Signals and Systems - Electrical Engineering

96 C H A P T E R 1: Continuous-Time Signals

grid

axis([min(t) max(t) -1 5])

function [ye,yo] = evenodd(t,y)

% even/odd decomposition

% t: time

% y: analog signal

% ye, yo: even and odd components

% USE [ye,yo] = evenodd(t,y)

%

yr = fliplr(t,y);

ye = 0.5 * (y + yr);

yo = 0.5 * (y - yr);

The MATLAB functionfliplrreverses the values of the vectorygiving the reflected signal. n

nExample 1.18

Use symbolic MATLAB to generate the following analog signals.

(a) For the damped sinusoid signal

x(t)=e−tcos( 2 πt)

obtain a script to generatex(t)and its envelope.

(b) For a rough approximation of a periodic pulse generated by adding three cosines of

frequencies multiples of 0 =π/10—that is

x 1 (t)= 1 +1.5 cos( 2  0 t)−0.6 cos( 4  0 t)

write a script to generatex 1 (t).

Solution

The following script generates the damped sinusoid signal, and its envelopey(t)=±e−t.

%%%%%%%%%%%%%%%%%%%

% Example 1.18 --- damped sinusoid

%%%%%%%%%%%%%%%%%%%

t = sym(’t’);

x = exp(-t) * cos(2 * pi * t);

y = exp(-t);

ezplot(x,[-2,4])

grid

hold on

ezplot(y,[-2,4])