Principles of Digital Audio, Sixth Edition, 6th Edition

APPENDIXThe Sampling Theorem

Discrete time sampling is founded on the concept of a rectangular impulse of infinitesimal width. In practice, the width of a rectangular pulse is considered to be of finite width. Although data signals are often characterized by their time-domain properties, the transmission channel is usually best described by its frequency-domain properties. Specifically, it is important to know the bandwidth required for transmission of a sampled signal. The Fourier transform describes a time-domain function in the frequency domain. Given a single rectangular pulse of duration, the transformation of the pulse yields a sin(x)/x function.

This sin(x)/x function is composed of a fundamental cosine wave and its harmonics, its maximum ...