Question

Design a linear phase, minimum-length, band-pass FIR digital filter in MATLAB to meet the specifications listed below. Use Rectangular Windowing (MATLAB function: fir1)

pass-band frequencies: f_p1 = 0.35, f_p2 = 0.65

stop-band frequencies: f_s1 = 0.10, f_s2 = 0.80

pass-band tolerance: d_p <= 0.1

stop-band tolerance: d_s <= 0.1

I am attempting to learn more about MATLAB and I am having trouble with specific filter design and it would be helpful to have an example.

Answer 1

Script:

clc;close all;clear all;

%Pass band and stop band edge frequencies

ws1=0.1;wp1=0.35;wp2=0.65;ws2=0.8;

tranwidth = min((wp1-ws1),(ws2-wp2));

%Cut off frequencies

wc1=(wp1+ws1)/2;

wc2=(wp2+ws2)/2;

wc=[wc1 wc2];

%For rectangular window , main lobe width is 4pi/N

N=round(4*pi/tranwidth);

M=N+1;n=0:1:M-1;

%Impulse response

hd=fir1(M-1,wc,'bandpass');

wR=rectwin(M)';

h=hd.*wR;

%Frequency response

w=0:0.01*pi:pi;

[H,w]=freqz(h,[1],w);

figure;

subplot(221)

stem(n,h)

title('Impulse response h(n)')

xlabel('n');grid;

ylabel('h(n)')

subplot(222)

plot(w/pi,abs(H),'b')

title('Magnitude response |H(w)|')

xlabel('w/pi');grid;

ylabel('|H(exp(jw)|')

subplot(223)

plot(w/pi,20*log10(abs(H)),'r')

title('Magnitude response in db ')

xlabel('w/pi');grid;

ylabel('|H(exp(jw)| in db')

subplot(224)

plot(w/pi,angle(H),'b')

title('Phase response ')

xlabel('w/pi');grid;

ylabel('<H(exp(jw)>')