meyer (Wavelet Toolbox)

Meyer wavelet.

[PHI,PSI,T] = meyer(LOWB,UPPB,N)
[PHI,T] = meyer(LOWB,UPPB,N,'phi')
[PSI,T] = meyer(LOWB,UPPB,N,'psi')

Description

[PHI,PSI,T] = meyer(LOWB,UPPB,N) returns Meyer wavelet and scaling functions evaluated on an N point regular grid on the interval [LOWB,UPPB].

N must be a power of two.

Output arguments are the scaling function PHI and the wavelet function PSI computed on the grid T. These functions have [-8 8] as effective support.

A fourth argument is allowed if only one function is required:
[PHI,T] = meyer(LOWB,UPPB,N,'phi')
[PSI,T] = meyer(LOWB,UPPB,N,'psi')

when the fourth argument is used but not equal to 'phi' or 'psi'. Outputs are the same as in the main option.

The Meyer wavelet and scaling function are defined in the frequency domain by:

where

By changing the auxiliary function (see meyeraux), you get a family of different wavelets. For the required properties of the auxiliary function

, see References in Chapter 6.

Examples

% Set effective support and grid parameters. 
    lowb = -8; uppb = 8; n = 1024; 

% Compute and plot Meyer wavelet and scaling function. 
    [phi,psi,x] = meyer(lowb,uppb,n); 
    subplot(211), plot(x,psi) 
    title('Meyer wavelet') 
    subplot(212), plot(x,phi) 
    title('Meyer scaling function')

Algorithm

Starting from an explicit form of the Fourier transform

, meyer computes the values of

on a regular grid and then the values of

are computed using instdfft, the inverse nonstandard discrete FFT.

The procedure for

is along the same lines.