Engee documentation

kaiser

The Kaiser’s window.

Library

EngeeDSP

Syntax

Function call

  • w = kaiser(L,beta) — returns L-Kaiser point window with form factor beta.

Arguments

Input arguments

# L — window length

+ positive integer

Details

The window length specified as a positive integer.

If you set L as a non-integer number, the function will round it to the nearest integer value.
Data types

Float32, Float64, Int8, Int16, Int32, Int64, UInt8, UInt16, UInt32, UInt64

# beta — form factor

+ 0.5 (by default) | positive real scalar

Details

The coefficient of the form, given as a positive real scalar. The argument beta affects the weakening of the side lobes of the Fourier transform of the window.

Data types

Float32, Float64

Output arguments

# w — Kaiser’s window

+ column vector

Details

The Kaiser window returned as a column vector.

Algorithms

The coefficients of the Kaiser window are calculated using the following equation:

Where — modified Bessel function of the first kind of zero order. Length . Challenge kaiser(L,beta) equivalent to

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

To get the Kaiser window, which is a FIR filter with attenuation of the side lobes dB, use the following expression for

β

increasing expands the main lobe and reduces the amplitude of the side lobes (i.e. increases attenuation).

Literature

  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., and Ronald W. Schafer, with John R. Buck. Discrete-Time Signal Processing. Upper Saddle River, NJ: Prentice Hall, 1999.