DSP Practical - Experiment 5

Aim

To implement a decimator and interpolator for a given signal using MATLAB, with decimation and interpolation factors of 2.

Problem Statement

Given the signal:

          x(n) = 10 * cos(2 * pi * fm * n * Ts)

Where fm = 200Hz, fs = 5000Hz. Perform the decimation and interpolation process with factors of M = 2 and L = 2.

Theory

Decimation and interpolation are two operations used in signal processing to reduce or increase the sampling rate of a signal.

Decimation: This process involves reducing the sampling rate by an integer factor. For decimation by a factor of M, every Mth sample of the signal is taken.
Interpolation: This process involves increasing the sampling rate by an integer factor. For interpolation by a factor of L, new samples are inserted between the original samples.

In this experiment, we will apply both operations (with M = L = 2) on the given signal and observe the effects.

MATLAB Code

% MATLAB Code for Decimation and Interpolation

clc;
clear all;
close all;

% Given parameters
L = 2;   % Interpolation factor
M = 2;   % Decimation factor
fm = 200; % Frequency of the signal
fs = 5000; % Sampling frequency
n = 0:39; % Time index for the signal

% Original signal
x = 10 * cos(2 * pi * fm / fs * n);

% Plotting the original signal
subplot(3,1,1);
stem(n, x);
title('Original signal x(n)');
xlabel('Sample Index');
ylabel('Amplitude');

% Decimating the signal by factor of M
x_decimated = decimate(x, M);

% Plotting the decimated signal
subplot(3,1,2);
stem(1:length(x_decimated), x_decimated);
title('Decimated signal x(Mn)');
xlabel('Sample Index');
ylabel('Amplitude');

% Interpolating the signal by factor of L
x_interpolated = interp(x, L);

% Plotting the interpolated signal
subplot(3,1,3);
stem(1:length(x_interpolated), x_interpolated);
title('Interpolated signal x(n/L)');
xlabel('Sample Index');
ylabel('Amplitude');

Expected Output

The MATLAB code generates three plots:

Original Signal: The first plot shows the original signal x(n), which is a cosine wave with a frequency of 200 Hz.
Decimated Signal: The second plot shows the signal after decimation by a factor of 2, effectively reducing the number of samples in the signal.
Interpolated Signal: The third plot shows the signal after interpolation by a factor of 2, effectively increasing the number of samples between the original ones.

These plots visually demonstrate the effect of decimation and interpolation on a discrete-time signal. Decimation reduces the sample rate, while interpolation increases it by inserting additional samples between the original ones.