Digital Audio Technology, 4th Edition

2 Principles of sampling

The Nyquist theorem

By definition, an analog signal varies continuously with time. To enable it to be converted into a digital signal, it is necessary that the signal is first sampled, i.e., at certain points in time a sample of the input value must be taken (Figure 2.1). The fixed time intervals between each sample are called sampling intervals (t_s).

Although the sampling operation may seem to introduce a rather drastic modification of the input signal (as it ignores all the signal changes that occur between the sampling times), it can be shown that the sampling process in principle removes no information whatsoever, as long as the sampling frequency is at least present in the input signal. This is the famous Nyquist ...