Chapt8 IIR Filter Design.ppt

Chapter 8 IIR Filter Design
Gao Xinbo
School of ., Xidian Univ.
Xbgao@
./teach/matlabdsp/
Introduction
IIR filter have infinite-duration impulse responses, hence they can be matched to analog filters, all of which generally have infinitely long impulse responses.
The basic technique of IIR filter design transforms well-known analog filters into digital filters plex-valued mappings.
The advantage of this technique lies in the fact that both analog filter design (AFD) tables and the mappings are available extensively in the literature.
Introduction
The basic technique is called the A/D filter transformation.
However, the AFD tables are available only for lowpass filters. We also want design other frequency-selective filters (highpass, bandpass, bandstop, etc.)
To do this, we need to apply frequency-band transformations to lowpass filters. These transformations are plex-valued mappings, and they are also available in the literature.
Two approaches
Approach 1, used in Matlab
Approach 2, study
IIR Filter Design Steps
Design analog lowpass filter
Study and apply filter transformations to obtain digital lowpass filter
Study and apply frequency-band transformations to obtain other digital filters from digital lowpass filter
The main problem
We have no control over the phase characteristics of the IIR filter.
Hence IIR filter designs will be treated as magnitude-only designs.
Main Content of This Chapter
Analog filter specifications and the properties of the magnitude-squared response used in specifying analog filters.
Characteristics of three widely used analog filters
Butterworth, Chebyshev, and Elliptic filter
Transformation to convert these prototype analog filters into different frequency-selective digital filter
Some Preliminaries
Relative linear scale
The lowpass filter specifications on the magnitude-squared response are given by
Where epsilon is a passband ripple parameter, Omega_p is the passband cutoff frequency in rad/sec, A i