Audio Engineering

Recording Consoles 801

an output sequence like that illustrated in the fi gure: that’s to say, an infi nitely
decaying series of values. Once again, so primordial is this characteristic that this
category of fi lter is termed an infi nite impulse response (IIR) fi lter.

IIR fi lters have both disadvantages and advantages over the FIR type. First, they are
very much more complicated to design because their impulse response is not simply
refl ected by the tap coeffi cients, as in the FIR. Second, it is in the nature of any
feedback system (like an analogue amplifi er) that some conditions may cause the
fi lter to become unstable if it is has not been thoroughly designed, simulated, and
tested. Furthermore, the inherent infi nite response may cause distortion and/or
rounding problems as calculations on smaller and smaller values of data are
performed. Indeed, it’s possible to draw a parallel between IIR fi lters and analogue
fi lter circuits: they share the disadvantages of complexity of design and possible
instability and distortion, but they also share the great benefi t that they are
effi cient. An IIR confi guration can be made to implement complex fi lter functions
with only a few stages, whereas the equivalent FIR fi lter would require many
hundreds of taps with all the drawbacks of cost and signal delay that this implies.
(Sometimes FIR and IIR fi lters are referred to as “ recursive ” and “ nonrecursive, ”
respectively; these terms directly refl ect the fi lter architecture.)

Design of Digital Filters

Digital fi lters are nearly always designed from knowledge of the required impulse
response. IIR and FIR fi lters are both designed in this way, although the design

In Out

Unit impulse Impulse response

z^1  1 sample delay

1/2 z^1



Figure F27.1 : Infi nite impulse response fi lter.