SAMPLING: THE BRIDGE FROM [CONTINUOUS TO](#page-13-0) DISCRETE

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SAMPLING: THE BRIDGE FROM CONTINUOUS TO DISCRETE

A continuous-time signal can be processed by applying its samples through a discrete-time system. For this purpose, it is important to maintain the signal sampling rate high enough to permit the reconstruction of the original signal from these samples without error (or with an error within a given tolerance). The necessary quantitative framework for this purpose is provided by the sampling theorem derived in Sec. 8.1.

Sampling theory is the bridge between the continuous-time and discrete-time worlds. The information inherent in a sampled continuous-time signal is equivalent to that of a discrete-time signal. A sampled continuous-time signal is a sequence of impulses, while a discrete-time signal presents the same information as a sequence of numbers. These are basically two different ways of presenting the same data. Clearly, all the concepts in the analysis of sampled signals apply to discrete-time signals. We should not be surprised to see that the Fourier spectra of the two kinds of signal are also the same (within a multiplicative constant).