Audio Engineering

Representation of Audio Signals 467

as high a precision as possible for as long as possible. Each time that the audio signal has
its precision reduced it inevitably must become noisier.

15.8 Digital Filtering .....................................................................................................

Although it may be clear that the multiplication process controls the signal level, it is not
immediately obvious that the multiplicative process is intrinsic to any form of fi ltering.
Thus multipliers are at the heart of any signifi cant digital signal processing, and modern
digital signal processing would not be possible without the availability of suitable IC
technology. You will need to accept, at this stage, that the process of representing an
analogue audio signal in the form of a sequence of numbers is readily achieved and
thus we are free to consider how the equivalent analogue processes of fi ltering and
equalization may be carried out on the digitized form of the signal.

In fact, the processes required to perform digital fi ltering are performed daily by many
people without giving the process much thought. Consider the waveform of the tidal
height curve of Figure 15.15. The crude method by which we obtained this curve ( Figure
15.1 ) contained only an approximate method for removing the effect of ripples in the
water by including a simple dashpot linked to the recording mechanism. If we were
to look at this trace more closely we would see that it was not perfectly smooth due to
local effects such as passing boats and wind-driven waves. Of course tidal heights do not
normally increase by 100 mm within a few seconds and so it is sensible to draw a line
that passes through the average of these disturbances. This averaging process is fi ltering
and, in this case, it is an example of low-pass fi ltering. To achieve this numerically we
could measure the height indicated by the tidal plot each minute and calculate the average
height for each 4-min span (and this involves measuring the height at fi ve time points):

hh

t

t

average



1 

5

4

τ

τ

τ

∑.

Done simply, this would result in a stepped curve that still lacks the smoothness of a
simple line. We could reduce the stepped appearance by using a moving average in which
we calculate the average height in a 4-min span but we move the reference time forward
by a single minute each time we perform the calculation. The inclusion of each of the
height samples was made without weighting their contribution to the average and this
is an example of rectangular windowing. We could go one step further by weighting the