The Lanczos 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 Lanczos 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 Lanczos window is as follows.
The magnitude response of the same filter is shown on the graph below.
Measures for the Lanczos window
The following is a comparison of the discrete Fourier transform of the Lanczos window and the rectangular window.
The Lanczos window measures are as follows.