meyer

Meyer wavelet

Syntax

[PHI,PSI,T] = meyer(LB,UB,N)

Description

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

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.

If only one function is required, a fourth argument is allowed:

[PHI,T] = meyer(LB,UB,N,'phi')
[PSI,T] = meyer(LB,UB,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 changing the auxiliary function (see meyeraux for more information), you get a family of different wavelets.

Examples

% Set effective support and grid parameters. 
lb = -8; ub = 8; n = 1024; 

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

More About

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Algorithms

Starting from an explicit form of the Fourier transform ϕ^ of ϕ, meyer computes the values of ϕ^ on a regular grid, and then the values of ϕ are computed using instdfft, the inverse nonstandard discrete FFT.

The procedure for ψ is along the same lines.

References

Daubechies, I. (1992), Ten lectures on wavelets, CBMS-NSF conference series in applied mathematics, SIAM Ed., pp. 117–119, 137, 152.

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