Chapt6 Digital Filter Structures.ppt

Chapter 6. Digital Filter Structures
Gao Xinbo
School of ., Xidian Univ.
xbgao@
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./teach/matlabdsp/
Introduction
In earlier chapters we studied the theory of discrete systems in both the time and frequency domains.
We will now use this theory for the processing of digital signals.
To process signals, we have to design and implement systems called filters.
The filter design issue is influenced by such factors as
The type of the filter: IIR or FIR
The form of its implementation: structures
Different filter structures dictate different design strategies.
Introduction
IIR filters are characterized by infinite-duration impulse response. Some of these impulse responses can be modeled by
Rational system functions
Difference equations
ARMA or recursive filters
We will treat FIR filter separately from IIR filters for both design and implementation purposes.
Introduction
Since our filters are LTI systems, we need the following three elements to describe digital filter structures.
Adder
Multiplier (Gain)
Delay element (shift or memory)
IIR Filter Structures
The system function of an IIR filter is given by
The order of such an IIR filter is called N if aN~=0.
The difference equation representation of an IIR filter is expressed as
Three different structures can be used to implement an IIR filter:
Direct form
In this form, there are two parts to this filter, the moving average part and the recursive part (or the numerator and denominator parts)
Two version: direct form I and direct form II
Cascade form
The system function H(z) is factored into smaller second-order sections, called biquads. H(z) is then represented as a product of these biquads.
Each biquad is implemented in a direct form, and the entire system function is implemented as a cascade of biquad sections.
Parallel form
H(z) is represented as a sum of smaller second-order sections.
Each section is again implemented in a direct form.
The entire system function is impl