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.
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.
|Equivalent noise bandwidth||1.30|
|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 dB||1.26 bins|
|Main lobe is -6 dB||1.74 bins|
|Overlap correlation at 50% overlap||0.272|
|Amplitude flatness at 50% overlap||0.785|
|Overlap correlation at 75% overlap||0.733|
|Amplitude flatness at 75% overlap||0.947|