Sampling

Abstract

Physical sources of signals such as speech, images, and all observable electrical waveforms are analog and continuous time in nature. The first step to convert signals to digital form is sampling. An analog continuously fluctuating waveform can usually be characterized completely from a knowledge of its amplitude values at a countable set of points in time so that we can in effect “throw away” the rest of the signal. We do not need to observe how it behaves in between any two isolated instances of observation. This is at the same time remarkable and intuitively obvious. It is remarkable that we can discard so much of the waveform and still be able to accurately recover the missing parts. The intuitive idea is that if we sample periodically at regularly spaced instants in time, and the signal does not fluctuate too quickly so that no unexpected wiggles can appear between two consecutive sampling instants, then we can expect to recover the complete waveform by a simple process of interpolation or smoothing, where a smooth curve is drawn that passes through the known amplitude values at the sampling instants.