DigitalVideoAndHDTVAlgorithmsAndInterfaces.pdf

Compensation of undesired
phase response in a filter is
known as equalization. This is
unrelated to the equalization
pulses that form part of sync.
The terms nonrecursive and recursive
are best used to describe filter
implementation structures.
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In an IIR filter having just one tap, the designer’s ability
to tailor frequency response is severely limited. An IIR
filter can be extended by storing several previous filter
results, and adding (or subtracting) a fraction of each to
a fraction of the current input sample. In such a multitap
IIR filter, a fine degree of control can be exercised
over frequency response using just a handful of taps.
Just three or four taps in an IIR filter can achieve frequency
response that might take 20 taps in an FIR filter.
However, there’s a catch: In an IIR filter, both attenuation
and delay depend upon frequency. In the terminology
of the previous section, an IIR filter exhibits
nonlinear phase. Typically, low-frequency signals are
delayed more than high-frequency signals. As I have
explained, variation of delay as a function of frequency
is potentially a very serious problem in video.
An IIR filter cannot have exactly linear phase, although
a complex IIR filter can be designed to have arbitrarily
small phase error. Because IIR filters usually have poor
phase response, they are not ordinarily used in video.
(A notable exception is the use of field- and framebased
IIR filters in temporal noise reduction, where the
delay element comprises a field or frame of storage.)
Owing to the dependence of an IIR filter’s result upon
its previous results, an IIR filter is necessarily recursive.
However, certain recursive filters have finite impulse
response, so a recursive filter does not necessarily have
infinite impulse response.
CHAPTER 16 FILTERING AND SAMPLING 161
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Figure 16.22 IIR (“recursive”) filter computes a weighted
sum of input samples (here, just 1 ⁄ 4 times the current sample),
and adds to this a weighted sum of previous result samples.
Every IIR filter exhibits nonlinear phase response.