PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

DTFT, DFT, ZT, and FFT 505

5.4 Examples

Example 5.1

Let f(n) = 0.6nu(n).

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

b. Create the script fi le DTFT that returns the magnitude and phase plots of the DTFT

of f(n) = 0.6nu(n) of part a, over the range −π < W < π.

c. Repeat part b by using the MATLAB function freqz.

d. Evaluate the magnitude and phase errors of the two techniques employed (part b

and part c).

ANALYTICAL Solution

Part a

FejW f n ejWn

n

()
 ()


 



∑

FejW nun ejWn

n

()
 .()


 



∑^06 −

Fe e e

e

jW n jWn

n

jW

n

n

()


. (. ) . jW







(^0606) 
1
00106
∑∑−
FIGURE 5.17
Plots of R.5.144.
Auto-correlation of fl(n)
20
10
0
Amplitude
− 7 − 6 − 5 − 4 − 3 − 2 −10 12 3 45 6 7
40
20
0
Amplitude
− 7 − 6 − 5 − 4 − 3 − 2 −10 12 3 45 6 7
40
20
0
Amplitude
− 7 − 6 − 5 − 4 − 3 − 2 −10 12 3 45 6 7
Cross-correlation of f2(n) with f1(n)
Cross-correlation of f1(n) with f2(n)
time index n
time index n
time index n