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parzenwin

Parzen (de la Vallée Poussin) window

Syntax

`w = parzenwin(L)`

Description

`w = parzenwin(L)` returns the `L`-point Parzen (de la Vallée Poussin) window in a column vector, `w`. Parzen windows are piecewise-cubic approximations of Gaussian windows. Parzen window sidelobes fall off as 1/ω4. See Definitions for the equation that defines the Parzen window.

Examples

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Compare 64-point Parzen and Gaussian windows. Display the result using `wvtool`.

```gw = gausswin(64); pw = parzenwin(64); wvtool(gw,pw) ```

Definitions

The following equation defines the `N`–point Parzen window over the interval $-\frac{\left(N-1\right)}{2}\le n\le \frac{\left(N-1\right)}{2}$:

`$w\left(n\right)=\left\{\begin{array}{cc}1-6{\left(\frac{|n|}{N/2}\right)}^{2}+6{\left(\frac{|n|}{N/2}\right)}^{3}& 0\le |n|\le \left(N-1\right)/4\\ 2{\left(1-\frac{|n|}{N/2}\right)}^{3}& \left(N-1\right)/4<|n|\le \left(N-1\right)/2\end{array}$`

References

[1] Harris, Fredric J. "On the Use of Windows for Harmonic Analysis with the Discrete Fourier Transform." Proceedings of the IEEE®. Vol. 66, January 1978, pp. 51–83.