parzenwin

Parzen (de la Vallée Poussin) window

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Syntax

w = parzenwin(L)

w = parzenwin(L,typeName)

Description

w = parzenwin(L) returns the L-point Parzen (de la Vallée Poussin) window.

example

w = parzenwin(L,typeName) specifies the option to return the window w with single or double precision.

Examples

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Parzen and Gaussian Windows

Open Live Script

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

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

$Figure Window Visualization Tool contains 2 axes objects and other objects of type uimenu, uitoolbar, uipanel. Axes object 1 with title Time domain, xlabel Samples, ylabel Amplitude contains 2 objects of type line. Axes object 2 with title Frequency domain, xlabel Normalized Frequency (\times\pi rad/sample), ylabel Magnitude (dB) contains 2 objects of type line.$

Input Arguments

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`L` — Window length
positive integer

Window length, specified as a positive integer.

Note

If you specify L as noninteger, the function rounds it to the nearest integer value.

`typeName` — Output data type
`"double"` (default) | `"single"`

Since R2024b

Output data type (class), specified as one of these:

"double" — Use this option to return a double-precision output w.
"single" — Use this option to return a single-precision output w.

Data Types: char | string

Output Arguments

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`w` — Parzen window
column vector

Parzen window, returned as a column vector of length L. For the equation that defines the Parzen window, see Algorithms.

Algorithms

Parzen windows are piecewise-cubic approximations of Gaussian windows. Parzen window sidelobes fall off as 1/ω⁴.

This equation defines the N–point Parzen window over the interval $- \frac{(N - 1)}{2} \leq n \leq \frac{(N - 1)}{2}$ :

$w (n) = {\begin{matrix} 1 - 6 {(\frac{| n |}{N / 2})}^{2} + 6 {(\frac{| n |}{N / 2})}^{3} & 0 \leq | n | \leq (N - 1) / 4 \\ 2 {(1 - \frac{| n |}{N / 2})}^{3} & (N - 1) / 4 < | n | \leq (N - 1) / 2 \end{matrix}$

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.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced before R2006a

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R2024b: Generate Single-Precision Outputs

The parzenwin function supports single-precision outputs.

parzenwin

Syntax

Description