The Kaiser-Bessel window coefficients are given by the following formula
where N is the length of the filter and k = 0, 1, …, N – 1.
Consider a finite impulse response (FIR) low pass filter of length N = 201. The following is the Kaiser-Bessel window.
Given a sampling frequency of 2000 Hz and a filter cutoff frequency of 40 Hz, the impulse response of the filter with a rectangular window (with no window) and with the Kaiser-Bessel window is as follows.
The magnitude response of the same filter is shown on the graph below.
Measures for the Kaiser-Bessel window
The following is a comparison of the discrete Fourier transform of the Kaiser-Bessel window and the rectangular window.
The Kaiser-Bessel window measures are as follows.
|Equivalent noise bandwidth||1.80|
|Processing gain||-2.55 dB|
|Scalloping loss||-1.02 dB|
|Worst case processing loss||-3.57 dB|
|Highest sidelobe level||-65.3 dB|
|Sidelobe falloff||-11.8 dB / octave, -39.3 dB / decade|
|Main lobe is -3 dB||1.70 bins|
|Main lobe is -6 dB||2.40 bins|
|Overlap correlation at 50% overlap||0.072|
|Amplitude flatness at 50% overlap||0.608|
|Overlap correlation at 75% overlap||0.537|
|Amplitude flatness at 75% overlap||1.000|