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.