parzenwin

Parzen (de la Vallée Poussin) window

Syntax

w = parzenwin(L)

w = parzenwin(L,typeName)

Description

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

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

Examples

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)

Input Arguments

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.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

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

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 $$-\frac{(N-1)}{2}\le n\le \frac{(N-1)}{2}$$:

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

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.

Extended Capabilities

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

Version History

Introduced before R2006a

R2024b: Generate Single-Precision Outputs

The parzenwin function supports single-precision outputs.