PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

76 Practical MATLAB® Applications for Engineers

Example 1.15

Let the discrete sequence

f(n) = 4n0.8nu(n)

be contaminated by a random noisy signal with a magnitude less than 1.

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

a. f(n) versus n

b. noise signal[n(t)] versus n

c. [f(n) + n(t)] versus n

d. [f(n) + n(t)] moving average using two terms versus n

e. [f(n) + n(t)] moving average using three terms versus n

f. [f(n) + n(t)] moving average using four terms versus n

g. Estimate the best moving average approximation for [f(n) + n(t)] versus n, by exe-

cuting the script fi le at least three times and observing and recording the results

Where the L point moving average is defi ned by

{}()moving aver.L

L

fn k

k

L




1 

0

1

∑

for L = 2 , 3 , and 4 , over the range 0 ≤ n ≤ 20.

MATLAB Solution

% Script file: averages

n = 0:1:20;

figure(1)

subplot(3,1,1)

signal = 4.*n.*(.8.^n);stem(n,signal);hold on;

plot(n,signal,n,signal,’o’);

title(‘Signal vs. n’)

ylabel(‘Amplitude’);xlabel(‘time index n’);

subplot(3,1,2)

noise = 2.*rand(1,21)-1.0;y = zeros(1,21);

FIGURE 1.62
Plot of adding the even and odd parts of f(t) of Example 1.14.

[feven(t)+fodd(t)] versus t

15

10

5

0

− 5

Amplitude [feven(t)+fodd(t)]

− 10 − 8 − 6 − 4 − 2 02 46810

time