Wavelet Toolbox

Complex Wavelets

Some complex wavelet families are available in the toolbox.

Complex Gaussian Wavelets: cgau

This family is built starting from the complex Gaussian function

by taking the derivative of . The integer is the parameter of this family and in the previous formula, is such that

where is the derivative of f.

You can obtain a survey of the main properties of this family by typing waveinfo('cgau') from the MATLAB command line.

Figure 6-22: Complex Gaussian Wavelet cgau8

Complex Morlet Wavelets: cmor

See [Teo98] pages 62-65.

A complex Morlet wavelet is defined by

depending on two parameters:

• is a bandwidth parameter.
• is a wavelet center frequency.

You can obtain a survey of the main properties of this family by typing waveinfo('cmor') from the MATLAB command line.

Figure 6-23: Complex Morlet Wavelet morl 1.5-1

Complex Frequency B-Spline Wavelets: fbsp

See [Teo98] pages 62-65.

A complex frequency B-spline wavelet is defined by

depending on three parameters:

• is an integer order parameter ().
• is a bandwidth parameter.
• is a wavelet center frequency.

You can obtain a survey of the main properties of this family by typing waveinfo('fbsp') from the MATLAB command line.

Figure 6-24: Complex Frequency B-Spline Wavelet fbsp 2-1-0.5

Complex Shannon Wavelets: shan

See [Teo98] pages 62-65.

This family is obtained from the frequency B-spline wavelets by setting m to 1.

A complex Shannon wavelet is defined by

depending on two parameters:

• is a bandwidth parameter.
• is a wavelet center frequency.

You can obtain a survey of the main properties of this family by typing waveinfo('shan') from the MATLAB command line.

Figure 6-25: Complex Shannon Wavelet shan 1-0.5

Other Real Wavelets

Summary of Wavelet Families and Associated Properties (Part 1)