You are a Neuroengineer interested in developing better A$/$D convertors for biomedical sensors$,$ hearing

aids, and neural signal processing systems. A$/$D conversion involves quantization, the process by which

continuous amplitudes of a signal are digitized. Quantization involves reducing the number of possible

signal amplitudes to a finite # a computer can store. Signal amplitudes are sampled and stored as binary

numbers. The resolution of the A$/$D conversion is determined by the # of available bits, typically, $8,12,$

$16,24$ or $36$ bits. The greater the # of bits available, the greater the resolution. For example, for

auditory, sound wave applications, the quality of the sound improves with the # of bits used by a signal

processor.

Assume that:

a$)$ A quantizer, or A$/$D converter with N bits, can represent $2$N possible signal amplitude values

b$)$ The resolution of an A$/$D convertor can be determined as: Signal Input Range divided by the #

of signal amplitude values that can be represented by the A$/$D converter

c$)$ To accurately represent a signal, the signal needs to be quantized, or digitized by an A$/$D

converter at a sampling rate of at least twice the frequency of the signal