CODE 1.(AM-Modulation).
clc; % Clear command window
clear;
close all; % Close all figure windows
% Parameters
m = 1; % Modulation index or Modulation Factor or Modulation depth
Am = 5; % Amplitude of modulating signal
fm = 2000; % Frequency of modulating signal (Hz)
Tm = 1 / fm; % Period of modulating signal (s)
t = 0:Tm/999:6*Tm; % Time vector for 6 periods of the modulating
signal
Ac = Am / m; % Amplitude of carrier signal
fc = fm * 10; % Frequency of carrier signal (10 times the modulating
signal frequency)
Tc = 1 / fc; % Period of carrier signal (s)
% Modulating Signal
Ym = Am * sin(2 * pi * fm * t); % Modulating (message) signal
subplot(3,1,1); % Create the first subplot
plot(t, Ym, 'b', 'LineWidth', 0.8); % Blue line with thicker width for
better visibility
title('Modulating Signal');
xlabel('Time (s)');
ylabel('Amplitude');
grid on;
% Carrier Signal
Yc = Ac * sin(2 * pi * fc * t); % Carrier signal
subplot(3,1,2); % Create the second subplot
plot(t, Yc, 'r', 'LineWidth', 0.8); % Red line with thicker width
title('Carrier Signal');
xlabel('Time (s)');
ylabel('Amplitude');
grid on;
% Amplitude Modulated (AM) Signal
AMsig = Ac * (1 + m * sin(2 * pi * fm * t)) .* sin(2 * pi * fc * t); % AM
signal
subplot(3,1,3); % Create the third subplot
plot(t, AMsig, 'g', 'LineWidth', 0.8); % Green line with thicker width
title('Amplitude Modulated Signal');
xlabel('Time (s)');
ylabel('Amplitude');
grid on;
CODE 2.(PERIODIC & APERIODIC SEQUENCES).
% Define the sample points from 0 to 50
n = 0:1:50;
% Generate the first sine wave with frequency 0.2*pi
x1 = sin(0.2*pi*n);
% Generate the second sine wave with frequency 0.4*pi
x2 = sin(0.4*pi*n);
% Create a signal that is the superposition of the two previous
sine waves
x3 = sin(0.2*pi*n) + sin(0.4*pi*n);
% Generate a fourth sine wave with frequency 0.5
x4 = sin(0.5*n);
% Create a 2x2 subplot layout
% First subplot - Display the first sine wave
subplot(2, 2, 1);
stem(n, x1);
xlabel('n');
ylabel('x1(n)');
axis([0 50 -1 1]); % Set axis limits
% Second subplot - Display the second sine wave
subplot(2, 2, 2);
stem(n, x2);
xlabel('n');
ylabel('x2(n)');
axis([0 50 -1 1]); % Set axis limits
% Third subplot - Display the superposition of the two sine waves
subplot(2, 2, 3);
stem(n, x3);
xlabel('n');
ylabel('x3(n)');
axis([0 50 -2 2]); % Set axis limits (note the larger y-range to
accommodate the superposition)
% Fourth subplot - Display the fourth sine wave
% Note: Fixed variable name from 'n1' to 'n' to match the defined
variable
subplot(2, 2, 4);
stem(n, x4); % Changed n1 to n
xlabel('n');
ylabel('x4(n)');
axis([0 50 -1 1]); % Set axis limits
CODE 3.(DISCRETE FOURIER TRANSFORM).
clc; % Clear command window
% Define the input sequence x (time domain signal)
x = [1, 2, 3, 4, 0, 0, 0, 0]; % Input sequence with 4 non-zero values
followed by 4 zeros
N = 8; % Length of the sequence/number of DFT points
% Compute the discrete Fourier transform (DFT)
% This transforms the time-domain signal into frequency domain
y = fft(x, N);
% Calculate magnitude and phase of the DFT result
mag = abs(y); % Magnitude spectrum (absolute value of complex
numbers)
phase = angle(y); % Phase spectrum (angle of complex numbers
in radians)
% Create the index vector for plotting (0 to N-1)
n = 0:1:N-1;
% Create a new figure window
figure;
% First subplot - Display the input sequence (time domain)
subplot(2, 2, 1);
stem(n, x);
xlabel('n');
ylabel('x(n)');
title('Input Sequence (Time Domain)');
% Second subplot - Display the magnitude spectrum
subplot(2, 2, 2);
stem(n, mag);
xlabel('n');
ylabel('Magnitude');
title('Magnitude Spectrum');
% Third subplot - Display the phase spectrum
subplot(2, 2, 3);
stem(n, phase);
xlabel('n');
ylabel('Phase (radians)');
title('Phase Spectrum');
% Display the DFT result in the command window
disp('DFT Result:');
disp(y);
CODE 4.(INVERSE DISCRETE F.T).
clc; % Clear command window
% Define the input sequence x
x = [4, 3, 2, 1, 0, 0, 0, 0]; % Input sequence with 4 non-zero values
and 4 zeros
N = 8; % Length of the sequence/number of DFT points
% Compute the inverse discrete Fourier transform (IDFT)
% This gives us the time-domain representation of the frequency-
domain signal x
y = ifft(x, N);
% Calculate magnitude and phase of the IDFT result
mag = abs(y); % Magnitude (absolute value) of complex numbers
phase = angle(y); % Phase (angle) of complex numbers in radians
% Create the index vector for plotting (0 to N-1)
k = 0:1:N-1;
% Create a new figure window
figure;
% First subplot - Display the input sequence (frequency domain)
subplot(2, 2, 1);
stem(k, x);
xlabel('k');
ylabel('x(k)');
title('Input Sequence (Frequency Domain)');
% Second subplot - Display the magnitude of IDFT result
subplot(2, 2, 2);
stem(k, mag);
xlabel('k');
ylabel('Magnitude');
title('Magnitude of IDFT Result');
% Third subplot - Display the phase of IDFT result
subplot(2, 2, 3);
stem(k, phase);
xlabel('k');
ylabel('Angle (radians)'); % Corrected from 'angel' to 'Angle'
title('Phase of IDFT Result');
% Display the IDFT result (y) in the command window
disp('IDFT Result:');
disp(y);
