LP, HP, BP and BS FIR filters with the Blackman-Harris window.

Cuthbert Nyack
The Blackman window is a 3 term window given by :-
w(t) = 0.42 + 0.50 * cos(2pt/t) + 0.08 * cos(4pt/t) for |t| <=t/2.

The Blackman-Harris window extends the 3 term window to a 4 term window as shown below:-
w(t) = 0.35875 + 0.48829 * cos(2pt/t) + 0.14128 * cos(4pt/t) + 0.01168 * cos(6pt/t) for |t| <=t/2.

The numbers used here are taken from diracdelta.co.uk.

The applet shows the frequency response of a filter using w(t) in red and the following wv(t) with variable parameters in green.
wv(t) = {a + b * cos(2pt/t) + c * cos(4pt/t) + (1 - (a + b + c)) * cos(6pt/t)}n for |t| <=t/2.

The window function and impulse response are also shown.
Scrollbar 0 sets Fn which sets the type of filter Fn = 0/1/2 and 3 shows LP/HP/BP and BS filters. The parameters a, b, c, n and the cut off frequencies are set by the scrollbars indicated.



Below is a low pass filter with stop band attenuation of 118dB. Marginal improvement is possible by using variable parameters.

Below is a high pass filter with stop band attenuation of 118dB.

Below is a band pass filter with stop band attenuation of 112dB.

Below is a band stop filter with stop band attenuation of 119dB.

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COPYRIGHT 2008 Cuthbert Nyack.