linear quantization

analog signal

digital signal

quantization levels

quantum interval

quantization error

quantization noise

white noise

means of signals that are functions of a discrete variable and having a codomain

described by a continuous variable. Actually, the internal arithmetic of comput-

ing systems imposes a signal quantization, which can produce various kinds of

effects on the output sounds.

signal into a digital signal. If the word representing numerical data is b bits long,

the range of variation of the analog signal can be divided into 2

to the closest level. The processes of sampling and quantization are illustrated

in fig. 4 for a wordlength of 3 bits. The minimal amplitude difference that can

be represented is called the quantum interval and we indicate it with the symbol

q. We can notice from fig. 4 that, due to two's complement representation, the

representation levels for negative amplitude exceed by one the levels used for

positive amplitude. It is also evident from fig. 4 how quantization introduces an

tion is called quantization error and can be expressed as

noise can be considered as a noise superimposed to the unquantized signal. This

noise takes values in the range

2

2

signal.

variables and processes. We rather refer to signal processing books [58, 67, 65]

for a more accurate exposition.

trum) with values uniformly distributed in the interval (42), and that there is

no correlation between the noise and the unquantized signal. This assumption is

false in general but, nevertheless, it leads to results which are good estimates of