Signals and Systems - Electrical Engineering

678 C H A P T E R 11: Introduction to the Design of Discrete Filters

[b,a] = cheby1(lporder,R,wn,‘stop’); % stopband

end

[H,w] = freqz(b,a,256);

end

To illustrate the design of filters other than low-pass filters, consider the design of a Butterworth and

Chebyshev band-pass and band-stop filter of orderN=30 and half-power frequencies [0.4π, 0.6π].

The following script is the design, which is shown in Figure 11.19.

FIGURE 11.19

(a) Band-Stop Butterworth and (b)

Chebyshev filters: (clockwise for each

side from top left) poles and zeros,

magnitude, phase frequency responses,

and loss. (b)

(a)

− 1 01

− 1

−0.5

0

0.5

1

Real part

Imaginary part

0 0.2 0.4 0.6 0.8

0

50

100

150

200

Loss (dB)

ω/π

Real part

Imaginary part

Loss (dB)

ω/π

− 1

−0.5

0

0.5

1

600

400

200

0

− 1 01

0 0.2 0.4 0.6 0.8

0 0.2 0.4 0.6 0.8

0

0.2

0.4

0.6

0.8

1

Magnitude

ω/π

0 0.2 0.4 0.6 0.8

− 30

− 20

− 10

0

Phase (rad)

ω/π

Magnitude

ω/π

Phase (rad)

ω/π

0

0.5

1

− 30

− 40

− 50

− 20

− 10

0

0 0.2 0.4 0.6 0.8

0 0.2 0.4 0.6 0.8