PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Time Domain Representation of Continuous and Discrete Signals 83

Example 1.17

Create the script fi le up_down_samples that returns the approximation plots of the fol-

lowing time discrete function:

f(n) = cos(2 0.05n) + 2 sin(20.03n)

for a length of N = 100 samples, for the following cases:

1. Down-sample or decimate the sequence f(n) with the integer factors of M = 2 , 4 ,
   and 10.


2. Up-sample or interpolate the sequence f(n) with the integer factors of L = 2 , 4 ,
   and 10.


3. Resample f(n) by the ratio of the two integers given by L/M, for the following cases:
   L = 3 , M = 2 , and L = 2 , M = 3.

MATLAB Solution

% Script file: up _ down _ samples

n = 0:1:99;

f = cos(2*pi*.05*n)+2*sin(2*pi*.03*n);

yzero = zeros(1,500);

figure(1); % down-sample with M=2, 4, 10

subplot(2,2,1)

stem(n,f);hold on; plot(n,f,n,yzero(1:100))

title(‘f(n) vs n’); ylabel(‘Amplitude’);

xlabel(‘time index n’);

subplot(2,2,2)

gm2 = decimate(f,2,’fir’);

nm2 = 0:100/2-1;

stem(nm2,gm2(1:50)); hold on; plot(nm2,yzero(1:50));

title(‘f(n) is decimated with M=2’); ylabel(‘Amplitude’);

xlabel(‘time index n’);

subplot(2,2,3)

gm4 = decimate(f,4,’fir’);

nm4 = 0:100/4-1;

stem(nm4,gm4(1:25));hold on;

plot(nm4,gm4(1:25),nm4,yzero(1:25));

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

title(‘f(n) is decimated with M=4’)

subplot(2,2,4)

gm10 = decimate(f,10,‘fir’);

nm10=0:100/10-1;

stem(nm10,gm10(1:10));hold on;

plot(nm10,gm10(1:10),nm10,yzero(1:10));