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parzenwin

Parzen (de la Vallée Poussin) window

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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Parzen and Gaussian Windows

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.