# How to design a Butterworth filter?

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Todd on 29 Jun 2012
It is going to be a two-pole low-pass Butterworth filters with a nominal cutoff frequency of 15 Hz.
An additional note is "calculated breakpoint frequencies are 18 Hz and 19 Hz for the first and second pole respectively" not sure if this info is necessary

Yash on 30 Jun 2012
Edited: Walter Roberson on 1 Jul 2012
ah=a.*hann(length(a));
aN=length(ah);
indexa=[0:1:aN-1];
fs=8000;
fa=[0:1:aN-1]*fs/aN;
aff=abs(fft(ah))/aN;
figure % for siren 1
plot (fa,aff);
xlabel(' FFT of Siren 1');
n = 1; % Filter order
lf = .5e3; % low frequency cutoff for bandpass
hf = 1.5e3; % high frequency cutoff for bandpass
[b,a] = butter(n, [lf hf]/(fs/2));
fout = filter(b,a,ah);
% Plot Spectrum figure
spec = fft(fout,nfft);
pfspec = spec(1:fix(nfft/2)); % Extract postive frequencies
plot(pfax/1e3,abs(pfspec))
xlabel('Hz')
ylabel('Magnitude')
title('Filter Signal Spectrum ')

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