# meyer

## Syntax

``[phi,psi,t] = meyer(lb,ub,n)``
``[phi,t] = meyer(lb,ub,n,'phi')``
``[psi,t] = meyer(lb,ub,n,'psi')``
``[phi,psi] = meyer(lb,ub,n,S)``

## Description

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````[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')``` ## 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 $\stackrel{^}{\varphi }$ of the scaling function ϕ, `meyer` computes the values of $\stackrel{^}{\varphi }$ 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.

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

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