Signals and Systems - Electrical Engineering

11.2 Frequency-Selective Discrete Filters 647

0 10 20 30 40 50 60 70 80 90 100

− 10

0

10

x[

n]

0 102030405060708090100

0 102030405060708090100

− 10

0

10

y

[n

]

− 10

0

10

n

n

n

z[

n]

(c)

0 0.5 1

0

0.5

1

1.5

ω/π

|H

(e

jω

)|

− 1 0 1

− 1

−0.5

0

0.5

1

11

Real part

Imaginary part

12

− 1

−0.5

0

0.5

1

Imaginary part− 101

Real part

0

2

4

|G

(e

jω

)|

0 0.5 1

ω/π

0 0.5 1

− 1

−0.5

0

0.5

1

<G

(e

jω

)

ω/π

(b)

0 0.5 1

− 1

−0.5

0

0.5

1

ω/π

<H

(e

jω

)

(a)

FIGURE 11.5
(a) Poles and zeros and frequency response of the FIR comb filterH(z)=(z^11 −0.8)/z^11 , and (b) the estimated
inverse IIR comb filterG(z)=z^12 /(z^12 −0.79). (c) The messagex[n]= 2 +cos(πn/ 4 )+cos(πn), the output
y[n]of channelH(z), and the outputz[n]of the estimated inverse filterG(z).