Lanczos window

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The Lanczos window coefficients are given by the following formula

Lanczos window 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.

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.

Impulse response of a low pass filter with and without the Lanczos window

The magnitude response of the same filter is shown on the graph below.

Magnitude response of a low pass filter with and without the Lanczos window

Measures for the Lanczos window

The following is a comparison of the discrete Fourier transform of the Lanczos window and the rectangular window.

Discrete Fourier transform of the Lanczos window

The Lanczos window measures are as follows.


Coherent gain0.59
Equivalent noise bandwidth1.30
Processing gain-1.14 dB
Scalloping loss-1.88 dB
Worst case processing loss-3.03 dB
Highest sidelobe level-26.4 dB
Sidelobe falloff-11.5 dB / octave, -38.3 dB / decade
Main lobe is -3 dB1.26 bins
Main lobe is -6 dB1.74 bins
Overlap correlation at 50% overlap0.272
Amplitude flatness at 50% overlap0.785
Overlap correlation at 75% overlap0.733
Amplitude flatness at 75% overlap0.947


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