Question

(From Mitra M7.5.) (using matlab)Design a digital Chebyshev-I lowpass filter operating at a sampling rate of 80 kHz with a passband edge frequency at 4 kHz, a passband ripple of 0.5 dB, and a minimum stopband attenuation of 45 dB at 20 kHz using the bilinear transformation method. Determine the order of the analog prototype using the command cheb1ord and then design the analog prototype using cheb1ap. Transform the analog filter into a digital one using the bilinear command. Plot the frequency response, pole-zero diagram and impulse response of the digital filter. Show the steps of the design procedure.

Answer 1

MATLAB:

clc;clear all;close all;
%Design of digital Chebyshev-I lowpass filter
%specifications
Rp=0.5; Rs=45;fp=4000; Fs=80000;fs=20000;
%Nomalized frequencies
Wp=2*fp/Fs;Ws=2*fs/Fs;

%Find order of the filter and cutoff frequency
[N,Wp] = cheb1ord(Wp,Ws,Rp,Rs)
[z,p,k] = cheb1ap(N,Rp);   
[num,den] = zp2tf(z,p,k);
%Bilinear transformation to get digital transfer function   
[b,a]=bilinear(num,den,1)
figure;%plot frequency response
freqz(b,a,1024,Fs)

figure;%plot pole zero plot
zplane(b,a)

figure;%Impulse response
N=50;n=0:1:N-1;
h=impz(b,a,N)
stem(n,h);grid;
xlabel('n')
ylabel('h(n)')
title('Impulse response')

Plot: