VLSI implementation of digital signal processing algorithms requires
fixed-point arithmetic for the sake of cost and speed. It
is necessary to use the fewest number of bits possible to carry
each signal in the systems. However, if the number of bits is too
small, quantization noise will degrade the system performance to an
unacceptable level. Much research has been conducted for optimizing
the signal word-length of time-invariant digital filters using analytical,
time-domain, or frequency-domain analysis