kaiser

Syntax

w = kaiser(L,beta)

Description

example

w = kaiser(L,beta) returns an L-point Kaiser window with shape factor beta.

Examples

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Create a 200-point Kaiser window with a beta of 2.5. Display the result using wvtool.

w = kaiser(200,2.5);
wvtool(w)

Input Arguments

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Window length, specified as a positive integer.

Data Types: single | double

Shape factor, specified as a positive real scalar. The parameter beta affects the sidelobe attenuation of the Fourier transform of the window.

Data Types: single | double

Output Arguments

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Kaiser window, returned as a column vector.

Algorithms

The coefficients of a Kaiser window are computed from the following equation:

w(n)=I0(β1(nN/2N/2)2)I0(β),0nN,

where I0 is the zeroth-order modified Bessel function of the first kind. The length L = N + 1. kaiser(L,beta) is equivalent to

besseli(0,beta*sqrt(1-(((0:L-1)-(L-1)/2)/((L-1)/2)).^2))/besseli(0,beta)

To obtain a Kaiser window that represents an FIR filter with sidelobe attenuation of α dB, use the following β.

β={0.1102(α8.7),α>500.5842(α21)0.4+0.07886(α21),50α210,α<21

Increasing β widens the mainlobe and decreases the amplitude of the sidelobes (i.e., increases the attenuation).

References

[1] Kaiser, James F. “Nonrecursive Digital Filter Design Using the I0-Sinh Window Function.” Proceedings of the 1974 IEEE® International Symposium on Circuits and Systems. April, 1974, pp. 20–23.

[2] Digital Signal Processing Committee of the IEEE Acoustics, Speech, and Signal Processing Society, eds. Selected Papers in Digital Signal Processing. Vol. II. New York: IEEE Press, 1976.

[3] Oppenheim, Alan V., Ronald W. Schafer, and John R. Buck. Discrete-Time Signal Processing. Upper Saddle River, NJ: Prentice Hall, 1999, p. 474.

Extended Capabilities

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

Introduced before R2006a