PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

508 Practical MATLAB® Applications for Engineers

Example 5.2

Given the sequences f 1 (n) = [0.3nu(n)] and f 2 (n) = [0.9nu(n)]

a. Evaluate by hand the DTFT of f 1 (n) and f 2 (n).

Create the script fi le DTFT_properties that returns the following:

b. Plots of f 1 (n) versus n and f 2 (n) versus n, over the range 0 ≤ n ≤ 9.

c. The magnitude and phase plots of DTFT of f1(n) and f 2 (n), over the range −π <

W < +π.

d. Verify the even symmetry of the relation real[F 1 (ejW)] = real[F 1 (e −jW)] and odd sym-

metry of imagl[F 1 (ejW)] = imag[−F 1 (e −jW)].

e. Use the linear property of DTFT and evaluate and plot the time–frequency relation

2f1(n) + 3f 2 (n) ⇔ 2F 1 (ejW) + 3F 2 (ejW).

f. Verify that F 1 (ejW) and F 2 (ejW) are periodic functions with periods of 2π, by plotting

each function over the range − 2 π < W < 2 π.

g. Compare the DTFT of Example 5.1 with the DTFT of part c and observe that if

f(n) = anu(n), then as a increases the BW decreases, as long as |a| < 1.

ANALYTICAL Solution

Part a

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MATLAB Solution
% Script file: DTFT _ properties
n = 0:9;
f1 = (0.3.ones(1,10)).^n;
f2 = (0.9.ones(1,10)).^n;
figure(1)
nn= [(-4:-1) n];f1nn =[zeros(1,4) f1];
subplot (2,1,1)