Audio Engineering

Representation of Audio Signals 465

(b)

 0.1 2 0 0.1 2 1.0 2 t

Figure 15.14(b) : The addition of two uncorrelated RPDF sequences gives rise to one with
triangular distribution (TPDF). When this dither signal is added to a digitized signal it will
always mark the output with some noise, as there is a fi nite possibility that the noise will
have a value greater than 0, so that as a digitized audio signal fades to zero value, the noise
background remains fairly constant. This behavior should be contrasted with that of RPDF
for which, when the signal fades to zero, there will come a point at which the accompanying
noise also switches off. This latter effect may be audible in some circumstances and is better
avoided. A wave form associated with this type of distribution will have values ranging from
 1.02 through 02 to  1.02.

Figure 15.14(c) : Noise in the analogue domain is often assumed to have a Gaussian

distribution. This can be understood as the likelihood of the waveform having a

particular amplitude. The probability of an amplitude x occurring can be expressed as

px() [( (e χμ σσπ)/2 ]/ 2^22

whereμ is the mean value, σ is the variance, and X is the

sum of the squares of the deviationsx from the mean. In practice, a “ random ” waveform,

which has a ratio between the peak to mean signal levels of 3, can be taken as being

suffi ciently Gaussian in character. The spectral balance of such a signal is a further factor

that must be taken into account if a full description of a random signal is to be described.

(c)

0

p (x)

x x