kaiser

Kaiser window

Syntax

w = kaiser(L,beta)

Description

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

Examples

Kaiser Window

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

L — Window length

positive integer

Window length, specified as a positive integer.

Data Types: single | double

beta — Shape factor

0.5 (default) | positive real scalar

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

w — Kaiser window

column vector

Kaiser window, returned as a column vector.

Algorithms

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

$$w(n)=\frac{I_0\left(\beta \sqrt{1-{\left(\frac{n-N/2}{N/2}\right)}^2}\right)}{I_0(\beta )},0\le n\le N,$$

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.

$$\beta =\{\begin{array}{ll}0.1102(\alpha -8.7),\hfill & \alpha >50\hfill \\ 0.5842{(\alpha -21)}^{0.4}+0.07886(\alpha -21),\hfill & 50\ge \alpha \ge 21\hfill \\ 0,\hfill & \alpha <21\hfill \end{array}$$

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

References

[1] 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.

[2] 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.

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

Extended Capabilities

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