FIR Bandpass Filter with Hamming

Hi,

How would you solve the following question of the bandpass filter with the hamming window - with w1=0.2*pi rad/sample and w2=0.4*pi rad/sample. With the order of the filter being 100. Whilst plotting the fequency and phase responses too.

This isn't homework.

Answer 1

[William Rose]

@Liam Nielson,

See code below.

%LiamsFilter     Liam Nielsen & W.Rose
%Requested filter order was 100, but I will use 101 for symmetry
n=-50:50;
w1=0.2*pi;
w2=0.4*pi;
h1=(w2/pi)*sin(n*w2)./(n*w2)-(w1/pi)*sin(n*w1)./(n*w1);   
h1(51)=w2/pi-w1/pi;             
h2=h1.*hamming(101)';           %apply Hamming window to h1
plot(n,h1,'rx-',n,h2,'bo-');    %plot impulse responses
xlabel('n'); ylabel('Impulse Response'); legend('h','hamm(h)');
fvtool(h1,'magnitude');
fvtool(h2,'magnitude');
fvtool(h1,'phase');
fvtool(h2,'phase');

Code above makes 5 plots:

• impulse response of h and hamming(h)
• magn(h)
• magn(hamm(h))
• phase(h)
• phase(hamm(h))

Plots 1 and 3 from list above are shown below.