WVLTTRANS - Wavelet frame transform

Usage

[c,g,shift,M,Ls,fb,tgtfl] = wvlttrans(f,fmin,sr,bins,bw,tgtfl)
[c,g,shift,M,Ls,fb,tgtfl] = wvlttrans(f,fmin,sr,bins,bw)
[c,g,shift,M,Ls,fb,tgtfl] = wvlttrans(f,fmin,sr,bins)
[c,g,shift,M,Ls,fb,tgtfl] = wvlttrans(f,fmin,sr)
[c,g,shift,M,Ls,fb,tgtfl] = wvlttrans(f,fmin)
[c,g,shift,M,Ls,fb] = wvlttrans(...)
[c,g,shift,M,Ls] = wvlttrans(...)
[c,g,shift,M] = wvlttrans(...)
c = wvlttrans(...)

Input parameters

f Input signal
fmin Desired minimum center frequency (in Hz)
sr Sampling rate of f (in Hz)
bins Desired number of bins per octave
bw Desired bandwidth in the first frequency band (in Hz)
winfun String containing the desired window function name

Output parameters

c Cell array of Wavelet coefficients
g Cell array of Fourier transforms of the analysis Wavelets
shift Vector of frequency shifts
M Number of time steps
Ls Original signal length
fb Frame bounds (vector)
tgtfl Tightflag (1 if frame is tight)

Description

This is a wrapper function for the painless Wavelet transform via nonstationary Gabor filterbank. Given a signal f and minimum frequency fmin, a tight system with \(4\) scales per octave is constructed using logarithmically sampled Hann windows with 3/4 overlap. The additional parameters sr, bins, bw and winfun can be specified to individually construct different Wavelet systems.

To construct systems with specific overlap factors \((n-1)/n\) , choose \(bw = 2^{n/(2 bins)}-2^{-n/(2 bins)}\) .

In addition to the Wavelet coefficients c, also the analysis system g, shift, M can be returned, as can the length Ls of the input signal f, the frame bounds of the system g, shift, M and a flag indicating if a tight frame was used. These parameters are necessary to perform reconstruction with the inverse Wavelet transform wrapper invwvlttrans.

References:

P. Balazs, M. Dörfler, F. Jaillet, N. Holighaus, and G. A. Velasco. Theory, implementation and applications of nonstationary Gabor Frames. J. Comput. Appl. Math., 236(6):1481-1496, 2011.