## 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].