Signals and Systems - Electrical Engineering

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

− 1 −0.5 0 0.5 1

− 1

−0.5

0

0.5

1

4

Real part

Imaginary part

(^001000200030004000)
2
4
6
8
|H
(f
)|
f(Hz)
0 1000 2000 3000 4000
− 6
− 4
− 2
0
<H
(f
)
f(Hz)
0 1000 2000 3000 4000
− 20
− 15
− 10
− 5
0
α
(f
) dB
f(Hz)
FIGURE 11.15
Low-pass filter for filtering of an analog signal.
Since this filter is used to filter an analog signal the frequency scale of the magnitude and the
phase responses of the filter is given in hertz (see Figure 11.15). To verify that the specifications
are satisfied the loss function is plotted and compared with the losses corresponding tofhpandfst.
The loss atfhp=2250 Hz coincides with the dc loss plus 3 dB, and the loss atfst=2700 Hz is
above the specified value. n

11.4.3 Design of Chebyshev Low-Pass Discrete Filters

The design of Chebyshev low-pass filters is very similar to the design of Butterworth low-pass filters.

The constantKcof the bilinear transform for the Chebyshev filter is calculated by transforming the normalized

pass frequency′p= 1 into the discrete frequencyωp:

Kc=

1

tan(0.5ωp)

(11.32)