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CHAPTER 6
Implementation
of Discrete-time
Filters
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 (or spectrum analyzers in some contexts). The filter
design issue is influenced by such factors as the type of the filter (i.e., IIR
or FIR) or the form of its implementation (structures). Hence, before we
discuss the design issue, we first concern ourselves with how these filters
can be implemented in practice. This is an important concern because
different filter structures dictate different design strategies.
IIR filters as designed and used in DSP, can be modeled by rational
system functions or, equivalently, by difference equations. Such filters are
termed autoregressive moving average (ARMA) or, more generally, as recursive
filters. Although ARMA filters include moving average filters that
are FIR filters, we will treat FIR filters separately from IIR filters for both
design and implementation purposes.
In addition to describing various filter structures, we also begin to consider
problems associated with quantization effects when finite-precision
arithmetic is used in the implementation. Digital hardware contains processing
elements that use finite-precision arithmetic. When filters are implemented
either in hardware or in software, filter coefficients as well as
filter operations are subjected to the effects of these finite-precision operations.
In this chapter, we treat the effects on filter frequency response
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