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The Hong Kong University of Science and Technology
Department of Electronic and Computer Engineering
ELEC 212 Chapter 7
IIR Filter Design Techniques
2
0910 Fall ELEC 212
IIR Filter Design Techniques
Introduction
±
The design of filters involves the following stages:
–T
h
e
specification
of the desired properties of the system
h
e
approximation
of the specifications using a causal discretetime system
h
e
realization
of the system
(
recall previous lecture
)
±
These steps are certainly not independent
±
We focus primarily on the
second step
– First step largely depends on specific application
– Third step largely depends on specific technology used for implementation
±
Specifications for both the discretetime filter and the effective continuous
time filter are typically given in the
frequency domain
– This is especially common for frequencyselective filters such as lowpass,
bandpass and highpass filters
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0910 Fall ELEC 212
IIR Filter Design Techniques
Design Specification
±
Specifications are given in frequencydomain in terms of the
desired
magnitude and phase responses
of the filter
±
The phase specification of the filter is constrained by the stable and
causal properties
±
Specifications:
– Sampling rate of the system
– Passband frequency
– Stopband frequency
– Transition band (width)
– Passband ripple
– Stopband ripple
– Stopband attenuation (gain)
±
Usually measured in
dB
Objective:
design a system function of a
discretetime system which has frequency
response falling within tolerances and
meeting cutoff frequency specifications.
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0910 Fall ELEC 212
IIR Filter Design Techniques
DiscreteTime IIR Filter Design
±
Common method
for IIR filter design:
Transform a continuoustime filter into a
discretetime filter meeting prescribed specifications
–
I.e., map
s
plane to
z
plane to obtain desired IIR filter
±
Alternative method
:
Directly design IIR digital filter in
z
plane
–
I.e., select poles and zeros in
z
plane directly, and adjust their locations according to
prescribed specifications iteratively to approach the response
±
We will focus on designing discretetime IIR filters based on continuous
time filters
.
Why:
1.
Continuoustime IIR filter design is
highly advanced
. It is advantageous to use the design
procedures already developed for continuoustime filters
2.
Many useful continuoustime IIR design methods have relatively
simple closedform
design formulas
. Therefore, discretetime IIR filter design methods based on such
standard continuoustime filter design formulas are rather simple to carry out
3.
Standard approximation methods that work well for continuoustime IIR filters
do not
lead to simple closedform design formulas
when these methods are applied directly to
the discretetime IIR case
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0910 Fall ELEC 212
IIR Filter Design Techniques
Conversion from ContinuousTime Filters to
DiscreteTime IIR Filters
±
To convert from continuoustime prototype filter to discretetime IIR filter,
we
must obtain
H(z)
from
H
a
(s)
±
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This note was uploaded on 03/27/2011 for the course ELEC 212 taught by Professor Prof.matthewmckay during the Spring '11 term at HKUST.
 Spring '11
 Prof.MatthewMcKay
 Digital Signal Processing, Signal Processing

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