updownsample.m

clc; clear;

Fs1 = 100;
n = 0:1/Fs1:100-(1/Fs1);
N = length(n);

% Original signals
sin_wave = sin(5*n*2*pi);          % 5 Hz sine
random = 2*round(rand(1,N))-1;     % Random ±1

% Lowpass filter (bandwidth limit to 0.1 * Fs)
coeffs = firls(30, [0 0.2 0.22 1], [1 1 0 0]);
sin_bwlimited = filter(coeffs, 1, sin_wave);
random_bwlimited = filter(coeffs, 1, random);

% Normalized frequency axis
f_norm = (-N/2:N/2-1) / N;

%% Decimation by M=5
M = 5;
sin_decimated = sin_bwlimited(1:M:end);
random_decimated = random_bwlimited(1:M:end);

N_dec = length(sin_decimated);
f_norm_dec = (-N_dec/2:N_dec/2-1) / N_dec;

%% Upsampling (Interpolation) by L=5
L = 5;

% Zero-stuffing
sin_upsampled = zeros(1, N_dec * L);
sin_upsampled(1:L:end) = sin_decimated;
random_upsampled = zeros(1, N_dec * L);
random_upsampled(1:L:end) = random_decimated;

% Interpolation filter (lowpass to remove images, gain = L)
coeffs_interp = L * firls(30, [0 0.2/L 0.22/L 1], [1 1 0 0]);
sin_interpolated = filter(coeffs_interp, 1, sin_upsampled);
random_interpolated = filter(coeffs_interp, 1, random_upsampled);

N_up = length(sin_interpolated);
f_norm_up = (-N_up/2:N_up/2-1) / N_up;

%% Figure
figure('Position', [100 100 1200 800]);

% Row 1: Time domain - Original and Filtered
subplot(3,4,1);  % (a) Original sine
stem(sin_wave, 'o', 'MarkerSize', 2);
xlim([200 250]); ylim([-1.5 1.5]); grid;
xlabel('Discrete time (n)'); ylabel('Amplitude');
title('(a) Original Sine');

subplot(3,4,2);  % (b) Original random
stem(random, 'o', 'MarkerSize', 2);
xlim([200 250]); ylim([-1.5 1.5]); grid;
xlabel('Discrete time (n)'); ylabel('Amplitude');
title('(b) Original Random');

subplot(3,4,3);  % (c) Filtered sine
stem(sin_bwlimited, 'o', 'MarkerSize', 2);
xlim([200 250]); ylim([-1.5 1.5]); grid;
xlabel('Discrete time (n)'); ylabel('Amplitude');
title('(c) Filtered Sine');

subplot(3,4,4);  % (d) Filtered random
stem(random_bwlimited, 'o', 'MarkerSize', 2);
xlim([200 250]); ylim([-1.5 1.5]); grid;
xlabel('Discrete time (n)'); ylabel('Amplitude');
title('(d) Filtered Random');

% Row 2: FFT of filtered and decimated
subplot(3,4,5);  % (e) FFT of filtered sine
sin_fft = 20*log10(abs(fftshift(fft(sin_bwlimited))));
plot(f_norm, sin_fft, 'k');
xlim([-0.5 0.5]); ylim([-200 0]); grid;
xlabel('Frequency f_{s1}'); ylabel('Magnitude (dB)');
title('(e) FFT Filtered Sine');

subplot(3,4,6);  % (f) FFT of filtered random
random_fft = 20*log10(abs(fftshift(fft(random_bwlimited))));
plot(f_norm, random_fft, 'k');
xlim([-0.5 0.5]); ylim([-200 0]); grid;
xlabel('Frequency f_{s1}'); ylabel('Magnitude (dB)');
title('(f) FFT Filtered Random');

subplot(3,4,7);  % (g) FFT of decimated sine
sin_dec_fft = 20*log10(abs(fftshift(fft(sin_decimated))));
plot(f_norm_dec, sin_dec_fft, 'k');
xlim([-0.5 0.5]); ylim([-200 0]); grid;
xlabel('Frequency f_{s2}'); ylabel('Magnitude (dB)');
title('(g) FFT Decimated Sine (M=5)');

subplot(3,4,8);  % (h) FFT of decimated random
random_dec_fft = 20*log10(abs(fftshift(fft(random_decimated))));
plot(f_norm_dec, random_dec_fft, 'k');
xlim([-0.5 0.5]); ylim([-200 0]); grid;
xlabel('Frequency f_{s2}'); ylabel('Magnitude (dB)');
title('(h) FFT Decimated Random (M=5)');

% Row 3: Upsampled time domain and FFT
subplot(3,4,9);  % (i) Upsampled sine time domain
stem(sin_interpolated, 'o', 'MarkerSize', 2);
xlim([200 250]); ylim([-1.5 1.5]); grid;
xlabel('Discrete time (n)'); ylabel('Amplitude');
title('(i) Interpolated Sine (L=5)');

subplot(3,4,10);  % (j) Upsampled random time domain
stem(random_interpolated, 'o', 'MarkerSize', 2);
xlim([200 250]); ylim([-1.5 1.5]); grid;
xlabel('Discrete time (n)'); ylabel('Amplitude');
title('(j) Interpolated Random (L=5)');

subplot(3,4,11);  % (k) FFT of upsampled sine
sin_up_fft = 20*log10(abs(fftshift(fft(sin_interpolated))));
plot(f_norm_up, sin_up_fft, 'k');
xlim([-0.5 0.5]); ylim([-200 0]); grid;
xlabel('Frequency f_{s1}'); ylabel('Magnitude (dB)');
title('(k) FFT Interpolated Sine');

subplot(3,4,12);  % (l) FFT of upsampled random
random_up_fft = 20*log10(abs(fftshift(fft(random_interpolated))));
plot(f_norm_up, random_up_fft, 'k');
xlim([-0.5 0.5]); ylim([-200 0]); grid;
xlabel('Frequency f_{s1}'); ylabel('Magnitude (dB)');
title('(l) FFT Interpolated Random');

sgtitle('Decimation (M=5) and Interpolation (L=5) Demo');