Audio Engineering

472 Chapter 15

requires more rigor in its approach and practice. Figure 15.17 shows examples of simple
forms of fi rst- and second-order fi lter structures. Processing an audio signal in the digital
domain can provide a fl exibility that analogue processing denies. You may notice from the
examples how readily the characteristics of a fi lter can be changed simply by adjustment
of the coeffi cients used in the multiplication process. The equivalent analogue process
would require much switching and component matching. Moreover, each digital fi lter or
process will provide exactly the same performance for a given set of coeffi cient values,
which is a far cry from the miasma of tolerance problems that beset the analogue designer.

The complicated actions of digital audio equalization are an obvious candidate for
implementation using infi nite impulse response fi lters and the fi eld has been heavily
researched in recent years. Much research has been directed toward overcoming some
of the practical problems, such as limited arithmetic resolution or precision and limited
processing time. Practical hardware considerations force the resulting precision of any
digital arithmetic operation to be limited. The limited precision also affects the choice of

 Singledelay

X(n)

a 0 0.5

Y(n)

(c)

Figure 15.16(c) : This simple function can be emulated by using a single multiplier and adder

element if some of the output signal is fed back and subtracted from the input. Use of a

multiplier in conjunction with an adder is often referred to as a multiplier-accumulator or

MAC. With the correct choice of coeffi cient in the feedback path, the exponential decay

response can be exactly emulated: YXnnn0.5Y 1. This form of fi lter will continue to

produce a response forever unless the arithmetic elements are no longer able to handle the

decreasing size of the numbers involved. For this reason, it is known as an infi nite impulse

response (IIR) fi lter or, because of the feedback structure, a recursive fi lter. Whereas the

response characteristics of FIR fi lters can be gleaned comparatively easily by inspecting the

values of the coeffi cients used, the same is not true of IIR fi lters. A more complex algebra is

needed in order to help in the design and analysis, which are not covered here.