Digital Signal Processing Reference
In-Depth Information
Chapter 6
Infinite Impulse Response Digital Filter
Design
There are a variety of methods that can be used to design digital filters as we will
see in this chapter and the next. One commonly used method is to use the analog
filter approximation functions that have already been developed and simply
translate them in a way that will make them usable for discrete-time systems. This
method, which will be studied in this chapter, makes use of the large backlog of
filter design theory and tables of transfer functions that are readily available. Most
of the filters designed using this method will be recursive in nature. That is, the
output of the filter will depend on previous values of the output (as well as past
and current values of the input). These types of filters can theoretically have
impulse responses that continue forever and therefore are commonly referred to as
infinite impulse response (IIR) filters.
Another method of designing discrete-time filters will be discussed in the next
chapter. That method does not depend on analog filter theory, but rather uses the
frequency response of the desired filter to directly determine the digital filter
coefficients. The method generally yields nonrecursive filters that have outputs
depending only on past and current values of the input. These types of filters
generally have an impulse response containing only a finite number of values and
thus are commonly called finite impulse response (FIR) filters. As we are about to
see, both the IIR and FIR design methods will differ from the analog filter design
techniques studied in the first part of the text. (A more complete comparison of
IIR and FIR filters will be given in Section 8.1.)
In the first three sections of this chapter, we will investigate different methods
of translating an analog filter's characteristics into those of a digital filter. As we
will see, there is no perfect digital equivalent to an analog filter at all frequencies;
however, we can develop filters that closely match the important filter
characteristics. In the final section of this chapter, we will develop the C code
necessary to evaluate the frequency response characteristics of IIR digital filters.
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