What is sampling? What is a sampling rate?
Sampling can be (roughly) defined as the capture of a continuously varying quantity at a precisely defined instant in time. Most usually, signals are sampled at a set of sample-points spaced regularly in time. Note that sampling in itself implies nothing about the representation of sample magnitude by a number. That process is called quantisation. The Nyquist theorem states that in order to faithfully capture all of the information in a signal of one-sided bandwidth B, it must be sampled at a rate greater than 2B. A direct corollary of this is that if we wish to sample at a rate of 2B then we must pre-filter the signal to a one-sided bandwidth of B, otherwise it will not be possible to accurately reconstruct the original signal from the samples. The frequency 2B that is the minimum sample rate to retain all of the signal information is called the Nyquist frequency. The spectrum of the sampled signal is the same as the spectrum of the continuous signal except that copies (known as alias
