value of the random number generator.
`nbclimb`	number of crazy climbers.
`flag.int`	if set to TRUE, the weighted occupation measure is computed.
`chain`	if set to TRUE, chaining of the ridges is done.
`flag.temp`	if set to TRUE: constant temperature.

Value

Returns a 2D array called beemap containing the (weighted or unweighted) occupation measure (integrated with respect to time)

References

See discussion in text of “Practical Time-Frequency Analysis”.

Crazy Climbers Reconstruction by Penalization

Description

Reconstructs a real valued signal from the output of crc (wavelet case) by minimizing an appropriate quadratic form.

Usage

crcrec(siginput, inputwt, beemap, noct, nvoice, compr, minnbnodes=2,
w0=2 * pi, bstep=5, ptile=0.01, epsilon=0, fast=FALSE, para=5, real=FALSE,
plot=2)
crcrec(siginput, inputwt, beemap, noct, nvoice, compr, minnbnodes=2,
w0=2 * pi, bstep=5, ptile=0.01, epsilon=0, fast=FALSE, para=5, real=FALSE,
plot=2)

Arguments

`siginput`	original signal.
`inputwt`	wavelet transform.
`beemap`	occupation measure, output of `crc`.
`noct`	number of octaves.
`nvoice`	number of voices per octave.
`compr`	compression rate for sampling the ridges.
`minnbnodes`	minimal number of points per ridge.
`w0`	center frequency of the wavelet.
`bstep`	size (in the time direction) of the steps for chaining.
`ptile`	relative threshold of occupation measure.
`epsilon`	constant in front of the smoothness term in penalty function.
`fast`	if set to TRUE, uses trapezoidal rule to evaluate $Q_2$.
`para`	scale parameter for extrapolating the ridges.
`real`	if set to TRUE, uses only real constraints.
`plot`	1: displays signal,components,and reconstruction one after another. 2: displays signal, components and reconstruction.

Details

When ptile is high, boundary effects may appeare. para controls extrapolation of the ridge.

Value

Returns a structure containing the following elements:

`rec`	reconstructed signal.
`ordered`	image of the ridges (with different colors).
`comp`	2D array containing the signals reconstructed from ridges.

Display chained ridges

Description

displays a family of chained ridges, output of cfamily.

Usage

crfview(beemap, twod=TRUE)
crfview(beemap, twod=TRUE)

Arguments

`beemap`	Family of chained ridges, output of `cfamily`.
`twod`	If set to T, displays the ridges as an image. If set to F, displays as a series of curves.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Continuous Wavelet Transform

Description

Computes the continuous wavelet transform with for the (complex-valued) Morlet wavelet.

Usage

cwt(input, noctave, nvoice=1, w0=2 * pi, twoD=TRUE, plot=TRUE)
cwt(input, noctave, nvoice=1, w0=2 * pi, twoD=TRUE, plot=TRUE)

Arguments

`input`	input signal (possibly complex-valued)
`noctave`	number of powers of 2 for the scale variable
`nvoice`	number of scales in each octave (i.e. between two consecutive powers of 2).
`w0`	central frequency of the wavelet.
`twoD`	logical variable set to T to organize the output as a 2D array (signal\_size x nb\_scales), otherwise, the output is a 3D array (signal\_size x noctave x nvoice).
`plot`	if set to T, display the modulus of the continuous wavelet transform on the graphic device.

Details

The output contains the (complex) values of the wavelet transform of the input signal. The format of the output can be

2D array (signal\_size x nb\_scales)

3D array (signal\_size x noctave x nvoice)

Since Morlet's wavelet is not strictly speaking a wavelet (it is not of vanishing integral), artifacts may occur for certain signals.

Value

continuous (complex) wavelet transform

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Examples

    x <- 1:512
    chirp <- sin(2*pi * (x + 0.002 * (x-256)^2 ) / 16)
    retChirp <- cwt(chirp, noctave=5, nvoice=12)
x <- 1:512
    chirp <- sin(2*pi * (x + 0.002 * (x-256)^2 ) / 16)
    retChirp <- cwt(chirp, noctave=5, nvoice=12)

Continuous Wavelet Transform Display

Description

Converts the output (modulus or argument) of cwtpolar to a 2D array and displays on the graphic device.

Usage

cwtimage(input)
cwtimage(input)

Arguments

input

3D array containing a continuous wavelet transform

Details

The output contains the (complex) values of the wavelet transform of the input signal. The format of the output can be

2D array (signal\_size x nb\_scales)

3D array (signal\_size x noctave x nvoice)

Value

2D array continuous (complex) wavelet transform

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Examples

    x <- 1:512
    chirp <- sin(2*pi * (x + 0.002 * (x-256)^2 ) / 16)
    retChirp <- cwt(chirp, noctave=5, nvoice=12, twoD=FALSE, plot=FALSE)
    retPolar <- cwtpolar(retChirp)
    retImageMod <- cwtimage(retPolar$modulus)
    retImageArg <- cwtimage(retPolar$argument)
x <- 1:512
    chirp <- sin(2*pi * (x + 0.002 * (x-256)^2 ) / 16)
    retChirp <- cwt(chirp, noctave=5, nvoice=12, twoD=FALSE, plot=FALSE)
    retPolar <- cwtpolar(retChirp)
    retImageMod <- cwtimage(retPolar$modulus)
    retImageArg <- cwtimage(retPolar$argument)

Continuous Wavelet Transform with Phase Derivative

Description

Computes the continuous wavelet transform with (complex-valued) Morlet wavelet and its phase derivative.

Usage

cwtp(input, noctave, nvoice=1, w0=2 * pi, twoD=TRUE, plot=TRUE)
cwtp(input, noctave, nvoice=1, w0=2 * pi, twoD=TRUE, plot=TRUE)

Arguments

`input`	input signal (possibly complex-valued)
`noctave`	number of powers of 2 for the scale variable
`nvoice`	number of scales in each octave (i.e., between two consecutive powers of 2).
`w0`	central frequency of the wavelet.
`twoD`	logical variable set to `T` to organize the output as a 2D array (signal size $\times$ nb scales), otherwise, the output is a 3D array (signal size $\times$ noctave $\times$ nvoice).
`plot`	if set to `TRUE`, display the modulus of the continuous wavelet transform on the graphic device.

Value

list containing the continuous (complex) wavelet transform and the phase derivative

`wt`	array of complex numbers for the values of the continuous wavelet transform.
`f`	array of the same dimensions containing the values of the derivative of the phase of the continuous wavelet transform.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Examples

    ## discards imaginary part with error,
    ## c code does not account for Im(input)
    x <- 1:512
    chirp <- sin(2*pi * (x + 0.002 * (x-256)^2 ) / 16)
    chirp <- chirp + 1i * sin(2*pi * (x + 0.004 * (x-256)^2 ) / 16)
    retChirp <- cwtp(chirp, noctave=5, nvoice=12)
## discards imaginary part with error,
    ## c code does not account for Im(input)
    x <- 1:512
    chirp <- sin(2*pi * (x + 0.002 * (x-256)^2 ) / 16)
    chirp <- chirp + 1i * sin(2*pi * (x + 0.004 * (x-256)^2 ) / 16)
    retChirp <- cwtp(chirp, noctave=5, nvoice=12)

Conversion to Polar Coordinates

Description

Converts one of the possible outputs of the function cwt to modulus and phase.

Usage

cwtpolar(cwt, threshold=0)
cwtpolar(cwt, threshold=0)

Arguments

`cwt`	3D array containing the values of a continuous wavelet transform in the format (signal size $\times$ noctave $\times$ nvoice) as in the output of the function `cwt` with the logical flag `twodimension` set to FALSE.
`threshold`	value of a level for the absolute value of the modulus below which the value of the argument of the output is set to $-\pi$ .

Details

The output contains the (complex) values of the wavelet transform of the input signal. The format of the output can be

2D array (signal size $\times$ nb\_scales)

3D array (signal size $\times$ noctave $\times$ nvoice)

Value

Modulus and Argument of the values of the continuous wavelet transform

`output1`	3D array giving the values (in the same format as the input) of the modulus of the input.
`output2`	3D array giving the values of the argument of the input.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Examples

    x <- 1:512
    chirp <- sin(2*pi * (x + 0.002 * (x-256)^2 ) / 16)
    retChirp <- cwt(chirp, noctave=5, nvoice=12, twoD=FALSE, plot=FALSE)
    retPolar <- cwtpolar(retChirp)
x <- 1:512
    chirp <- sin(2*pi * (x + 0.002 * (x-256)^2 ) / 16)
    retChirp <- cwt(chirp, noctave=5, nvoice=12, twoD=FALSE, plot=FALSE)
    retPolar <- cwtpolar(retChirp)

Squeezed Continuous Wavelet Transform

Description

Computes the synchrosqueezed continuous wavelet transform with the (complex-valued) Morlet wavelet.

Usage

cwtsquiz(input, noctave, nvoice=1, w0=2 * pi, twoD=TRUE, plot=TRUE)
cwtsquiz(input, noctave, nvoice=1, w0=2 * pi, twoD=TRUE, plot=TRUE)

Arguments

`input`	input signal (possibly complex-valued)
`noctave`	number of powers of 2 for the scale variable
`nvoice`	number of scales in each octave (i.e. between two consecutive powers of 2).
`w0`	central frequency of the wavelet.
`twoD`	logical variable set to T to organize the output as a 2D array (signal size $\times$ nb scales), otherwise, the output is a 3D array (signal size $\times$ noctave $\times$ nvoice).
`plot`	logical variable set to T to T to display the modulus of the squeezed wavelet transform on the graphic device.

Details

The output contains the (complex) values of the squeezed wavelet transform of the input signal. The format of the output can be

2D array (signal size $\times$ nb scales),

3D array (signal size $\times$ noctave $\times$ nvoice).

Value

synchrosqueezed continuous (complex) wavelet transform

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Cauchy's wavelet transform

Description

Compute the continuous wavelet transform with (complex-valued) Cauchy's wavelet.

Usage

cwtTh(input, noctave, nvoice=1, moments, twoD=TRUE, plot=TRUE)
cwtTh(input, noctave, nvoice=1, moments, twoD=TRUE, plot=TRUE)

Arguments

`input`	input signal (possibly complex-valued).
`noctave`	number of powers of 2 for the scale variable.
`nvoice`	number of scales in each octave (i.e. between two consecutive powers of 2).
`moments`	number of vanishing moments.
`twoD`	logical variable set to `T` to organize the output as a 2D array (signal size x nb scales), otherwise, the output is a 3D array (signal size x noctave x nvoice).
`plot`	if set to `T`, display the modulus of the continuous wavelet transform on the graphic device.

Details

The output contains the (complex) values of the wavelet transform of the input signal. The format of the output can be

2D array (signal size $\times$ nb scales)

3D array (signal size $\times$ noctave $\times$ nvoice)

Value

tmp

continuous (complex) wavelet transform.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Examples

    x <- 1:512
    chirp <- sin(2*pi * (x + 0.002 * (x-256)^2 ) / 16)
    retChirp <- cwtTh(chirp, noctave=5, nvoice=12, moments=20)
x <- 1:512
    chirp <- sin(2*pi * (x + 0.002 * (x-256)^2 ) / 16)
    retChirp <- cwtTh(chirp, noctave=5, nvoice=12, moments=20)

Transient Signal

Description

Transient signal.

Usage

data(D0)
data(D0)

Format

A vector containing 1024 observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Transient Signal

Description

Transient signal.

Usage

data(D4)
data(D4)

Format

A vector containing 1024 observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Continuous Wavelet Transform with derivative of Gaussian

Description

Computes the continuous wavelet transform with for (complex-valued) derivative of Gaussian wavelets.

Usage

DOG(input, noctave, nvoice=1, moments, twoD=TRUE, plot=TRUE)
DOG(input, noctave, nvoice=1, moments, twoD=TRUE, plot=TRUE)

Arguments

`input`	input signal (possibly complex-valued).
`noctave`	number of powers of 2 for the scale variable.
`moments`	number of vanishing moments of the wavelet (order of the derivative).
`nvoice`	number of scales in each octave (i.e. between two consecutive powers of 2)
`twoD`	logical variable set to T to organize the output as a 2D array (signal\_size x nb\_scales), otherwise, the output is a 3D array (signal\_size x noctave x nvoice)
`plot`	if set to T, display the modulus of the continuous wavelet transform on the graphic device

Details

The output contains the (complex) values of the wavelet transform of the input signal. The format of the output can be

2D array (signal\_size x nb\_scales)

3D array (signal\_size x noctave x nvoice)

Value

continuous (complex) wavelet transform

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Inverse Dyadic Wavelet Transform

Description

Invert the dyadic wavelet transform.

Usage

dwinverse(wt, filtername="Gaussian1")
dwinverse(wt, filtername="Gaussian1")

Arguments

`wt`	dyadic wavelet transform
`filtername`	filters used. ("Gaussian1" stands for the filters corresponds to those of Mallat and Zhong's wavlet. And "Haar" stands for the filters of Haar basis.

Value

Reconstructed signal

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Heart Rate Data

Description

Successive beat-to-beat intervals for a normal patient.

Usage

data(Ekg)
data(Ekg)

Format

A vector containing 16,042 observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Plot Dyadic Wavelet Transform Extrema

Description

Plot dyadic wavelet transform extrema (output of ext).

Usage

epl(dwext)
epl(dwext)

Arguments

dwext

dyadic wavelet transform (output of ext).

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Extrema of Dyadic Wavelet Transform

Description

Compute the local extrema of the dyadic wavelet transform modulus.

Usage

ext(wt, scale=FALSE, plot=TRUE)
ext(wt, scale=FALSE, plot=TRUE)

Arguments

`wt`	dyadic wavelet transform.
`scale`	flag indicating if the extrema at each resolution will be plotted at the same scale.
`plot`	if set to TRUE, displays the transform on the graphics device.

Value

Structure containing:

`original`	original signal.
`extrema`	extrema representation.
`Sf`	coarse resolution of signal.
`maxresoln`	number of decomposition scales.
`np`	size of signal.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Kernel for Reconstruction from Gabor Ridges

Description

Computes the cost from the sample of points on the estimated ridge and the matrix used in the reconstruction of the original signal, using simple trapezoidal rule for integrals.

Usage

fastgkernel(node, phinode, freqstep, scale, x.inc=1, x.min=node[1],
x.max=node[length(node)], plot=FALSE)
fastgkernel(node, phinode, freqstep, scale, x.inc=1, x.min=node[1],
x.max=node[length(node)], plot=FALSE)

Arguments

`node`	values of the variable b for the nodes of the ridge
`phinode`	values of the frequency variable $\omega$ for the nodes of the ridge
`freqstep`	sampling rate for the frequency axis
`scale`	size of the window
`x.inc`	step unit for the computation of the kernel.
`x.min`	minimal value of x for the computation of $G_2$ .
`x.max`	maximal value of x for the computation of $G_2$ .
`plot`	if set to TRUE, displays the modulus of the matrix of $G_2$ .

Details

Uses trapezoidal rule (instead of Romberg's method) to evaluate the kernel.

Value

matrix of the $G_2$ kernel.

References

See discussions in the text of “Time-Frequency Analysis”.

Kernel for Reconstruction from Wavelet Ridges

Description

Computes the cost from the sample of points on the estimated ridge and the matrix used in the reconstruction of the original signal, using simple trapezoidal rule for integrals.

Usage

fastkernel(node, phinode, nvoice, x.inc=1, x.min=node[1],
x.max=node[length(node)], w0=2 * pi, plot=FALSE)
fastkernel(node, phinode, nvoice, x.inc=1, x.min=node[1],
x.max=node[length(node)], w0=2 * pi, plot=FALSE)

Arguments

`node`	values of the variable b for the nodes of the ridge.
`phinode`	values of the scale variable a for the nodes of the ridge.
`nvoice`	number of scales within 1 octave.
`x.inc`	step unit for the computation of the kernel
`x.min`	minimal value of x for the computation of $Q_2$ .
`x.max`	maximal value of x for the computation of $Q_2$ .
`w0`	central frequency of the wavelet
`plot`	if set to TRUE, displays the modulus of the matrix of $Q_2$ .

Details

Uses trapezoidal rule (instead of Romberg's method) to evaluate the kernel.

Value

matrix of the $Q_2$ kernel.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Examples

# The function is currently defined as
function(node, phinode, nvoice, x.inc = 1, x.min = node[1], x.max = node[length(node)], w0 = 2 * pi, plot = F)
{
#########################################################################
#     fastkernel:   
#     -----------
#	   Same as kernel, except that the kernel is computed
#	     using Riemann sums instead of Romberg integration.
#
#     Input:
#     ------
#      node: values of the variable b for the nodes of the ridge
#      phinode: values of the scale variable a for the nodes of the ridge
#      nvoice: number of scales within 1 octave
#      x.inc: step unit for the computation of the kernel
#      x.min: minimal value of x for the computation of Q2
#      x.max: maximal value of x for the computation of Q2
#      w0: central frequency of the wavelet
#      plot: if set to TRUE, displays the modulus of the matrix of Q2
#
#     Output:
#     -------
#      ker: matrix of the Q2 kernel
#
#########################################################################
	lng <- as.integer((x.max - x.min)/x.inc) + 1
	nbnode <- length(node)
	b.start <- x.min - 50
	b.end <- x.max + 50
	ker.r <- matrix(0, lng, lng)
	ker.i <- matrix(0, lng, lng)
	dim(ker.r) <- c(lng * lng, 1)
	dim(ker.i) <- c(lng * lng, 1)
	phinode <- 2 * 2^(phinode/nvoice)
	z <- .C(fastkernel,
		ker.r = as.double(ker.r),
		ker.i = as.double(ker.i),
		as.integer(x.min),
		as.integer(x.max),
		as.integer(x.inc),
		as.integer(lng),
		as.double(node),
		as.double(phinode),
		as.integer(nbnode),
		as.double(w0),
		as.double(b.start),
		as.double(b.end))
	ker.r <- z$ker.r
	ker.i <- z$ker.i
	dim(ker.r) <- c(lng, lng)
	dim(ker.i) <- c(lng, lng)
	ker <- matrix(0, lng, lng)
	i <- sqrt(as.complex(-1))
	ker <- ker.r + i * ker.i
	if(plot == T) {
		par(mfrow = c(1, 1))
		image(Mod(ker))
		title("Matrix of the reconstructing kernel (modulus)")
	}
	ker
}# The function is currently defined as
function(node, phinode, nvoice, x.inc = 1, x.min = node[1], x.max = node[length(node)], w0 = 2 * pi, plot = F)
{
#########################################################################
#     fastkernel:   
#     -----------
#	   Same as kernel, except that the kernel is computed
#	     using Riemann sums instead of Romberg integration.
#
#     Input:
#     ------
#      node: values of the variable b for the nodes of the ridge
#      phinode: values of the scale variable a for the nodes of the ridge
#      nvoice: number of scales within 1 octave
#      x.inc: step unit for the computation of the kernel
#      x.min: minimal value of x for the computation of Q2
#      x.max: maximal value of x for the computation of Q2
#      w0: central frequency of the wavelet
#      plot: if set to TRUE, displays the modulus of the matrix of Q2
#
#     Output:
#     -------
#      ker: matrix of the Q2 kernel
#
#########################################################################
	lng <- as.integer((x.max - x.min)/x.inc) + 1
	nbnode <- length(node)
	b.start <- x.min - 50
	b.end <- x.max + 50
	ker.r <- matrix(0, lng, lng)
	ker.i <- matrix(0, lng, lng)
	dim(ker.r) <- c(lng * lng, 1)
	dim(ker.i) <- c(lng * lng, 1)
	phinode <- 2 * 2^(phinode/nvoice)
	z <- .C(fastkernel,
		ker.r = as.double(ker.r),
		ker.i = as.double(ker.i),
		as.integer(x.min),
		as.integer(x.max),
		as.integer(x.inc),
		as.integer(lng),
		as.double(node),
		as.double(phinode),
		as.integer(nbnode),
		as.double(w0),
		as.double(b.start),
		as.double(b.end))
	ker.r <- z$ker.r
	ker.i <- z$ker.i
	dim(ker.r) <- c(lng, lng)
	dim(ker.i) <- c(lng, lng)
	ker <- matrix(0, lng, lng)
	i <- sqrt(as.complex(-1))
	ker <- ker.r + i * ker.i
	if(plot == T) {
		par(mfrow = c(1, 1))
		image(Mod(ker))
		title("Matrix of the reconstructing kernel (modulus)")
	}
	ker
}

Generate Gabor function

Description

Generates a Gabor for given location and frequency.

Usage

gabor(sigsize, location, frequency, scale)
gabor(sigsize, location, frequency, scale)

Arguments

`sigsize`	length of the Gabor function.
`location`	position of the Gabor function.
`frequency`	frequency of the Gabor function.
`scale`	size parameter for the Gabor function.

Value

complex 1D array of size sigsize.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Crazy Climbers Reconstruction by Penalization

Description

Reconstructs a real-valued signal from ridges found by crazy climbers on a Gabor transform.

Usage

gcrcrec(siginput, inputgt, beemap, nvoice, freqstep, scale, compr,
        bstep=5, ptile=0.01, epsilon=0, fast=TRUE, para=5, minnbnodes=3,
        hflag=FALSE, real=FALSE, plot=2)
gcrcrec(siginput, inputgt, beemap, nvoice, freqstep, scale, compr,
        bstep=5, ptile=0.01, epsilon=0, fast=TRUE, para=5, minnbnodes=3,
        hflag=FALSE, real=FALSE, plot=2)

Arguments

`siginput`	original signal.
`inputgt`	Gabor transform.
`beemap`	occupation measure, output of `crc`.
`nvoice`	number of frequencies.
`freqstep`	sampling step for frequency axis.
`scale`	size of windows.
`compr`	compression rate to be applied to the ridges.
`bstep`	size (in the time direction) of the steps for chaining.
`ptile`	threshold of ridge
`epsilon`	constant in front of the smoothness term in penalty function.
`fast`	if set to TRUE, uses trapezoidal rule to evaluate $Q_2$ .
`para`	scale parameter for extrapolating the ridges.
`minnbnodes`	minimal number of points per ridge.
`hflag`	if set to FALSE, uses the identity as first term in the kernel. If not, uses $Q_1$ instead.
`real`	if set to `TRUE`, uses only real constraints.
`plot`	1 displays signal,components, and reconstruction one after another. 2 displays signal, components and reconstruction.

Details

When ptile is high, boundary effects may appear. para controls extrapolation of the ridge.

Value

Returns a structure containing the following elements:

`rec`	reconstructed signal.
`ordered`	image of the ridges (with different colors).
`comp`	2D array containing the signals reconstructed from ridges.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Kernel for Reconstruction from Gabor Ridges

Description

Computes the cost from the sample of points on the estimated ridge and the matrix used in the reconstruction of the original signal.

Usage

gkernel(node, phinode, freqstep, scale, x.inc=1, x.min=node[1],
x.max=node[length(node)], plot=FALSE)
gkernel(node, phinode, freqstep, scale, x.inc=1, x.min=node[1],
x.max=node[length(node)], plot=FALSE)

Arguments

`node`	values of the variable b for the nodes of the ridge.
`phinode`	values of the scale variable a for the nodes of the ridge.
`freqstep`	sampling rate for the frequency axis.
`scale`	size of the window.
`x.inc`	step unit for the computation of the kernel.
`x.min`	minimal value of x for the computation of $Q_2$ .
`x.max`	maximal value of x for the computation of $Q_2$ .
`plot`	if set to TRUE, displays the modulus of the matrix of $Q_2$ .

Value

matrix of the $Q_2$ kernel

References

See discussions in the text of “Time-Frequency Analysis”.

Reconstruction from a Ridge

Description

Reconstructs signal from a “regularly sampled” ridge, in the Gabor case.

Usage

gregrec(siginput, gtinput, phi, nbnodes, nvoice, freqstep, scale,
epsilon=0, fast=FALSE, plot=FALSE, para=0, hflag=FALSE, real=FALSE,
check=FALSE)
gregrec(siginput, gtinput, phi, nbnodes, nvoice, freqstep, scale,
epsilon=0, fast=FALSE, plot=FALSE, para=0, hflag=FALSE, real=FALSE,
check=FALSE)

Arguments

`siginput`	input signal.
`gtinput`	Gabor transform, output of `cgt`.
`phi`	unsampled ridge.
`nbnodes`	number of nodes used for the reconstruction.
`nvoice`	number of different scales per octave
`freqstep`	sampling rate for the frequency axis
`scale`	size parameter for the Gabor function.
`epsilon`	coefficient of the $Q_2$ term in reconstruction kernel
`fast`	if set to T, the kernel is computed using trapezoidal rule.
`plot`	if set to TRUE, displays original and reconstructed signals
`para`	scale parameter for extrapolating the ridges.
`hflag`	if set to TRUE, uses $Q_1$ as first term in the kernel.
`real`	if set to TRUE, uses only real constraints on the transform.
`check`	if set to TRUE, computes `cwt` of reconstructed signal.

Value

Returns a list containing:

`sol`	reconstruction from a ridge.
`A`	<gaborlets,dualgaborlets> matrix.
`lam`	coefficients of dual wavelets in reconstructed signal.
`dualwave`	array containing the dual wavelets.
`gaborets`	array containing the wavelets on sampled ridge.
`solskel`	Gabor transform of sol, restricted to the ridge.
`inputskel`	Gabor transform of signal, restricted to the ridge.
`Q2`	second part of the reconstruction kernel.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Reconstruction from a Ridge

Description

Reconstructs signal from sample of a ridge, in the Gabor case.

Usage

gridrec(gtinput, node, phinode, nvoice, freqstep, scale, Qinv,
epsilon, np, real=FALSE, check=FALSE)
gridrec(gtinput, node, phinode, nvoice, freqstep, scale, Qinv,
epsilon, np, real=FALSE, check=FALSE)

Arguments

`gtinput`	Gabor transform, output of `cgt`.
`node`	time coordinates of the ridge samples.
`phinode`	frequency coordinates of the ridge samples.
`nvoice`	number of different frequencies.
`freqstep`	sampling rate for the frequency axis.
`scale`	scale of the window.
`Qinv`	inverse of the matrix $Q$ of the quadratic form.
`epsilon`	coefficient of the $Q_2$ term in reconstruction kernel
`np`	number of samples of the reconstructed signal.
`real`	if set to TRUE, uses only constraints on the real part of the transform.
`check`	if set to TRUE, computes `cgt` of reconstructed signal.

Value

Returns a list containing the reconstructed signal and the chained ridges.

`sol`	reconstruction from a ridge.
`A`	<gaborlets,dualgaborlets> matrix.
`lam`	coefficients of dual gaborlets in reconstructed signal.
`dualwave`	array containing the dual gaborlets.
`gaborets`	array of gaborlets located on the ridge samples.
`solskel`	Gabor transform of sol, restricted to the ridge.
`inputskel`	Gabor transform of signal, restricted to the ridge.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Sampled Identity

Description

Generate a sampled identity matrix.

Usage

gsampleOne(node, scale, np)
gsampleOne(node, scale, np)

Arguments

`node`	location of the reconstruction gabor functions.
`scale`	scale of the gabor functions.
`np`	size of the reconstructed signal.

Value

diagonal of the “sampled” $Q_1$ term (1D vector)

References

See discussions in the text of “Time-Frequency Analysis”.

Gabor Functions on a Ridge

Description

Generation of Gabor functions located on the ridge.

Usage

gwave(bridge, omegaridge, nvoice, freqstep, scale, np, N)
gwave(bridge, omegaridge, nvoice, freqstep, scale, np, N)

Arguments

`bridge`	time coordinates of the ridge samples
`omegaridge`	frequency coordinates of the ridge samples
`nvoice`	number of different scales per octave
`freqstep`	sampling rate for the frequency axis
`scale`	scale of the window
`np`	size of the reconstruction kernel
`N`	number of complex constraints

Value

Array of Gabor functions located on the ridge samples

References

See discussions in the text of "Time-Frequency Analysis”.

Real Gabor Functions on a Ridge

Description

Generation of the real parts of gabor functions located on a ridge. (modification of gwave.)

Usage

gwave2(bridge, omegaridge, nvoice, freqstep, scale, np, N)
gwave2(bridge, omegaridge, nvoice, freqstep, scale, np, N)

Arguments

`bridge`	time coordinates of the ridge samples
`omegaridge`	frequency coordinates of the ridge samples
`nvoice`	number of different scales per octave
`freqstep`	sampling rate for the frequency axis
`scale`	scale of the window
`np`	size of the reconstruction kernel
`N`	number of complex constraints

Value

Array of real Gabor functions located on the ridge samples

References

See discussions in the text of “Time-Frequency Analysis”.

How Are You?

Description

Example of speech signal.

Usage

data(HOWAREYOU)
data(HOWAREYOU)

Format

A vector containing 5151 observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Estimate Hurst Exponent

Description

Estimates Hurst exponent from a wavelet transform.

Usage

hurst.est(wspec, range, nvoice, plot=TRUE)
hurst.est(wspec, range, nvoice, plot=TRUE)

Arguments

`wspec`	wavelet spectrum (output of `tfmean`)
`range`	range of scales from which estimate the exponent.
`nvoice`	number of scales per octave of the wavelet transform.
`plot`	if set to `TRUE`, displays regression line on current plot.

Value

complex 1D array of size sigsize.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Examples

# White Noise Hurst Exponent: The plots on the top row of Figure 6.8
# were produced by the folling S-commands. These make use of the two
# functions Hurst.est (estimation of Hurst exponent from CWT) and
# wspec.pl (display wavelet spectrum).

# Compare the periodogram and the wavelet spectral estimate.
wnoise <- rnorm(8192)
plot.ts(wnoise)
spwnoise <- fft(wnoise)
spwnoise <- Mod(spwnoise)
spwnoise <- spwnoise*spwnoise
plot(spwnoise[1:4096], log="xy", type="l")
lswnoise <- lsfit(log10(1:4096), log10(spwnoise[1:4096]))
abline(lswnoise$coef)
cwtwnoise <- DOG(wnoise, 10, 5, 1, plot=FALSE)
mcwtwnoise <- Mod(cwtwnoise)
mcwtwnoise <- mcwtwnoise*mcwtwnoise
wspwnoise <- tfmean(mcwtwnoise, plot=FALSE)
wspec.pl(wspwnoise, 5)
hurst.est(wspwnoise, 1:50, 5)
# White Noise Hurst Exponent: The plots on the top row of Figure 6.8
# were produced by the folling S-commands. These make use of the two
# functions Hurst.est (estimation of Hurst exponent from CWT) and
# wspec.pl (display wavelet spectrum).

# Compare the periodogram and the wavelet spectral estimate.
wnoise <- rnorm(8192)
plot.ts(wnoise)
spwnoise <- fft(wnoise)
spwnoise <- Mod(spwnoise)
spwnoise <- spwnoise*spwnoise
plot(spwnoise[1:4096], log="xy", type="l")
lswnoise <- lsfit(log10(1:4096), log10(spwnoise[1:4096]))
abline(lswnoise$coef)
cwtwnoise <- DOG(wnoise, 10, 5, 1, plot=FALSE)
mcwtwnoise <- Mod(cwtwnoise)
mcwtwnoise <- mcwtwnoise*mcwtwnoise
wspwnoise <- tfmean(mcwtwnoise, plot=FALSE)
wspec.pl(wspwnoise, 5)
hurst.est(wspwnoise, 1:50, 5)

Ridge Estimation by ICM Method

Description

Estimate a (single) ridge from a time-frequency representation, using the ICM minimization method.

Usage

icm(modulus, guess, tfspec=numeric(dim(modulus)[2]), subrate=1,
mu=1, lambda=2 * mu, iteration=100)
icm(modulus, guess, tfspec=numeric(dim(modulus)[2]), subrate=1,
mu=1, lambda=2 * mu, iteration=100)

Arguments

`modulus`	Time-Frequency representation (real valued).
`guess`	Initial guess for the algorithm.
`tfspec`	Estimate for the contribution of the noise to modulus.
`subrate`	Subsampling rate for ridge estimation.
`mu`	Coefficient of the ridge's second derivative in cost function.
`lambda`	Coefficient of the ridge's derivative in cost function.
`iteration`	Maximal number of moves.

Details

To accelerate convergence, it is useful to preprocess modulus before running annealing method. Such a preprocessing (smoothing and subsampling of modulus) is implemented in icm. The parameter subrate specifies the subsampling rate.

Value

Returns the estimated ridge and the cost function.

`ridge`	1D array (of same length as the signal) containing the ridge.
`cost`	1D array containing the cost function.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Kernel for Reconstruction from Wavelet Ridges

Description

Computes the cost from the sample of points on the estimated ridge and the matrix used in the reconstruction of the original signal

Usage

kernel(node, phinode, nvoice, x.inc=1, x.min=node[1],
x.max=node[length(node)], w0=2 * pi, plot=FALSE)
kernel(node, phinode, nvoice, x.inc=1, x.min=node[1],
x.max=node[length(node)], w0=2 * pi, plot=FALSE)

Arguments

`node`	values of the variable b for the nodes of the ridge.
`phinode`	values of the scale variable a for the nodes of the ridge.
`nvoice`	number of scales within 1 octave.
`x.inc`	step unit for the computation of the kernel.
`x.min`	minimal value of x for the computation of $Q_2$ .
`x.max`	maximal value of x for the computation of $Q_2$ .
`w0`	central frequency of the wavelet.
`plot`	if set to TRUE, displays the modulus of the matrix of $Q_2$ .

Details

The kernel is evaluated using Romberg's method.

Value

matrix of the $Q_2$ kernel

References

See discussions in the text of "Time-Frequency Analysis".

Trim Dyadic Wavelet Transform Extrema

Description

Trimming of dyadic wavelet transform local extrema, using bootstrapping.

Usage

mbtrim(extrema, scale=FALSE, prct=0.95)
mbtrim(extrema, scale=FALSE, prct=0.95)

Arguments

`extrema`	dyadic wavelet transform extrema (output of `ext`).
`scale`	when set, the wavelet transform at each scale will be plotted with the same scale.
`prct`	percentage critical value used for thresholding

Details

The distribution of extrema of dyadic wavelet transform at each scale is generated by bootstrap method, and the 95% critical value is used for thresholding the extrema of the signal.

Value

Structure containing

`original`	original signal.
`extrema`	trimmed extrema representation.
`Sf`	coarse resolution of signal.
`maxresoln`	number of decomposition scales.
`np`	size of signal.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Trim Dyadic Wavelet Transform Extrema

Description

Trimming of dyadic wavelet transform local extrema, assuming normal distribution.

Usage

mntrim(extrema, scale=FALSE, prct=0.95)
mntrim(extrema, scale=FALSE, prct=0.95)

Arguments

`extrema`	dyadic wavelet transform extrema (output of `ext`).
`scale`	when set, the wavelet transform at each scale will be plotted with the same scale.
`prct`	percentage critical value used for thresholding

Details

The distribution of extrema of dyadic wavelet transform at each scale is generated by simulation, assuming a normal distribution, and the 95% critical value is used for thresholding the extrema of the signal.

Value

Structure containing

`original`	original signal.
`extrema`	trimmed extrema representation.
`Sf`	coarse resolution of signal.
`maxresoln`	number of decomposition scales.
`np`	size of signal.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Morlet Wavelets

Description

Computes a Morlet wavelet at the point of the time-scale plane given in the input

Usage

morlet(sigsize, location, scale, w0=2 * pi)
morlet(sigsize, location, scale, w0=2 * pi)

Arguments

`sigsize`	length of the output.
`location`	time location of the wavelet.
`scale`	scale of the wavelet.
`w0`	central frequency of the wavelet.

Details

The details of this construction (including the definition formulas) are given in the text.

Value

Returns the values of the complex Morlet wavelet at the point of the time-scale plane given in the input

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Ridge Morvelets

Description

Generates the Morlet wavelets at the sample points of the ridge.

Usage

morwave(bridge, aridge, nvoice, np, N, w0=2 * pi)
morwave(bridge, aridge, nvoice, np, N, w0=2 * pi)

Arguments

`bridge`	time coordinates of the ridge samples.
`aridge`	scale coordinates of the ridge samples.
`nvoice`	number of different scales per octave.
`np`	number of samples in the input signal.
`N`	size of reconstructed signal.
`w0`	central frequency of the wavelet.

Value

Returns the Morlet wavelets at the samples of the time-scale plane given in the input: complex array of Morlet wavelets located on the ridge samples

References

See discussions in the text of “Time-Frequency Analysis”.

Real Ridge Morvelets

Description

Generates the real parts of the Morlet wavelets at the sample points of a ridge

Usage

morwave2(bridge, aridge, nvoice, np, N, w0=2 * pi)
morwave2(bridge, aridge, nvoice, np, N, w0=2 * pi)

Arguments

`bridge`	time coordinates of the ridge samples.
`aridge`	scale coordinates of the ridge samples.
`nvoice`	number of different scales per octave.
`np`	number of samples in the input signal.
`N`	size of reconstructed signal.
`w0`	central frequency of the wavelet.

Value

Returns the real parts of the Morlet wavelets at the samples of the time-scale plane given in the input: array of Morlet wavelets located on the ridge samples

References

See discussions in the text of “Time-Frequency Analysis”.

Reconstruct from Dyadic Wavelet Transform Extrema

Description

Reconstruct from dyadic wavelet transform modulus extrema. The reconstructed signal preserves locations and values at extrema.

Usage

mrecons(extrema, filtername="Gaussian1", readflag=FALSE)
mrecons(extrema, filtername="Gaussian1", readflag=FALSE)

Arguments

`extrema`	the extrema representation.
`filtername`	filter used for dyadic wavelet transform.
`readflag`	if set to T, read reconstruction kernel from precomputed file. This is not supported in the current package, and will cause an error.

Details

The reconstruction involves only the wavelet coefficients, without taking care of the coarse scale component. The latter may be added a posteriori.

Value

Structure containing

`f`	the reconstructed signal.
`g`	reconstructed signal plus mean of original signal.
`h`	reconstructed signal plus coarse scale component of original signal.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Dyadic Wavelet Transform

Description

Dyadic wavelet transform, with Mallat's wavelet. The reconstructed signal preserves locations and values at extrema.

Usage

mw(inputdata, maxresoln, filtername="Gaussian1", scale=FALSE, plot=TRUE)
mw(inputdata, maxresoln, filtername="Gaussian1", scale=FALSE, plot=TRUE)

Arguments

`inputdata`	either a text file or an R object containing data.
`maxresoln`	number of decomposition scales.
`filtername`	name of filter (either Gaussian1 for Mallat and Zhong's wavelet or Haar wavelet).
`scale`	when set, the wavelet transform at each scale is plotted with the same scale.
`plot`	indicate if the wavelet transform at each scale will be plotted.

Details

The decomposition goes from resolution 1 to the given maximum resolution.

Value

Structure containing

`original`	original signal.
`Wf`	dyadic wavelet transform of signal.
`Sf`	multiresolution of signal.
`maxresoln`	number of decomposition scales.
`np`	size of signal.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Noisy Gravitational Wave

Description

Noisy gravitational wave.

Usage

data(noisywave)
data(noisywave)

Format

A vector containing 8192 observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Prepare Graphics Environment

Description

Splits the graphics device into prescrivbed number of windows.

Usage

npl(nbrow)
npl(nbrow)

Arguments

nbrow

number of plots.

Plot Dyadic Wavelet Transform Extrema

Description

Plot extrema of dyadic wavelet transform.

Usage

plotResult(result, original, maxresoln, scale=FALSE, yaxtype="s")
plotResult(result, original, maxresoln, scale=FALSE, yaxtype="s")

Arguments

`result`	result.
`original`	input signal.
`maxresoln`	number of decomposition scales.
`scale`	when set, the extrema at each scale is plotted withe the same scale.
`yaxtype`	y axis type (see R manual).

References

See discussions in the text of “Time-Frequency Analysis”.

Plot Dyadic Wavelet Transform

Description

Plot dyadic wavelet transform.

Usage

plotwt(original, psi, phi, maxresoln, scale=FALSE, yaxtype="s")
plotwt(original, psi, phi, maxresoln, scale=FALSE, yaxtype="s")

Arguments

`original`	input signal.
`psi`	dyadic wavelet transform.
`phi`	scaling function transform at last resolution.
`maxresoln`	number of decomposition scales.
`scale`	when set, the wavelet transform at each scale is plotted with the same scale.
`yaxtype`	axis type (see R manual).

References

See discussions in the text of “Time-Frequency Analysis”.

Pure Gravitational Wave

Description

Pure gravitational wave.

Usage

data(purwave)
data(purwave)

Format

A vector containing 8192 observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Reconstruction from a Ridge

Description

Reconstructs signal from a “regularly sampled” ridge, in the wavelet case.

Usage

regrec(siginput, cwtinput, phi, compr, noct, nvoice, epsilon=0,
w0=2 * pi, fast=FALSE, plot=FALSE, para=0, hflag=FALSE,
check=FALSE, minnbnodes=2, real=FALSE)
regrec(siginput, cwtinput, phi, compr, noct, nvoice, epsilon=0,
w0=2 * pi, fast=FALSE, plot=FALSE, para=0, hflag=FALSE,
check=FALSE, minnbnodes=2, real=FALSE)

Arguments

`siginput`	input signal.
`cwtinput`	wavelet transform, output of `cwt`.
`phi`	unsampled ridge.
`compr`	subsampling rate for the wavelet coefficients (at scale 1)
`noct`	number of octaves (powers of 2)
`nvoice`	number of different scales per octave
`epsilon`	coefficient of the $Q_2$ term in reconstruction kernel
`w0`	central frequency of Morlet wavelet
`fast`	if set to TRUE, the kernel is computed using trapezoidal rule.
`plot`	if set to TRUE, displays original and reconstructed signals
`para`	scale parameter for extrapolating the ridges.
`hflag`	if set to TRUE, uses $Q_1$ as first term in the kernel.
`check`	if set to TRUE, computes `cwt` of reconstructed signal.
`minnbnodes`	minimum number of nodes for the reconstruction.
`real`	if set to TRUE, uses only real constraints on the transform.

Value

Returns a list containing:

`sol`	reconstruction from a ridge.
`A`	<wavelets,dualwavelets> matrix.
`lam`	coefficients of dual wavelets in reconstructed signal.
`dualwave`	array containing the dual wavelets.
`morvelets`	array containing the wavelets on sampled ridge.
`solskel`	wavelet transform of sol, restricted to the ridge.
`inputskel`	wavelet transform of signal, restricted to the ridge.
`Q2`	second part of the reconstruction kernel.
`nbnodes`	number of nodes used for the reconstruction.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Reconstruction from a Ridge

Description

Reconstructs signal from a “regularly sampled” ridge, in the wavelet case, from a precomputed kernel.

Usage

regrec2(siginput, cwtinput, phi, nbnodes, noct, nvoice, Q2,
epsilon=0.5, w0=2 * pi, plot=FALSE)
regrec2(siginput, cwtinput, phi, nbnodes, noct, nvoice, Q2,
epsilon=0.5, w0=2 * pi, plot=FALSE)

Arguments

`siginput`	input signal.
`cwtinput`	wavelet transform, output of `cwt`.
`phi`	unsampled ridge.
`nbnodes`	number of samples on the ridge
`noct`	number of octaves (powers of 2)
`nvoice`	number of different scales per octave
`Q2`	second term of the reconstruction kernel
`epsilon`	coefficient of the $Q_2$ term in reconstruction kernel
`w0`	central frequency of Morlet wavelet
`plot`	if set to TRUE, displays original and reconstructed signals

Details

The computation of the kernel may be time consuming. This function avoids recomputing it if it was computed already.

Value

Returns a list containing:

`sol`	reconstruction from a ridge.
`A`	<wavelets,dualwavelets> matrix.
`lam`	coefficients of dual wavelets in reconstructed signal.
`dualwave`	array containing the dual wavelets.
`morvelets`	array containing the wavelets on sampled ridge.
`solskel`	wavelet transform of sol, restricted to the ridge.
`inputskel`	wavelet transform of signal, restricted to the ridge.
`nbnodes`	number of nodes used for the reconstruction.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Sampling Gabor Ridge

Description

Given a ridge phi (for the Gabor transform), returns a (regularly) subsampled version of length nbnodes.

Usage

RidgeSampling(phi, nbnodes)
RidgeSampling(phi, nbnodes)

Arguments

`phi`	ridge (1D array).
`nbnodes`	number of samples.

Details

Gabor ridges are sampled uniformly.

Value

Returns a list containing the discrete values of the ridge.

`node`	time coordinates of the ridge samples.
`phinode`	frequency coordinates of the ridge samples.

References

See discussions in the text of "Time-Frequency Analysis”.

Reconstruction from a Ridge

Description

Reconstructs signal from sample of a ridge, in the wavelet case.

Usage

ridrec(cwtinput, node, phinode, noct, nvoice, Qinv, epsilon, np,
w0=2 * pi, check=FALSE, real=FALSE)
ridrec(cwtinput, node, phinode, noct, nvoice, Qinv, epsilon, np,
w0=2 * pi, check=FALSE, real=FALSE)

Arguments

`cwtinput`	wavelet transform, output of `cwt`.
`node`	time coordinates of the ridge samples.
`phinode`	scale coordinates of the ridge samples.
`noct`	number of octaves (powers of 2).
`nvoice`	number of different scales per octave.
`Qinv`	inverse of the matrix $Q$ of the quadratic form.
`epsilon`	coefficient of the $Q_2$ term in reconstruction kernel
`np`	number of samples of the reconstructed signal.
`w0`	central frequency of Morlet wavelet.
`check`	if set to TRUE, computes `cwt` of reconstructed signal.
`real`	if set to TRUE, uses only constraints on the real part of the transform.

Value

Returns a list containing the reconstructed signal and the chained ridges.

`sol`	reconstruction from a ridge
`A`	<wavelets,dualwavelets> matrix
`lam`	coefficients of dual wavelets in reconstructed signal.
`dualwave`	array containing the dual wavelets.
`morvelets`	array of morlet wavelets located on the ridge samples.
`solskel`	wavelet transform of sol, restricted to the ridge
`inputskel`	wavelet transform of signal, restricted to the ridge

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Kernel for Reconstruction from Wavelet Ridges

Description

Computes the cost from the sample of points on the estimated ridge and the matrix used in the reconstruction of the original signal, in the case of real constraints. Modification of the function kernel.

Usage

rkernel(node, phinode, nvoice, x.inc=1, x.min=node[1],
x.max=node[length(node)], w0=2 * pi, plot=FALSE)
rkernel(node, phinode, nvoice, x.inc=1, x.min=node[1],
x.max=node[length(node)], w0=2 * pi, plot=FALSE)

Arguments

`node`	values of the variable b for the nodes of the ridge.
`phinode`	values of the scale variable a for the nodes of the ridge.
`nvoice`	number of scales within 1 octave.
`x.inc`	step unit for the computation of the kernel.
`x.min`	minimal value of x for the computation of $Q_2$ .
`x.max`	maximal value of x for the computation of $Q_2$ .
`w0`	central frequency of the wavelet.
`plot`	if set to TRUE, displays the modulus of the matrix of $Q_2$ .

Details

Uses Romberg's method for computing the kernel.

Value

matrix of the $Q_2$ kernel

References

See discussions in the text of "Time-Frequency Analysis".

Simple Reconstruction from Crazy Climbers Ridges

Description

Reconstructs signal from ridges obtained by crc, using the restriction of the transform to the ridge.

Usage

scrcrec(siginput, tfinput, beemap, bstep=5, ptile=0.01, plot=2)
scrcrec(siginput, tfinput, beemap, bstep=5, ptile=0.01, plot=2)

Arguments

`siginput`	input signal.
`tfinput`	time-frequency representation (output of `cwt` or `cgt`.
`beemap`	output of crazy climber algorithm
`bstep`	used for the chaining (see `cfamily`).
`ptile`	threshold on the measure beemap (see `cfamily`).
`plot`	1: displays signal,components, and reconstruction one after another. 2: displays signal, components and reconstruction. Else, no plot.

Value

Returns a list containing the reconstructed signal and the chained ridges.

`rec`	reconstructed signal
`ordered`	image of the ridges (with different colors)
`comp`	2D array containing the signals reconstructed from ridges

References

See discussions in the text of “Practical Time-Frequency Analysis”.

File from historical Swave package.

Description

The package maintainer believes this file was read or written by a C function (signal_W_tilda) called from mrecons, and was a precomputed kernel. All C function disk reads and writes have been disabled, but the files are preserved for historical purposes.

Usage

data(sig_W_tilda.1)data(sig_W_tilda.1)

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

File from historical Swave package.

Description

Usage

data(sig_W_tilda.1)data(sig_W_tilda.1)

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

File from historical Swave package.

Description

Usage

data(sig_W_tilda.1)data(sig_W_tilda.1)

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

File from historical Swave package.

Description

Usage

data(sig_W_tilda.1)data(sig_W_tilda.1)

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

File from historical Swave package.

Description

Usage

data(sig_W_tilda.1)data(sig_W_tilda.1)

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

File from historical Swave package.

Description

Usage

data(signal_W_tilda.1)data(signal_W_tilda.1)

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

File from historical Swave package.

Description

Usage

data(signal_W_tilda.1)data(signal_W_tilda.1)

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

File from historical Swave package.

Description

Usage

data(signal_W_tilda.1)data(signal_W_tilda.1)

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

File from historical Swave package.

Description

Usage

data(signal_W_tilda.1)data(signal_W_tilda.1)

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

File from historical Swave package.

Description

Usage

data(signal_W_tilda.1)data(signal_W_tilda.1)

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

File from historical Swave package.

Description

Usage

data(signal_W_tilda.1)data(signal_W_tilda.1)

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

File from historical Swave package.

Description

Usage

data(signal_W_tilda.1)data(signal_W_tilda.1)

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

File from historical Swave package.

Description

Usage

data(signal_W_tilda.1)data(signal_W_tilda.1)

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

File from historical Swave package.

Description

Usage

data(signal_W_tilda.1)data(signal_W_tilda.1)

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Reconstruction from Dual Wavelets

Description

Computes the reconstructed signal from the ridge, given the inverse of the matrix Q.

Usage

skeleton(cwtinput, Qinv, morvelets, bridge, aridge, N)
skeleton(cwtinput, Qinv, morvelets, bridge, aridge, N)

Arguments

`cwtinput`	continuous wavelet transform (as the output of cwt)
`Qinv`	inverse of the reconstruction kernel (2D array)
`morvelets`	array of Morlet wavelets located at the ridge samples
`bridge`	time coordinates of the ridge samples
`aridge`	scale coordinates of the ridge samples
`N`	size of reconstructed signal

Value

Returns a list of the elements of the reconstruction of a signal from sample points of a ridge

`sol`	reconstruction from a ridge
`A`	matrix of the inner products
`lam`	coefficients of dual wavelets in reconstructed signal. They are the Lagrange multipliers $\lambda$ 's of the text.
`dualwave`	array containing the dual wavelets.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Reconstruction from Dual Wavelet

Description

Computes the reconstructed signal from the ridge in the case of real constraints.

Usage

skeleton2(cwtinput, Qinv, morvelets, bridge, aridge, N)
skeleton2(cwtinput, Qinv, morvelets, bridge, aridge, N)

Arguments

`cwtinput`	continuous wavelet transform (as the output of cwt).
`Qinv`	inverse of the reconstruction kernel (2D array).
`morvelets`	array of Morlet wavelets located at the ridge samples.
`bridge`	time coordinates of the ridge samples.
`aridge`	scale coordinates of the ridge samples.
`N`	size of reconstructed signal.

Value

Returns a list of the elements of the reconstruction of a signal from sample points of a ridge

`sol`	reconstruction from a ridge.
`A`	matrix of the inner products.
`lam`	coefficients of dual wavelets in reconstructed signal. They are the Lagrange multipliers $\lambda$ 's of the text.
`dualwave`	array containing the dual wavelets.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Smoothing Time Series

Description

Smooth a time series by averaging window.

Usage

smoothts(ts, windowsize)
smoothts(ts, windowsize)

Arguments

`ts`	Time series.
`windowsize`	Length of smoothing window.

Value

Smoothed time series (1D array).

References

See discussions in the text of “Time-Frequency Analysis”.

Smoothing and Time Frequency Representation

Description

smooth the wavelet (or Gabor) transform in the time direction.

Usage

smoothwt(modulus, subrate, flag=FALSE)
smoothwt(modulus, subrate, flag=FALSE)

Arguments

`modulus`	Time-Frequency representation (real valued).
`subrate`	Length of smoothing window.
`flag`	If set to TRUE, subsample the representation.

Value

2D array containing the smoothed transform.

References

See discussions in the text of “Time-Frequency Analysis”.

Ridge Estimation by Snake Method

Description

Estimate a ridge from a time-frequency representation, using the snake method.

Usage

snake(tfrep, guessA, guessB, snakesize=length(guessB),
tfspec=numeric(dim(modulus)[2]), subrate=1, temprate=3, muA=1,
muB=muA, lambdaB=2 * muB, lambdaA=2 * muA, iteration=1000000,
seed=-7, costsub=1, stagnant=20000, plot=TRUE)
snake(tfrep, guessA, guessB, snakesize=length(guessB),
tfspec=numeric(dim(modulus)[2]), subrate=1, temprate=3, muA=1,
muB=muA, lambdaB=2 * muB, lambdaA=2 * muA, iteration=1000000,
seed=-7, costsub=1, stagnant=20000, plot=TRUE)

Arguments

`tfrep`	Time-Frequency representation (real valued).
`guessA`	Initial guess for the algorithm (frequency variable).
`guessB`	Initial guess for the algorithm (time variable).
`snakesize`	the length of the initial guess of time variable.
`tfspec`	Estimate for the contribution of the noise to modulus.
`subrate`	Subsampling rate for ridge estimation.
`temprate`	Initial value of temperature parameter.
`muA`	Coefficient of the ridge's derivative in cost function (frequency component).
`muB`	Coefficient of the ridge's derivative in cost function (time component).
`lambdaB`	Coefficient of the ridge's second derivative in cost function (time component).
`lambdaA`	Coefficient of the ridge's second derivative in cost function (frequency component).
`iteration`	Maximal number of moves.
`seed`	Initialization of random number generator.
`costsub`	Subsampling of cost function in output.
`stagnant`	maximum number of steps without move (for the stopping criterion)
`plot`	when set (by default), certain results will be displayed

Value

Returns a structure containing:

`ridge`	1D array (of same length as the signal) containing the ridge.
`cost`	1D array containing the cost function.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Restriction to a Snake

Description

Restrict time-frequency transform to a snake.

Usage

snakeview(modulus, snake)
snakeview(modulus, snake)

Arguments

`modulus`	Time-Frequency representation (real valued).
`snake`	Time and frequency components of a snake.

Details

Recall that a snake is a (two components) R structure.

Value

2D array containing the restriction of the transform modulus to the snake.

References

See discussions in the text of “Time-Frequency Analysis”.

Modified Snake Method

Description

Estimate a ridge from a time-frequency representation, using the modified snake method (modified cost function).

Usage

snakoid(modulus, guessA, guessB, snakesize=length(guessB),
tfspec=numeric(dim(modulus)[2]), subrate=1, temprate=3, muA=1,
muB=muA, lambdaB=2 * muB, lambdaA=2 * muA, iteration=1000000,
seed=-7, costsub=1, stagnant=20000, plot=TRUE)
snakoid(modulus, guessA, guessB, snakesize=length(guessB),
tfspec=numeric(dim(modulus)[2]), subrate=1, temprate=3, muA=1,
muB=muA, lambdaB=2 * muB, lambdaA=2 * muA, iteration=1000000,
seed=-7, costsub=1, stagnant=20000, plot=TRUE)

Arguments

`modulus`	Time-Frequency representation (real valued).
`guessA`	Initial guess for the algorithm (frequency variable).
`guessB`	Initial guess for the algorithm (time variable).
`snakesize`	The length of the first guess of time variable.
`tfspec`	Estimate for the contribution of srthe noise to modulus.
`subrate`	Subsampling rate for ridge estimation.
`temprate`	Initial value of temperature parameter.
`muA`	Coefficient of the ridge's derivative in cost function (frequency component).
`muB`	Coefficient of the ridge's derivative in cost function (time component).
`lambdaB`	Coefficient of the ridge's second derivative in cost function (time component).
`lambdaA`	Coefficient of the ridge's second derivative in cost function (frequency component).
`iteration`	Maximal number of moves.
`seed`	Initialization of random number generator.
`costsub`	Subsampling of cost function in output.
`stagnant`	Maximum number of stationary iterations before stopping.
`plot`	when set(default), some results will be displayed

Value

Returns a structure containing:

`ridge`	1D array (of same length as the signal) containing the ridge.
`cost`	1D array containing the cost function.
`plot`	when set(default), some results will be displayed.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Simple Reconstruction from Ridge

Description

Simple reconstruction of a real valued signal from a ridge, by restriction of the transform to the ridge.

Usage

sridrec(tfinput, ridge)
sridrec(tfinput, ridge)

Arguments

`tfinput`	time-frequency representation.
`ridge`	ridge (1D array).

Value

(real) reconstructed signal (1D array)

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Singular Value Decomposition

Description

Computes singular value decomposition of a matrix.

Usage

SVD(a)
SVD(a)

Arguments

`a`	input matrix.

Details

R interface for Numerical Recipes singular value decomposition routine.

Value

a structure containing the 3 matrices of the singular value decomposition of the input.

References

See discussions in the text of “Time-Frequency Analysis”.

Time-Frequency Transform Global Maxima

Description

Computes the maxima (for each fixed value of the time variable) of the modulus of a continuous wavelet transform.

Usage

tfgmax(input, plot=TRUE)
tfgmax(input, plot=TRUE)

Arguments

`input`	wavelet transform (as the output of the function `cwt`)
`plot`	if set to TRUE, displays the values of the energy as a function of the scale.

Value

`output`	values of the maxima (1D array)
`pos`	positions of the maxima (1D array)

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Time-Frequency Transform Local Maxima

Description

Computes the local maxima (for each fixed value of the time variable) of the modulus of a time-frequency transform.

Usage

tflmax(input, plot=TRUE)
tflmax(input, plot=TRUE)

Arguments

`input`	time-frequency transform (real 2D array).
`plot`	if set to T, displays the local maxima on the graphic device.

Value

values of the maxima (2D array).

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Average frequency by frequency

Description

Compute the mean of time-frequency representation frequency by frequency.

Usage

tfmean(input, plot=TRUE)
tfmean(input, plot=TRUE)

Arguments

`input`	time-frequency transform (output of `cwt` or `cgt`).
`plot`	if set to T, displays the values of the energy as a function of the scale (or frequency).

Value

1D array containing the noise estimate.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Percentile frequency by frequency

Description

Compute a percentile of time-frequency representation frequency by frequency.

Usage

tfpct(input, percent=0.8, plot=TRUE)
tfpct(input, percent=0.8, plot=TRUE)

Arguments

`input`	time-frequency transform (output of `cwt` or `cgt`).
`percent`	percentile to be retained.
`plot`	if set to T, displays the values of the energy as a function of the scale (or frequency).

Value

1D array containing the noise estimate.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Variance frequency by frequency

Description

Compute the variance of time-frequency representation frequency by frequency.

Usage

tfvar(input, plot=TRUE)
tfvar(input, plot=TRUE)

Arguments

`input`	time-frequency transform (output of `cwt` or `cgt`).
`plot`	if set to T, displays the values of the energy as a function of the scale (or frequency).

Value

1D array containing the noise estimate.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Undocumented Functions in Rwave

Description

Numerous functions were not documented in the original Swave help files.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

DOG Wavelet Transform on one Voice

Description

Compute DOG wavelet transform at one scale.

Usage

vDOG(input, scale, moments)
vDOG(input, scale, moments)

Arguments

`input`	Input signal (1D array).
`scale`	Scale at which the wavelet transform is to be computed.
`moments`	number of vanishing moments.

Value

1D (complex) array containing wavelet transform at one scale.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Gabor Functions on a Ridge

Description

Generate Gabor functions at specified positions on a ridge.

Usage

vecgabor(sigsize, nbnodes, location, frequency, scale)
vecgabor(sigsize, nbnodes, location, frequency, scale)

Arguments

`sigsize`	Signal size.
`nbnodes`	Number of wavelets to be generated.
`location`	b coordinates of the ridge samples (1D array of length nbnodes).
`frequency`	frequency coordinates of the ridge samples (1D array of length nbnodes).
`scale`	size parameter for the Gabor functions.

Value

size parameter for the Gabor functions.

Morlet Wavelets on a Ridge

Description

Generate Morlet wavelets at specified positions on a ridge.

Usage

vecmorlet(sigsize, nbnodes, bridge, aridge, w0=2 * pi)
vecmorlet(sigsize, nbnodes, bridge, aridge, w0=2 * pi)

Arguments

`sigsize`	Signal size.
`nbnodes`	Number of wavelets to be generated.
`bridge`	b coordinates of the ridge samples (1D array of length nbnodes).
`aridge`	a coordinates of the ridge samples (1D array of length nbnodes).
`w0`	Center frequency of the wavelet.

Value

2D (complex) array containing wavelets located at the specific points.

Gabor Transform on one Voice

Description

Compute Gabor transform for fixed frequency.

Usage

vgt(input, frequency, scale, plot=FALSE)
vgt(input, frequency, scale, plot=FALSE)

Arguments

`input`	Input signal (1D array).
`frequency`	frequency at which the Gabor transform is to be computed.
`scale`	frequency at which the Gabor transform is to be computed.
`plot`	if set to TRUE, plots the real part of cgt on the graphic device.

Value

1D (complex) array containing Gabor transform at specified frequency.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Voice Wavelet Transform

Description

Compute Morlet's wavelet transform at one scale.

Usage

vwt(input, scale, w0=2 * pi)
vwt(input, scale, w0=2 * pi)

Arguments

`input`	Input signal (1D array).
`scale`	Scale at which the wavelet transform is to be computed.
`w0`	Center frequency of the wavelet.

Value

1D (complex) array containing wavelet transform at one scale.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Plot Dyadic Wavelet Transform.

Description

Plot dyadic wavelet transform(output of mw).

Usage

wpl(dwtrans)
wpl(dwtrans)

Arguments

dwtrans

dyadic wavelet transform (output of mw).

Sampling wavelet Ridge

Description

Given a ridge $\phi$ (for the wavelet transform), returns a (appropriately) subsampled version with a given subsampling rate.

Usage

wRidgeSampling(phi, compr, nvoice)
wRidgeSampling(phi, compr, nvoice)

Arguments

`phi`	ridge (1D array).
`compr`	subsampling rate for the ridge.
`nvoice`	number of voices per octave.

Details

To account for the variable sizes of wavelets, the sampling rate of a wavelet ridge is not uniform, and is proportional to the scale.

Value

Returns a list containing the discrete values of the ridge.

`node`	time coordinates of the ridge samples.
`phinode`	scale coordinates of the ridge samples.
`nbnode`	number of nodes of the ridge samples.

Log of Wavelet Spectrum Plot

Description

Displays normalized log of wavelet spectrum.

Usage

wspec.pl(wspec, nvoice)
wspec.pl(wspec, nvoice)

Arguments

`wspec`	wavelet spectrum.
`nvoice`	number of voices.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Wigner-Ville function

Description

Compute the Wigner-Ville transform, without any smoothing.

Usage

WV(input, nvoice, freqstep = (1/nvoice), plot = TRUE)
WV(input, nvoice, freqstep = (1/nvoice), plot = TRUE)

Arguments

`input`	input signal (possibly complex-valued)
`nvoice`	number of frequency bands
`freqstep`	sampling rate for the frequency axis
`plot`	if set to TRUE, displays the modulus of CWT on the graphic device.

Value

(complex) Wigner-Ville transform.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Logarithms of the Prices of Japanese Yen

Description

Logarithms of the prices of a contract of Japanese yen.

Usage

data(YN)
data(YN)

Format

A vector containing 500 observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Daily differences of Japanese Yen

Description

Daily differences of YN.

Usage

data(YNdiff)
data(YNdiff)

Format

A vector containing 499 observations.

Source

See discussions in the text of “Practical Time-Frequency Analysis”.

References

Carmona, R. A., W. L. Hwang and B Torresani (1998) Practical Time-Frequency Analysis: Gabor and Wavelet Transforms with an Implementation in S, Academic Press, San Diego.

Reconstruction from Wavelet Ridges

Description

Generate a zero kernel for reconstruction from ridges.

Usage

zerokernel(x.inc=1, x.min, x.max)
zerokernel(x.inc=1, x.min, x.max)

Arguments

`x.min`	minimal value of x for the computation of $Q_2$ .
`x.max`	maximal value of x for the computation of $Q_2$ .
`x.inc`	step unit for the computation of the kernel.

Value

matrix of the $Q_2$ kernel

Reconstruction from Dual Wavelets

Description

Computes the the reconstructed signal from the ridge when the epsilon parameter is set to zero

Usage

zeroskeleton(cwtinput, Qinv, morvelets, bridge, aridge, N)
zeroskeleton(cwtinput, Qinv, morvelets, bridge, aridge, N)

Arguments

`cwtinput`	continuous wavelet transform (as the output of `cwt`).
`Qinv`	inverse of the reconstruction kernel (2D array).
`morvelets`	array of Morlet wavelets located at the ridge samples.
`bridge`	time coordinates of the ridge samples.
`aridge`	scale coordinates of the ridge samples.
`N`	size of reconstructed signal.

Details

The details of this reconstruction are the same as for the function skeleton. They can be found in the text

Value

Returns a list of the elements of the reconstruction of a signal from sample points of a ridge

`sol`	reconstruction from a ridge.
`A`	matrix of the inner products.
`lam`	coefficients of dual wavelets in reconstructed signal. They are the Lagrange multipliers $\lambda$ 's of the text.
`dualwave`	array containing the dual wavelets.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Reconstruction from Dual Wavelets

Description

Computes the the reconstructed signal from the ridge when the epsilon parameter is set to zero, in the case of real constraints.

Usage

zeroskeleton2(cwtinput, Qinv, morvelets, bridge, aridge, N)
zeroskeleton2(cwtinput, Qinv, morvelets, bridge, aridge, N)

Arguments

`cwtinput`	continuous wavelet transform (output of `cwt`).
`Qinv`	inverse of the reconstruction kernel (2D array).
`morvelets`	array of Morlet wavelets located at the ridge samples.
`bridge`	time coordinates of the ridge samples.
`aridge`	scale coordinates of the ridge samples.
`N`	size of reconstructed signal.

Details

The details of this reconstruction are the same as for the function skeleton. They can be found in the text

Value

Returns a list of the elements of the reconstruction of a signal from sample points of a ridge

`sol`	reconstruction from a ridge.
`A`	matrix of the inner products.
`lam`	coefficients of dual wavelets in reconstructed signal. They are the Lagrange multipliers $\lambda$ 's of the text.
`dualwave`	array containing the dual wavelets.

References

See discussions in the text of “Practical Time-Frequency Analysis”.

Package 'Rwave'

Help Index

Transient Signal

Description

Usage

Format

Source

References

Transient Signal

Description

Usage

Format

Source

References

Zero Padding

Description

Usage

Arguments

Value

References

Pixel from Amber Camara

Description

Usage

Format

Source

References

Pixel from Amber Camara

Description

Usage

Format

Source

References

Pixel from Amber Camara

Description

Usage

Format

Source

References

Transient Signal

Description

Usage

Format

Source

References

Transient Signal

Description

Usage

Format

Source

References

Acoustic Returns

Description

Usage

Format

Source

References

Acoustic Returns

Description

Usage

Format

Source

References

Acoustic Returns

Description

Usage

Format

Source

References

Transient Signal

Description

Usage

Format

Source

References

Transient Signal

Description

Usage

Format

Source

References