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.