Question

Consider a 4th-order lowpass Chebychev I digital filter given by 0.055524 + 0.222173 +0.3331:2 +0.22212 +0.0555 24 - 0.749823 + 1.072522 – 0.55982 +0.2337 (2) 1. Assuming the sampling frequency of this filter is Fs = 10kHz, plot the frequency response of this filter in the first Nyquist zone, in units of Hz as opposed to a normalized frequency or units of radians w. Plot the magnitude using the dB scale. 2. Plot the poles and zeroes of this filter on the complex plane, assume an FFT size of N = 1024 or larger.

Answer 1

MATLAB CODE

b=[0.0555,0.2221,0.3331,0.2221,0.0555]; % Numerator Coefficient
a=[1,-0.7498,1.0725,-0.5598,0.2337]; %Denominator Coefficient
Fs=10e3; % Sampling Frequency
SysZ=tf(b,a,1/Fs) % Transfer Function
N=1024; % FFT Size
[h,w] = freqz(b,a,'whole',N);
figure(1)
plot(w/pi,20*log10(abs(h)),'*') % Magnitude Response
grid on
ax = gca;
ax.YLim = [-100 100];
ax.XTick = 0:.5:2;
xlabel('Normalized Frequency (\times\pi rad/sample)')
ylabel('Magnitude (dB)')
title('Magnitude Response')
figure(2)
zplane(b,a,'r') % Pole Zero plot

Result:

0.0555 z^4 + 0.2221 z^3 + 0.3331 z^2 + 0.2221 z + 0.0555
--------------------------------------------------------
z^4 - 0.7498 z^3 + 1.073 z^2 - 0.5598 z + 0.2337

Sample time: 0.0001 seconds
Discrete-time transfer function

Magnitude Response

Magnitude Response Magnitude (dB) 0.5 Normalized Frequency (xa rad/sample)

Pole Zero Plot