# Documentation

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# gauswavf

Gaussian wavelet

## Syntax

```[PSI,X] = gauswavf(LB,UB,N) [PSI,X] = gauswavf(LB,UB,N,P) [PSI,X] = gauswavf(LB,UB,N,WAVNAME) ```

## Description

`[PSI,X] = gauswavf(LB,UB,N)` returns the 1st order derivative of the Gaussian wavelet, `PSI`, on an `N`-point regular grid, `X`, for the interval `[LB,UB]`. The effective support of the Gaussian wavelets is `[-5 5]`.

`[PSI,X] = gauswavf(LB,UB,N,P)` returns the `P`th derivative. Valid values of `P` are integers from 1 to 8.

The Gaussian function is defined as ${C}_{p}{e}^{-{x}^{2}}$. Cp is such that the 2-norm of the `P`th derivative of `PSI` is equal to 1.

`[PSI,X] = gauswavf(LB,UB,N,WAVNAME)` uses the valid wavelet family short name `WAVNAME` plus the order of the derivative in a character vector, such as `'gaus4'`. To see valid character vectors for Gaussian wavelets, use `waveinfo('gaus')` or use `wavemngr('read',1)` and refer to the Gaussian section.

### Note

For visualizing the second or third order derivative of Gaussian wavelets, the convention is to use the negative of the normalized derivative. In the case of the second derivative, scaling by -1 produces a wavelet with its main lobe in the positive y direction. This scaling also makes the Gaussian wavelet resemble the Mexican hat, or Ricker, wavelet. The validity of the wavelet is not affected by the -1 scaling factor.

## Examples

```% Set effective support and grid parameters. lb = -5; ub = 5; n = 1000; % Compute Gaussian wavelet of order 8. [psi,x] = gauswavf(lb,ub,n,8); % Plot Gaussian wavelet of order 8. plot(x,psi), title('Gaussian wavelet of order 8'), grid ```