N(S) is named
the quantization error. A well designed quantizer should minminze this error
signal.
A quantizer is a function that applied to a digital signal produces other digital signal of
the same size, but where the number of possible sample values (representation levels) is
reduced. This process generates an irreversible loss of information in the signal. The
difference between the original samples Si and its quantized version N(S) is named
the quantization error. A well designed quantizer should minminze this error
signal.
When the quantization is scalar, this correspondence can be done using only an input sample for each output sample. A scalar quantizer with N representation levels is defined by
where
are the decision levels and where
is the quantization step size.