# Documentation

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# cgauwavf

Complex Gaussian wavelet

## Syntax

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

## Description

`[PSI,X] = cgauwavf(LB,UB,N)` returns the 1st order derivative of the complex-valued Gaussian wavelet, `PSI`, on an `N`-point regular grid, `X`, for the interval `[LB,UB]`. The effective support of the complex-valued 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 complex Gaussian function is defined as ${C}_{p}{e}^{-ix}{e}^{-{x}^{2}}$. 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 `'cgau4'`. To see valid character vectors for complex-valued Gaussian wavelets, use `waveinfo('cgau')` or use `wavemngr('read',1)` and refer to the Complex Gaussian section.

## Examples

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This example shows how to create a complex-valued Gaussian wavelet of order 4. The wavelet has an effective support of [-5,5] and is constructed using 1,000 samples.

```lb = -5; ub = 5; n = 1000; order = 4; [psi,x] = cgauwavf(lb,ub,n,order); subplot(211) plot(x,real(psi)) title('Real Part'); subplot(212) plot(x,imag(psi)) title('Imaginary Part');```