How to design a Butterworth filter?

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

Answer 1

[Yash]

i developed this code for my program, it may help you

a=wavread('1.wav');
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 ')