Signals and Systems - Electrical Engineering

8.2 Discrete-Time Signals 477

N = length(t);

y = zeros(1, N);

for i = 1:N,

if t(i)>=−ad,

y(i) = m∗(t(i) + ad);

end

end

Likewise, the following function generates unit-step signals with different time shifts (notice the
similarities with therampfunction).

function y = ustep(t, ad)

% generation of unit step

% t: time support

% ad : advance (positive), delay (negative)

N = length(t);

y = zeros(1, N);

for i = 1:N,

if t(i)>=−ad,

y(i) = 1;

end

end

Finally, the following function can be used to compute the even and the odd decomposition of a
discrete-time signal. The MATLAB functionflliplrreflects the signal as needed in the generation of
the even and the odd components.

function [ye, yo] = evenodd(y)

% even/odd decomposition

% NOTE: the support of the signal should be

% symmetric about the origin

% y: analog signal

% ye, yo: even and odd components

yr = fliplr(y);

ye = 0.5∗(y + yr);

yo = 0.5∗(y−yr);

The results are shown in Figure 8.7. The discrete-time signal is given as

y[n]=















0 n≤− 21

0.45n+ 9 − 20 ≤n≤− 6

−0.45n+ 3 − 7 ≤n≤ 0

3 1 ≤n≤ 19

0 n≥ 20

n