Digital Signal Processing: DISCRETE-TIME SYSTEMS IN THE TIME DOMAIN AND MOVING AVERAGE FILTER IN MATLAB

DIGITAL SIGNAL PROCESSING

DISCRETE-TIME SYSTEMS IN THE TIME DOMAIN

MOVING AVERAGE FILTER IN MATLAB

INTRODUCTION:

A discrete-time system processes an input signal in the time-domain to generate an output signal with more desirable properties by applying an algorithm composed of simple operations on the input signal and its delayed versions. The aim of this lab is to illustrate the simulation of some simple discrete-time systems on the computer using MATLAB.

THE MOVING AVERAGE SYSTEM:

A three-point smoothing filter is considered in the problem and it constitutes LTI FIR system. A causal version of the three-point smoothing filter is obtained by simply delaying the output by one sample period, resulting in the FIR filter described by

(1)

Generalizing the above equation we obtain

(2)

Which defines a causal M-point smoothing FIR filter. The system of equation (2) is also known as a moving average filter. We illustrate its use in filtering high-frequency components from a signal composed of a sum of several sinusoidal signals.

% Simulation of an M-point Moving Average Filter

% Generate the input signal

n = 0:100;

s1 = cos(2*pi*0.05*n); % A low frequency sinusoid

s2 = cos(2*pi*0.47*n); % A high frequency sinusoid

x = s1+s2;

% Implementation of the moving average filter

M = input('Desired length of the filter = ');

num = ones(1,M);

y = filter(num,1,x)/M;

% Display the input and output signals

clf;

subplot(2,2,1);

plot(n,s1);

axis([0, 100, -2, 2]);

xlabel('Time index n'); ylabel('Amplitude');

title('Signal # 1');

subplot(2,2,2);

plot(n,s2);

axis([0, 100, -2, 2]);

xlabel('Time index n'); ylabel('Amplitude');

title('Signal # 2');

subplot(2,2,3);

plot(n,x);

axis([0, 100, -2, 2]);

xlabel('Time index n'); ylabel('Amplitude');

title('Input Signal');

subplot(2,2,4);

plot(n,y);

axis([0, 100, -2, 2]);

xlabel('Time index n'); ylabel('Amplitude');

title('Output Signal');

axis;

RESULTS:

QUESTIONS

Q.1: Run the above program for M = 2 to generate the output signal with x[n] = s₁ [n] + s₂ [n] as the input. Which component of the input x[n] is suppressed by the discrete time system simulated by this program?

Q.2: Run Program P1 for other values of filter length M, and various values of the frequencies of the sinusoidal signals s₁ [n] and s₂ [n]. Comment on your results.