FIR Low Pass Filter with different windows(log).

Cuthbert Nyack

Frequency response of an FIR LP filter derived from a Fourier Series of the frequency response followed by the application of different windows to the impulse response.
For n from 0 to N within window, Windows used are:-
Rectangular window w(n) = 1.
Hamming window w(n) = 0.54 - 0.46 cos(2pi*n/N)
Hanning window w(n) = 0.50 - 0.50 cos(2pi*n/N)
Blackman window w(n) = 0.42 - 0.50 cos(2pi*n/N) + 0.08 cos(4pi*n/N)

N is the length of the impulse response.
fc/fs is the cutoff frequency expressed as a fraction of the sampling frequency.
When Fgain = 1 horizontal axis is from 0 to 0.5 of the sampling frequency.
When Vgain = 1 Vertical axis is 25dB/division.
Frequency response is in orange for the rectangular window, red for the Hamming window, green for the Hanning window and cyan for the Blackman window.

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