Documentation

kaiser

Kaiser window

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Syntax

w =凯er(L,beta)

Description

w =凯er(L,beta)returns anL-point Kaiser window in the column vectorw.betais the Kaiser window parameter that affects the sidelobe attenuation of the Fourier transform of the window. The default value forbetais 0.5.

Examples

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Open Live Script

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

w =凯er(200,2.5); wvtool(w)

Algorithms

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

w ( n ) = I 0 ( β 1 − ( n − N / 2 N / 2 ) 2 ) I 0 ( β ) , 0 ≤ n ≤ N ,

whereI0is the zeroth-order modified Bessel function of the first kind. The lengthL=N+ 1. Thuskaiser(L,beta)相当于

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

To obtain a Kaiser window that designs an FIR filter with sidelobe attenuation ofαdB, use the followingβ.

β = { 0.1102 ( α − 8.7 ) , α > 50 0.5842 ( α − 21 ) 0.4 + 0.07886 ( α − 21 ) , 50 ≥ α ≥ 21 0 , α < 21

Increasingβwidens 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™.

See Also

Apps

Functions

Introduced before R2006a

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