Representation of Audio Signals 477
combined with the incoming logic signal. Feedback is usually arranged to come from
earlier stages as well as the fi nal output stage. The arrangement can be considered as
a form of binary division. For certain combinations of feedback the output of the shift
register can be considered as a statistically dependable source of random numbers. In the
simplest form the random output can be formed in the analogue domain by the simple
addition of a suitable low-pass fi lter. Such a random noise generator has the useful
property that the noise waveform is repeated, which allows the results of stimulating a
system with such a signal to be averaged.
When a sequence of samples with a nominally random distribution of values is correlated
with itself, the result is identical to a band-limited impulse ( Figure 15.19 ). If such a
random signal is used to stimulate a system (this could be an artifi cial reverberation
device, an equalizer, or a loudspeaker under test) and the resulting output is correlated
with the input sequence, the result will be the impulse response of the system under test.
The virtue of using a repeatable excitation noise is that measurements can be made in
the presence of other random background noise or interference, and if further accuracy
is required, the measurement is simply repeated and the results averaged. True random
R(t)
t
τ
Figure 15.19 : Correlation is a process in which one sequence of sample values is checked
against another to see just how similar both sequences are. A sinusoidal wave correlated
with itself (a process called auto correlation) will produce a similar sinusoidal wave. By
comparison, a sequence of random sample values will have an autocorrelation function
that will be zero everywhere except at the point where the samples are exactly in phase,
yielding a band-limited impulse.