Audio Engineering

Representation of Audio Signals 471

We have drawn examples of digital fi ltering without explicit reference to their use in
digital audio. The reason is that the principles of digital signal processing hold true no
matter what the origin or use of the signal being processed. The ready accessibility of
analogue audio “ cook-books ” and the simplicity of the signal structure have drawn a
number of less than structured practitioners into the fi eld. For whatever inaccessible
reason, these practitioners have given the audio engineer the peculiar notions of
directional copper cables, especially colored capacitors, and compact discs outlined with
green felt tip pens. Bless them all, they have their place as entertainment and they remain
free in their pursuit of the arts of the audio witch doctor. The world of digital processing

System

t

Vi V 0

t

Example

(a)

Figure 15.16(a) : An impulse is applied to a simple system whose output is a simple

exponential decaying response: VV

0  ietRC/

.

a 10 a0.5 (^1) a0.25 (^2) 0.125a (^3) 0.063a (^4) 0.03125a (^5)

Y(n)
X(n)
(b)
Figure 15.16(b) : A digital fi lter based on an FIR structure would need to be implemented
as shown. The accuracy of this fi lter depends on just how many stages of delay and
multiplication we can afford to use. For the fi ve stages shown, the fi lter will cease to emulate
an exponential decay after only 24 dB of decay. The response to successive n samples is
YXnn 1 (1/2)Xn12 3(1/4)Xn (1/8)Xn (1/6)Xn 4.