PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

634 Practical MATLAB® Applications for Engineers

Example 6.11

Create the script fi le Cheby_1_2 that tests the design of the Chebyshev/types 1 and 2 HO

digital fi lter of Example 6.9 and returns their outputs by applying as input the signal

x(t) = 2 + cos(0.2 * t) + cos(0.5 * t) sampled at the rate T = 0.3.

a. Obtain plots of each component of x(t).

b. Obtain plots of the discrete input signal and the corresponding fi lter’s outputs.

c. Analyze and discuss each fi lter’s output and state which of the two has a better

performance.

MATLAB Solution

% Script file: Cheby _ 1 _ 2,

Pz1 = [0.8006 -2.4019 2.4019 -0.8006]; % num. and den. of digital filter

type 1

Qz1 = [1.0000 -2.5767 2.2067 -0.6217];

Pz2 = [0.9564 -2.8530 2.8530 -0.9564]; % num. and den. of digital filter

type 2

Qz2 = [1.0000 -2.8943 2.8098 -0.9147];

n = 0:1:300; % discrete time sequence

T = 0.3;

Dc = 2.*ones(1,301);

f1 = 2*cos(.2*T.*n);

f2 = cos(.5*T.*n);

figure(1)

subplot(3,1,1)

plot(n*T,dc);

FIGURE 6.60
Analog and discrete fi lter’s input and output of Example 6.10.

5

[x (t ) 
 2  cos (0.2.*t)  cos (4. *t)] versus t

4

3

2

1

012345

t in sec

Amplitude

0

Amplitude

4

3

2

1

0

0 2468

t in sec

y (t) versus t

0

0

1

2

3

4

5

x (nT) versus nT

Amplitude

123

time index nT

45

y (nT) versus nT

time index nT

02468

4

3

2

1

0

Amplitude