3. Given the transfer function of a continuous-time system as
ss À 5s
s 1s 2s 3s
, c ! 0:
(a) Show a plot of the poles and zeros of H(s).
(b) Discuss the stability of this system for the cases c 0 and c > 0.
4. Consider the circuit shown in Figure 6.3 with R 1
and C 1F. The input signal to the
circuit is expressed as
0 t 1
Show that the output is
yt 1 À e
ut À 1 À e
ut À 1:
5. Given the transfer function
s 1s 2
find the H(z) using the impulse-invariant method.
6. Given the transfer function of an analog IIR notch filter as
design a digital filter using bilinear transform with notch frequency 100 Hz and sampling rate
7. Given an analog IIR bandpass filter that has resonance at 1 radian/second with the transfer
design a digital resonant filter that resonates at 100 Hz with the sampling rate at 1 kHz.
8. Design a second-order digital Butterworth filter using bilinear transform. The cut-off
frequency is 1 kHz at a sampling frequency of 10 kHz.
9. Repeat the previous problem for designing a highpass filter with the same specifications.
10. Design a second-order digital Butterworth bandpass filter with the lower cut-off frequency
200 Hz, upper cut-off frequency 400 Hz, and sampling frequency 2000 Hz.
11. Design a second-order digital Butterworth bandstop filter that has the lower cut-off fre-
quency 200 Hz, upper cut-off frequency 400 Hz, and sampling frequency 2000 Hz.
12. Given the transfer function
À 1:1z 0:3
1:91z À 0:504
find the following realizations:
DESIGN AND IMPLEMENTATION OF IIR FILTERS