PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

530 Practical MATLAB® Applications for Engineers

Example 5.10

Let the audio analog signal f(t) be given by

ft

tTs

tTst Ts

Ts t Ts

()

cos( )

cos(

0064

7 2 1000 64 128

0 128 192

7

    

    



22 1000 tTst Ts) 192       256

















and sampling rate be Ts = 1/8000 samples/s.

Convert the continuous time function f(t) into a discrete sequence f(n).

Create the script fi le shift that uses the function f(n) to verify the property that states

that a shift in time only affects the phase spectrum and not the magnitude spectrum by

shifting f(n) by 32 time samples and return the following plots:

a. fi gure(1): f(n) versus n, abs{fft[f(n)]} versus f, and angle{fft[f(n)]} versus f (Figure 5.44)

b. fi gure(2): Repeat part a for f(n − 32) (Figure 5.45)

c. fi gure(3): [error in time = f(n) − f(n − 32)] versus t, [error_ mag = abs{fft[f(n)]} − abs{fft

[f(n − 32)]}] versus f, and [error_ phase = angle{fft[f(n)]} − angle{fft[f(n − 32)]}] versus

f (Figure 5.46)

d. Estimate the cumulative magnitude and phase errors in the frequency domain

− 2 20

− 2

0

2

46810121416

20

0

2

4

− 2

− 2

46810121416

20

0

2

− 2468

frequency W in rad.

10 12 14 16

Error analysis in time and frequency

Amplitude in time

[abs(DFTs)]

[angle(DFTs)]

time index n

W

× 10 −^15

× 10 −^15

× 10 −^15

FIGURE 5.43
Time and frequency error plots of Example 5.9.