Continuous wavelet transform
Purpose
Description
Macro Synopsis
Modules
Related Functions
References
Purpose
Continuous wavelet transform
Description
This function computes the continuous wavelet transform of the input
signal. Let f be the square integrable function as defined in the manual
section of the function "Decompose". The continuous wavelet transform consists
of the integrals
The difference to the discrete wavelet transform is that the
subsampling with factor 2 at each octave is omitted.
For the computation we use the following algorithm. Define
The step from octave i to octave i+1 is given by
where 
denotes a convolution operation.
The filters in these equation are obtained by inserting
zeros between two successive values of the
filters G and H (see Decompose).
The result is a CWT signal: In the window the signals 
are displayed with increasing octave from top to the bottom.
In the last channel the signal 
is displayed.
The only parameter is
- the number n of octaves (decomposition depth)
The advantage of the wavelet transform is its time resolution,
providing the possibility to analyse nonstationary time series.
Macro Synopsis
y = ContWaveletTrafo(x,n);
signal x,y;
int n;
Modules
Wavelet
Related Functions
Define wavelet, Load wavelet,
Save wavelet, Decompose,
Reconstruct, Wavelet packet decomposition.
References
Rioul/Duhamel [22].