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meyer

Description

example

[phi,psi,t] = meyer(lb,ub,n) returns the Meyer scaling and wavelet functions, phi and psi respectively, evaluated at t, an n-point regular grid in the interval [lb, ub]. Both functions have the interval [-8, 8] as effective support.

Note

meyer uses the auxiliary function meyeraux. If you change meyeraux, you get a family of different wavelets.

[phi,t] = meyer(lb,ub,n,'phi') returns only the Meyer scaling function.

[psi,t] = meyer(lb,ub,n,'psi') returns only the Meyer wavelet.

[phi,psi] = meyer(lb,ub,n,S) returns the Meyer scaling function and wavelet if S is not equal to 'phi' or 'psi'.

Examples

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Plot the Meyer wavelet and scaling functions.

lb = -8;
ub = 8;
n = 1024;
[phi,psi,x] = meyer(lb,ub,n);
subplot(2,1,1)
plot(x,phi)
grid on
title('Scaling Function')
subplot(2,1,2)
plot(x,psi)
grid on
title('Wavelet')

Figure contains 2 axes objects. Axes object 1 with title Scaling Function contains an object of type line. Axes object 2 with title Wavelet contains an object of type line.

Input Arguments

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Lower limit of interval, specified as a real-valued scalar.

Upper limit of interval, specified as a real-valued scalar.

Number of points, specified as a positive integer. n must be a power of 2.

Output Arguments

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Meyer scaling function, returned as a real-valued vector of length n.

Meyer wavelet, returned as a real-valued vector of length n.

Sampling instants, returned as a real-valued vector of length n.

Algorithms

The Meyer wavelet and scaling functions are defined in the Fourier domain. Starting from an explicit form of the Fourier transform ϕ^ of the scaling function ϕ, meyer computes the values of ϕ^ on a regular grid. The values of ϕ are computed using an inverse Fourier transform.

The procedure for the wavelet ψ is identical to the procedure for the scaling function.

References

[1] Daubechies, I. Ten Lectures on Wavelets, CBMS-NSF Regional Conference Series in Applied Mathematics. Philadelphia, PA: SIAM Ed, 1992.

Introduced before R2006a