patlab_10.m

close all;
clc;
clearvars;
%%

syms t k
% Original Signal
f0 = 10; 
original_signal = sin(2*pi*f0*t);

% Impulse Train for Sampling
Fs = 20;
N = 201;
k_values = linspace(0,1,N);
sampled_signal = zeros(size(k_values));
impulse_train_plot = zeros(size(k_values));


% sample the original using Impulse Train

for i = 1:length(k_values)
    % Create an impulse train using the heaviside function
    impulse_train = heaviside(t-k_values(i)/Fs);
    impulse_train_plot(i) = double(subs(impulse_train,t,k_values(i)));
    % Evaluate the product of original_signal and impulse_train 
    sampled_signal_sym  = subs(original_signal * impulse_train,t,k_values(i));
    % Convert the symbolic expression to double
    sampled_signal(i) = double(sampled_signal_sym);
end

dft_of_sample = abs(fftshift(fft(sampled_signal))) / N;
fft_time = linspace(-0.5,0.5,N);

% Plot the results
figure;
subplot(4, 1, 1);
fplot(original_signal, [0, 1]);
title('Original Signal');

subplot(4,1,2);
stem(k_values,impulse_train_plot);
title("Impulse_ Train");

subplot(4,1,3);
stem(k_values,sampled_signal);
title("Sampled Signal");

subplot(4,1,4);
stem(fft_time,dft_of_sample);
title("dft of sample");
%%
up=2;
down=2;

upsampled_signal = upsample(sampled_signal,up);
downsampled_signal = downsample(sampled_signal,down);

dft_of_upsample = abs(fftshift(fft(upsampled_signal))) / N;
dft_of_downsample = abs(fftshift(fft(downsampled_signal))) / N;

up_time = linspace(0,1,length(upsampled_signal));
down_time = linspace(0,1,length(downsampled_signal));

figure;
subplot(2,2,1);
stem(down_time,downsampled_signal);
title("downsampled signal");

subplot(2,2,2);
stem(up_time,upsampled_signal);
title("upsampled signal");

subplot(2,2,3);
stem(down_time,dft_of_downsample);
title("DFT of downsample")

subplot(2,2,4);
stem(uptime,dft_of_upsample);
title("DFT of upsample");