Experiment-4
Exercises
Exercise-1
%% Experiment - 4
% Exercise - 1
clc;
clear;
%% Low pass FIR filter design using the window method
w_p = 0.375; % Pass band frequency
w_s = 0.5; % Stop band frequency
w_c = w_p + (w_s - w_p) / 2; % Cut-off frequency
k = 4; % Hamming window
N = ceil((2 * k * pi) / (w_s - w_p)); % Order of filter
win = window(@hamming, N+1); % Hamming window
NUM = fir1(N, w_c, 'low', win); % Numerator coefficients of T[z]
DEN = [1]; % Denominator coefficients of T[z]
[H, W] = freqz(NUM, DEN); % Frequency response
figure; grid ON;
plot(W / pi, 20 * log10(abs(H))) % Magnitude spectrum
title('Magnitude spectrum of Low pass FIR filter', "Ashrith 200902016");
xlabel('Normalized Frequency (\times\pi rad/sample)'), ylabel('Gain (dB)');
figure;
zplane(NUM, DEN)
title('Pole-Zero Plot', "Ashrith 200902016");Exercise-2
%% Experiment - 4
% Exercise - 2
clc;
clear;
%% High pass FIR filter design using the window method
w_s = 0.2; % Stop band frequency
w_p = 0.3; % Pass band frequency
w_c = w_s + (w_p - w_s) / 2; % Cut-off frequency
k = 4; % Hamming window
N = ceil((2 * k * pi) / (w_p - w_s)); % Order of filter
win = window(@hamming, N+1); % Hamming window
NUM = fir1(N, w_s, 'high', win); % Numerator coefficients of T[z]
DEN = [1]; % Denominator coefficients of T[z]
[H, W] = freqz(NUM, DEN); % Frequency response
figure; grid ON;
plot(W / pi, 20 * log10(abs(H))) % Magnitude spectrum
title('Magnitude spectrum of High pass FIR filter', "Ashrith 200902016");
xlabel('Normalized Frequency (\times\pi rad/sample)'), ylabel('Gain (dB)');
figure;
zplane(NUM, DEN)
title('Pole-Zero Plot', "Ashrith 200902016");Exercise-3
%% Experiment - 4
% Exercise - 3
clc;
clear;
%% Band pass FIR filter design using the window method
Fs = 2000; % Sampling frequency
w_lp = 300 / Fs; % Lower pass band edge frequency
w_ls = 200 / Fs; % Lower stop band edge frequency
w_up = 600 / Fs; % Upper pass band edge frequency
w_us = 700 / Fs; % Upper stop band edge frequency
w_lc = w_ls + (w_lp - w_ls) / 2; % Lower cutoff frequency
w_uc = w_up + (w_us - w_up) / 2; % Upper cutoff frequency
% Stop band attenuation = 50dB
k = 4; % Hamming window
N = ceil((2 * k * pi) / (w_us - w_up)); % Order of filter
win = window(@hamming, N+1); % Hamming window
NUM = fir1(N, [w_lc, w_uc], 'bandpass', win); % Numerator coefficients of T[z]
DEN = [1]; % Denominator coefficients of T[z]
[H, W] = freqz(NUM, DEN); % Frequency response
figure; grid ON;
plot(W / pi, 20 * log10(abs(H))) % Magnitude spectrum
title('Magnitude spectrum of Band pass FIR filter', "Ashrith 200902016");
xlabel('Normalized Frequency (\times\pi rad/sample)'), ylabel('Gain (dB)');
figure;
zplane(NUM, DEN)
title('Pole-Zero Plot', "Ashrith 200902016");Exercise-4
%% Experiment - 4
% Exercise - 4
clc;
clear;
%% Band stop FIR filter design using the window method
Fs = 2000; % Sampling frequency
w_lp = 200 / Fs; % Lower pass band edge frequency
w_ls = 300 / Fs; % Lower stop band edge frequency
w_up = 700 / Fs; % Upper pass band edge frequency
w_us = 600 / Fs; % Upper stop band edge frequency
w_lc = w_lp + (w_ls - w_lp) / 2; % Lower cutoff frequency
w_uc = w_us + (w_up - w_us) / 2; % Upper cutoff frequency
% Stop band attenuation = 50dB
k = 4; % Hamming window
N = floor((2 * k * pi) / (w_up - w_us)); % Order of filter
win = window(@hamming, N+1); % Hamming window
NUM = fir1(N, [w_lc, w_uc], 'stop', win); % Numerator coefficients of T[z]
DEN = [1]; % Denominator coefficients of T[z]
[H, W] = freqz(NUM, DEN); % Frequency response
figure; grid ON;
plot(W / pi, 20 * log10(abs(H))) % Magnitude spectrum
title('Magnitude spectrum of Band stop FIR filter', "Ashrith 200902016");
xlabel('Normalized Frequency (\times\pi rad/sample)'), ylabel('Gain (dB)');
figure;
zplane(NUM, DEN)
title('Pole-Zero Plot', "Ashrith 200902016");Exercise-5
%% Experiment - 4
% Exercise - 5
clc;
clear;
%% (a) Simulate the signal having frequencies 10Hz, 30Hz and 50Hz.
Fs = 1024; % Sampling frequency
n_max = 5;
n = 0 : 1/Fs : n_max - 1; % Discrete time index
s_10 = sin(2 * pi * 10 * n);
s_30 = sin(2 * pi * 30 * n);
s_50 = sin(2 * pi * 50 * n);
x = s_10 + s_30 + s_50;
%% (b) Design suitable FIR filter to select only 30Hz component (Use Hamming window).
w_lp = 2 * pi * 28 / Fs; % Lower pass band edge frequency
w_ls = 2 * pi * 29 / Fs; % Lower stop band edge frequency
w_up = 2 * pi * 31 / Fs; % Upper pass band edge frequency
w_us = 2 * pi * 32 / Fs; % Upper stop band edge frequency
w_lc = w_ls + (w_lp - w_ls) / 2; % Lower cutoff frequency
w_uc = w_up + (w_us - w_up) / 2; % Upper cutoff frequency
k = 4; % Hamming window
N = ceil((2 * k * pi) / (w_us - w_up)); % Order of filter
win = window(@hamming, N+1); % Hamming window
NUM = fir1(N, [w_lc / pi, w_uc / pi], 'bandpass', win); % Numerator coefficients of T[z]
DEN = [1]; % Denominator coefficients of T[z]
[H, W] = freqz(NUM, DEN);
%% (c) Filter the signal using the designed filter.
y = filter(NUM, DEN, x);
figure;
hold on
plot(y, 'b')
plot(x, 'r')
hold off
title('Filter output', "Ashrith 200902016");
xlabel('n'), ylabel('Amplitude'), legend('y', 'x')
%% (d) Plot the spectrum of the input and the filtered signal.
figure;
subplot(211)
hold on
plot(n * Fs / n_max, abs(fft(x)), 'r')
hold off
title('Input Fourier Transform', "Ashrith 200902016");
xlabel('Frequency'), ylabel('Magnitude'), legend('x')
subplot(212)
hold on
plot(n * Fs / n_max, abs(fft(y)), 'b')
hold off
title('Output Fourier Transform', "Ashrith 200902016");
xlabel('Frequency'), ylabel('Magnitude'), legend('y')Last updated