design bandpass filter in specific range

Question

let say that we have signal with sampling frequency 100 hertz,i want to design FIR filter so that cut all frequency that are outsize of frequency range 15-20,if we convert it to the normalized frequency we will get 15/50=0.3 and 0.4,i know that for example i can use butter to design filter,for example like there http://www.emba.uvm.edu/~gmirchan/classes/EE275/Lab5.pdf

but could you help me please to design bandpass filter in matlab?let say we have some signal s(t),

this command

[b a] = butter(2, 400/(fs/2));

designs a second order Butterworth filter with cutoff frequency 400 and then this command

y = filter(b,a,swn);

filters given signal, but instead of one cut-off frequency, I need range 15-20, so how can I apply bandpass filter?

Answer 1

Actually, you can use that very same function butter() to design bandpass filters as well, simply by supplying a vector of cutoff frequencies instead of a scalar:

% filter design
fs = 100;
f1 = 15;
f2 = 20;

% normalized frequency
w1 = f1 / (fs/2);
w2 = f2 / (fs/2);

% second-order butterworth
[b, a] = butter(2, [w1 w2]);

% filtering
x = randn(1, 10000);
y = filter(b, a, x);

In your question, you're talking about the need for an FIR filter. However, a Butterworth filter has an infinite impulse response, as you can see from the fact that the function butter() returns a vector a with more than one element.