Flat top window

The flat top window coefficients are given by the following formula

Flat top window formula

where N is the length of the filter and k = 0, 1, …, N – 1.

An example flat top window

Consider a finite impulse response (FIR) low pass filter of length N = 201. The following is the flat top window.

Flat top 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 flat top window is as follows.

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

Measures for the flat top window

The following graph shows the discrete Fourier transform of the flat top window against the transform of the rectangular window.

Discrete Fourier transform of the flat top window

The following are selected measures for the flat top window.

Coherent gain 0.22
Equivalent noise bandwidth 3.78
Processing gain -5.77 dB
Scalloping loss -0.01 dB
Worst case processing loss -5.78 dB
Highest sidelobe level -93.6 dB
Sidelobe falloff -12.1 dB / octave, -40.1 dB / decade
Main lobe is -3 dB 3.72 bins
Main lobe is -6 dB 4.00 bins
Overlap correlation at 50% overlap -0.015
Amplitude flatness at 50% overlap -0.110
Overlap correlation at 75% overlap 0.044
Amplitude flatness at 75% overlap 0.938

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