PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

636 Practical MATLAB® Applications for Engineers

Note that the output of the Cheby type-1 fi lter is truly an HPF (only the frequency

w = 0.5 is present), whereas the output of the Cheby type-2 fi lter is similar to the compos-

ite input signal in which the two input frequencies are present.

Example 6.12

Example 6.12 involves an FIR fi lter, type 1 with symmetry, and length N = odd. Obtain

by hand expressions of the amplitude and phase of H(ejW), verifying that the phase is

linear if the impulse response sequence is given by

h(n) = [.5 1 .5] for n = 0, 1, and 2

ANALYTICAL Solution

HejW hnz e e

n

n

()

()njWjW..



0

2

∑ 05 1^052

He e e e
()[.jW
 05 jW 05. ]jW jW

He We
()[ cos]jW
 1 jW

He()jW 
1forcosW W 

∠He W
()jW
 for

FIGURE 6.62
Plots of the discrete input and the fi lter’s outputs of Example 6.11.

5

 5

0

Input sequence

0102030405060708090

5

 5

0

Output Chev 1

0 1020304050607080 90

5

 5

0

Output Chev 2

nT

0102030405060708090