# intwave

Integrate wavelet function psi (ψ)

## Syntax

``[integ,xval] = intwave(wname)``
``[integ,xval] = intwave(wname,prec)``
``[intdec,xval,intrec] = intwave(wname,prec)``
``[integ,xval] = intwave(wname,in2,in3)``

## Description

````[integ,xval] = intwave(wname)` computes the integral, `integ`, of the wavelet function ψ specified by `wname`. The function ψ is approximated on the 28 points grid `xval`.```

example

````[integ,xval] = intwave(wname,prec)` approximates the wavelet function on the 2`prec` points grid `xval`.```
````[intdec,xval,intrec] = intwave(wname,prec)` computes the integrals, `intdec` and `intrec`, of the wavelet decomposition function ψdec and the wavelet reconstruction function ψrec, respectively. This syntax is valid only for biorthogonal wavelets.```
````[integ,xval] = intwave(wname,in2,in3)` approximates the function ψ is on the 2`max`(`in2,in3`) points grid `xval` and plots the results.```

## Examples

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Specify a wavelet name.

`wname = "db4";`

Use `wavefun` to obtain the wavelet function. Specify seven iterations.

```iter = 7; [~,psi,xval] = wavefun(wname,iter);```

Compute the integrals of the wavelet approximation.

`[integ,~] = intwave(wname,iter);`

Plot the results.

```tiledlayout(2,1) nexttile plot(xval,psi) title("Wavelet") nexttile plot(xval,integ) title(["Wavelet Integrals Over [-Inf x] " ... "For Each Value of xval"]);```

## Input Arguments

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Wavelet, specified as a character vector or string scalar. For more information, see `waveinfo` and `wfilters`.

Data Types: `char` | `string`

Number of iterations used to approximate the wavelet function, specified as a positive integer.

For the special value `0`, `intwave(wname,0)` is equivalent to `intwave(wname,8)`.

Data Types: `double`

Number of iterations used to approximate the wavelet function, specified as a pair of positive integers. The number of iterations is equal to `max(in2,in3)`.

For the special value `0`, `intwave(wname,0,in3)` is equivalent to `intwave(wname,8,in3)`.

Data Types: `double`

## Output Arguments

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Integral of the wavelet function ψ, returned as a vector. The `intwave` function computes the integral of ψ (from −∞ to `xval` values): , for x in `xval`.

`integ` is a real- or complex valued vector, depending on the wavelet type.

Grid points where the wavelet function approximation is evaluated, returned as a real-valued vector.

Integral of the biorthogonal wavelet decomposition function ψdec, returned as a vector.

Integral of the biorthogonal wavelet reconstruction function ψrec, returned as a vector.

## Algorithms

First, the wavelet function is approximated on a grid of 2`prec` points using `wavefun`. A piecewise constant interpolation is used to compute the integrals using `cumsum`.

## Version History

Introduced before R2006a