# Quantization

Digital signals are discrete-time signals. Computers and digital hardware can only handle lists of numbers, not signals defined over a continuum (except symbolically). In addition to being discrete in time (sampled), digital signals also have to be discrete in amplitude. The value of a sample cannot be an arbitrary real or complex number because digital hardware cannot represent arbitrary real or complex numbers.

A digital representation of a sample occupies some number *N*
of bits. On a CD, for example, *N* = 16. In the telephone
network, *N* = 8, although some fancy encoding is used to make
it seem like more than 8 bits are being devoted to the samples of the
signal.

An *N* bit number can represent one of 2^{N}
possible values. Thus, when a signal is converted for digital representation,
there is inevitably some error,
since not all possible values can be represented.
The following applet allows you to experiment with the number of
bits used to represent a voice signal.

The entry box at the right specifies the number of bits.
For small numbers here, notice how the number of levels of the
output is 2^{N}.
Also notice that speech remains intelligible down to 1 bit per sample,
despite the substantial error in the representation.
This suggests that there is very little linguistic information in the
amplitude of the samples.