Experiment-5
Exercises
Exercise-1
%% Experiment - 5
% Exercise - 1
clc;
clear;
%% IIR Butterworth low-pass filter
F_s = 10000; % Sampling frequency
r_p = 1; % Pass band peak ripple
r_s = 40; % Stop band peak ripple
f_p = 100; w_p = 2 * f_p / F_s; % Pass band edge frequency
f_s = 500; w_s = 2 * f_s / F_s; % Stop band edge frequency
[N, Wn] = buttord(w_p, w_s, r_p, r_s); % Butterworth filter order
[NUM, DEN] = butter(N, Wn, 'low'); % Butterworth filter
[H, W] = freqz(NUM, DEN); % Frequency response
figure;
plot(W / pi, 20 * log10(abs(H))); grid ON;
title("Frequency response of IIR Butterworth low-pass filter", "Ashrith 200902016")
xlabel('Normalised frequency (\times \pi rad/sample)'), ylabel('Magnitude (dB)')
figure;
zplane(NUM, DEN);
title("Pole-Zero Plot", "Ashrith 200902016")Exercise-10
%% Experiment - 5
% Exercise - 10
clc;
clear;
%% IIR Chebyshev low-pass filter
F_s = 10000; % Sampling frequency
r_p = 1; % Pass band peak ripple
r_s = 80; % Stop band peak ripple
f_p = 100; w_p = 2 * f_p / F_s; % Pass band edge frequency
f_s = 2000; w_s = 2 * f_s / F_s; % Stop band edge frequency
[N, Wn] = cheb1ord(w_p, w_s, r_p, r_s); % Chebyshev filter order
[NUM, DEN] = cheby1(N, r_p, w_p, 'low'); % Chebyshev filter
[H, W] = freqz(NUM, DEN); % Frequency response
figure;
plot(W / pi, 20 * log10(abs(H))); grid ON;
title("Frequency response of analog IIR Chebyshev low-pass filter", "Ashrith 200902016")
xlabel('Normalised frequency (\times \pi rad/sample)'), ylabel('Magnitude (dB)')
%% Bilinear transformation
[NUMd,DENd] = bilinear(NUM, DEN, F_s);
[H, W] = freqz(NUMd, DENd); % Frequency response
figure;
plot(W / pi, 20 * log10(abs(H))); grid ON;
title("Frequency response of digital IIR Chebyshev low-pass filter", "Ashrith 200902016")
xlabel('Normalised frequency (\times \pi rad/sample)'), ylabel('Magnitude (dB)')
figure;
zplane(NUMd, DENd);
title("Pole-Zero Plot", "Ashrith 200902016")Exercise-2
%% Experiment - 5
% Exercise - 2
clc;
clear;
%% IIR Butterworth high-pass filter
F_s = 10000; % Sampling frequency
r_p = 10; % Pass band peak ripple (dB)
r_s = 40; % Stop band peak ripple (dB)
f_p = 3000; w_p = 2 * f_p / F_s; % Pass band edge frequency
f_s = 1000; w_s = 2 * f_s / F_s; % Stop band edge frequency
[N, Wn] = buttord(w_p, w_s, r_p, r_s); % Butterworth filter order
[NUM, DEN] = butter(N, Wn, 'high'); % Butterworth filter
[H, W] = freqz(NUM, DEN); % Frequency response
figure;
plot(W / pi, 20 * log10(abs(H))); grid ON;
title("Frequency response of IIR Butterworth high-pass filter", "Ashrith 200902016")
xlabel('Normalised frequency (\times \pi rad/sample)'), ylabel('Magnitude (dB)')
figure;
zplane(NUM, DEN);
title("Pole-Zero Plot", "Ashrith 200902016")Exercise-3
%% Experiment - 5
% Exercise - 3
clc;
clear;
%% IIR Butterworth band-pass filter
F_s = 10000; % Sampling frequency
r_p = 10; % Pass band peak ripple (dB)
r_s = 40; % Stop band peak ripple (dB)
f_p = [600 2000]; w_p = 2 * f_p / F_s; % Pass band edge frequency
f_s = [450 2300]; w_s = 2 * f_s / F_s; % Stop band edge frequency
[N, Wn] = buttord(w_p, w_s, r_p, r_s); % Butterworth filter order
[NUM, DEN] = butter(N, Wn); % Butterworth filter
[H, W] = freqz(NUM, DEN); % Frequency response
figure;
plot(W / pi, 20 * log10(abs(H))); grid ON;
title("Frequency response of IIR Butterworth band-pass filter", "Ashrith 200902016")
xlabel('Normalised frequency (\times \pi rad/sample)'), ylabel('Magnitude (dB)')
figure;
zplane(NUM, DEN);
title("Pole-Zero Plot", "Ashrith 200902016")Exercise-4
%% Experiment - 5
% Exercise - 4
clc;
clear;
%% IIR Butterworth band-stop filter
F_s = 10000; % Sampling frequency
r_p = 10; % Pass band peak ripple (dB)
r_s = 40; % Stop band peak ripple (dB)
f_p = [450 2300]; w_p = 2 * f_p / F_s; % Pass band edge frequency
f_s = [600 2000]; w_s = 2 * f_s / F_s; % Stop band edge frequency
[N, Wn] = buttord(w_p, w_s, r_p, r_s); % Butterworth filter order
[NUM, DEN] = butter(N, Wn, 'stop'); % Butterworth filter
[H, W] = freqz(NUM, DEN); % Frequency response
figure;
plot(W / pi, 20 * log10(abs(H))); grid ON;
title("Frequency response of IIR Butterworth band-stop filter", "Ashrith 200902016")
xlabel('Normalised frequency (\times \pi rad/sample)'), ylabel('Magnitude (dB)')
figure;
zplane(NUM, DEN);
title("Pole-Zero Plot", "Ashrith 200902016")Exercise-5
%% Experiment - 5
% Exercise - 5
clc;
clear;
%% IIR Chebyshev low-pass filter
F_s = 10000; % Sampling frequency
r_p = 1; % Pass band peak ripple (dB)
r_s = 80; % Stop band peak ripple (dB)
f_p = 100; w_p = 2 * f_p / F_s; % Pass band edge frequency
f_s = 2000; w_s = 2 * f_s / F_s; % Stop band edge frequency
[N, Wn] = cheb1ord(w_p, w_s, r_p, r_s); % Chebyshev filter order
[NUM, DEN] = cheby1(N, r_p, w_p, 'low'); % Chebyshev filter
[H, W] = freqz(NUM, DEN); % Frequency response
figure;
plot(W / pi, 20 * log10(abs(H))); grid ON;
title("Frequency response of IIR Chebyshev low-pass filter", "Ashrith 200902016")
xlabel('Normalised frequency (\times \pi rad/sample)'), ylabel('Magnitude (dB)')
figure;
zplane(NUM, DEN);
title("Pole-Zero Plot", "Ashrith 200902016")Exercise-6
%% Experiment - 5
% Exercise - 6
clc;
clear;
%% IIR Chebyshev high-pass filter
F_s = 10000; % Sampling frequency
r_p = 1; % Pass band peak ripple (dB)
r_s = 80; % Stop band peak ripple (dB)
f_p = 2000; w_p = 2 * f_p / F_s; % Pass band edge frequency
f_s = 100; w_s = 2 * f_s / F_s; % Stop band edge frequency
[N, Wn] = cheb1ord(w_p, w_s, r_p, r_s); % Chebyshev filter order
[NUM, DEN] = cheby1(N, r_p, w_p, 'high'); % Chebyshev filter
[H, W] = freqz(NUM, DEN); % Frequency response
figure;
plot(W / pi, 20 * log10(abs(H))); grid ON;
title("Frequency response of IIR Chebyshev high-pass filter", "Ashrith 200902016")
xlabel('Normalised frequency (\times \pi rad/sample)'), ylabel('Magnitude (dB)')
figure;
zplane(NUM, DEN);
title("Pole-Zero Plot", "Ashrith 200902016")Exercise-7
%% Experiment - 5
% Exercise - 7
clc;
clear;
%% Input signal
F_s = 1000; % Sampling frequency
n = 0 : 1/F_s : 1;
x_10 = sin(2 * pi * 10 * n);
x_30 = sin(2 * pi * 30 * n);
x_50 = sin(2 * pi * 50 * n);
x = x_10 + x_30 + x_50;
%% IIR Butterworth band-pass filter
r_p = 1; % Pass band peak ripple (dB)
r_s = 40; % Stop band peak ripple (dB)
f_p = [29 31]; w_p = 2 * f_p / F_s; % Pass band edge frequency
f_s = [25 40]; w_s = 2 * f_s / F_s; % Stop band edge frequency
[N, Wn] = buttord(w_p, w_s, r_p, r_s); % Butterworth filter order
[NUM, DEN] = butter(N, Wn); % Butterworth filter
[H, W] = freqz(NUM, DEN); % Frequency response
figure;
plot(W / pi, 20 * log10(abs(H))); grid ON;
title("Frequency response of IIR Butterworth band-pass filter", "Ashrith 200902016")
xlabel('Normalised frequency (\times \pi rad/sample)'), ylabel('Magnitude (dB)')
figure;
zplane(NUM, DEN);
title("Pole-Zero Plot", "Ashrith 200902016")
%% Spectrum of input and filtered signal
y = filter(NUM, DEN, x);
figure;
subplot(211)
plot(n, abs(fft(x))); grid ON;
title("Mangnitude Spectrum of Input signal", "Ashrith 200902016")
xlabel('Normalised frequency (\times \pi rad/sample)'), ylabel('Magnitude')
subplot(212)
plot(n, abs(fft(y))); grid ON;
title("Mangnitude Spectrum of Filtered signal", "Ashrith 200902016")
xlabel('Normalised frequency (\times \pi rad/sample)'), ylabel('Magnitude')Exercise-8
%% Experiment - 5
% Exercise - 8
clc;
clear;
%% Input signal
F_s = 1000; % Sampling frequency
n = 0 : 1/F_s : 1;
x_10 = sin(2 * pi * 10 * n);
x_30 = sin(2 * pi * 30 * n);
x_50 = sin(2 * pi * 50 * n);
x = x_10 + x_30 + x_50;
%% IIR Chebyshev band-pass filter
r_p = 10; % Pass band peak ripple (dB)
r_s = 40; % Stop band peak ripple (dB)
f_p = [29 31]; w_p = 2 * f_p / F_s; % Pass band edge frequency
f_s = [25 35]; w_s = 2 * f_s / F_s; % Stop band edge frequency
[N, Wn] = cheb1ord(w_p, w_s, r_p, r_s); % Chebyshev filter order
[NUM, DEN] = cheby1(N, r_p, w_p); % Chebyshev filter
[H, W] = freqz(NUM, DEN); % Frequency response
figure;
plot(W / pi, 20 * log10(abs(H))); grid ON;
title("Frequency response of IIR Chebyshev band-pass filter", "Ashrith 200902016")
xlabel('Normalised frequency (\times \pi rad/sample)'), ylabel('Magnitude (dB)')
figure;
zplane(NUM, DEN);
title("Pole-Zero Plot", "Ashrith 200902016")
%% Spectrum of input and filtered signal
y = filter(NUM, DEN, x);
figure;
subplot(211)
plot(n, abs(fft(x))); grid ON;
title("Mangnitude Spectrum of Input signal", "Ashrith 200902016")
xlabel('Normalised frequency (\times \pi rad/sample)'), ylabel('Magnitude')
subplot(212)
plot(n, abs(fft(y))); grid ON;
title("Mangnitude Spectrum of Filtered signal", "Ashrith 200902016")
xlabel('Normalised frequency (\times \pi rad/sample)'), ylabel('Magnitude')Exercise-9
%% Experiment - 5
% Exercise - 9
clc;
clear;
%% IIR Butterworth low-pass filter
F_s = 10000; % Sampling frequency
r_p = 1; % Pass band peak ripple
r_s = 40; % Stop band peak ripple
f_p = 100; w_p = 2 * pi * f_p / F_s; % Pass band edge frequency
f_s = 500; w_s = 2 * pi * f_s / F_s; % Stop band edge frequency
[N, Wn] = buttord(w_p, w_s, r_p, r_s, 's'); % Butterworth filter order
[NUM, DEN] = butter(N, Wn, 'low'); % Butterworth filter
[H, W] = freqz(NUM, DEN); % Frequency response
figure;
plot(W / pi, 20 * log10(abs(H))); grid ON;
title("Frequency response of analog IIR Butterworth low-pass filter", "Ashrith 200902016")
xlabel('Normalised frequency (\times \pi rad/sample)'), ylabel('Magnitude (dB)')
%% Bilinear transformation
[NUMd,DENd] = bilinear(NUM, DEN, F_s);
[H, W] = freqz(NUMd, DENd); % Frequency response
figure;
plot(W / pi, 20 * log10(abs(H))); grid ON;
title("Frequency response of digital IIR Butterworth low-pass filter", "Ashrith 200902016")
xlabel('Normalised frequency (\times \pi rad/sample)'), ylabel('Magnitude (dB)')
figure;
zplane(NUMd, DENd);
title("Pole-Zero Plot", "Ashrith 200902016")Last updated