PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

80 Practical MATLAB® Applications for Engineers

Example 1.16

Let f(t) = te−1000t u(t)

Create the script fi le sample_data that returns the following plots:

a. f(t) versus t, over the range 0 ≤ t ≤ 5 ms

b. f(nT) versus nt, for T = 0.2 ms, over the range 1 ≤ n ≤ 26

c. Reconstruct f(t) from f(nT) using

i. Summations of sinc functions (emulating a low-pass fi lter)

ii. Stair function

iii. Spine function

d. error(t) versus t, for the reconstruction process when a low-pass fi lter is used, where

error t f t fn nT c F t nT F

n ssS T

N

S

S

()
() ( )sin [ ()], 

1

(^261)
∑ for
MATLAB Solution
% Script file: sample _ data
t = 0:0.0005:0.005; % 26 time samples
fa = t.exp(-1000.t);
figure(1)
subplot(2,1,1)
plot(t,fa);title(‘f(t) vs t’)
ylabel(‘Amplitude’);xlabel(‘time t (msec)’);
subplot(2,1,2)
Ts = 0.0002; n = 0:1:25; Fs=1/Ts;
nTs = nTs;
fd = nTs.exp(-1000*nTs);
stem(nTs,fd);hold on;
plot(nTs,fd);
title(‘f(t) sample with Ts=.2msec.’);
ylabel(‘Amplitude’); xlabel(‘time index n (msec)’)
201816141210
time index n
86420
− 1
−0.5
0
1
2
1.5
error0.5
error=[mov.ave/2terms] versus t
FIGURE 1.66
Error plot of moving average using two terms of Example 1.15.