# Documentation

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# 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') ```

## Algorithms

Starting from an explicit form of the Fourier transform $\stackrel{^}{\varphi }$ of ϕ, `meyer` computes the values of $\stackrel{^}{\varphi }$ 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.