7–34 Altera Corporation
Stratix Device Handbook, Volume 2 September 2004
Infinite Impulse Response (IIR) Filters
Infinite Impulse
Response (IIR)
Filters
Another class of digital filters are IIR filters. These are recursive filters
where the current output is dependent on previous outputs. In order to
maintain stability in an IIR filter, careful design consideration must be
given, especially to the effects of word-length to avoid unbounded
conditions. The following section discusses the general theory and
applications behind IIR Filters.
IIR Filter Background
The impulse response of an IIR filter extends for an infinite amount of
time because their output is based on feedback from previous outputs.
The general expression for IIR filters is:
where a
i
and b
i
represent the coefficients in the feed-forward path and
feedback path, respectively, and n represents the filter order. These
coefficients determine where the poles and zeros of the IIR filter lie.
Consequently, they also determine how the filter functions (i.e., cut-off
frequencies, band pass, low pass, etc.).
The feedback feature makes IIR filters useful in high data throughput
applications that require low hardware usage. However, feedback also
introduces complications and caution must be taken to make sure these
filters are not exposed to situations in which they may become unstable.
The complications include phase distortion and finite word length effects,
but these can be overcome by ensuring that the filter always operates
within its intended range.
Figure 7–20 shows a direct form II structure of an IIR filter.
yn() ai()xn i–()
i0=
∑
bi()yn i–()
i1=
∑
–=
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