Digital Signal Processing Reference
In-Depth Information
(a)
(b)
Sample rate fs=8 Hz
0.4
1.5
Digital
filter
Analog
filter
0.3
1
0.2
Aliasing
0.5
0.1
0
0
0
5
10
15
20
0
2
4
6
8
Time (sec.)
Frequency (Hz)
(c)
(d)
Sample rate fs=16 Hz
0.2
1.5
Analog
filter
Digital
filter
0.15
1
0.1
0.5
Aliasing
0.05
0
0
0
10
20
30
40
0
5
10
15
Time (sec.)
Frequency (Hz)
FIGURE 8.29
Sampling interval effect in the impulse invariant IIR filter design.
EXAMPLE 8.16
Consider the following Laplace transfer function:
s
s
2
þ 2s þ 5
a. Determine HðzÞ using the impulse-invariant method if the sampling rate f
s
¼ 10 Hz.
b. Use MATLAB to plot the following:
1. the magnitude response jHðf Þj and phase response fðf Þ with respect to HðsÞ for the frequency range from
0tof
s
=2 Hz;
HðsÞ¼
2. the magnitude response
Hðe
jU
Þ
¼jHðe
j2pfT
Þj and phase response fðf Þ with respect to HðzÞ for the
frequency range from 0 to f
s
=2 Hz.
Solution:
a. Since HðsÞ has complex poles located at s ¼1 2j, we can write it in a quadratic form as
s
s
2
þ 2s þ 5
¼
s
ðs þ 1Þ
2
þ2
2
HðsÞ¼
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