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Not only do we have analog signals --- signals that are real- or complex-valued functions of a continuous variable such as timeor space --- we can define digital ones as well. Digital signals are sequences , functions defined only for the integers. We thus use the notation s n to denote a discrete-time one-dimensional signal such as a digital musicrecording and s m n for a discrete-"time" two-dimensional signal like a photo taken with a digital camera. Sequences are fundamentallydifferent than continuous-time signals. For example, continuity has no meaning for sequences.

Despite such fundamental differences, the theory underlying digital signal processing mirrors that for analog signals:Fourier transforms, linear filtering, and linear systems parallel what previous chapters described. These similaritiesmake it easy to understand the definitions and why we need them, but the similarities should not be construed as "analogwannabes." We will discover that digital signal processing is not an approximation to analog processing. We must explicitly worry about the fidelity of converting analogsignals into digital ones. The music stored on CDs, the speech sent over digital cellular telephones, and the video carried bydigital television all evidence that analog signals can be accurately converted to digital ones and back again.

The key reason why digital signal processing systems have a technological advantage today is the computer : computations, like the Fourier transform, can be performed quicklyenough to be calculated as the signal is produced,

Taking a systems viewpoint for the moment, a system that produces its output as rapidly as the input arises is said tobe a real-time system. All analog systems operate in real time; digital ones that depend on acomputer to perform system computations may or may not work in real time. Clearly, we need real-time signal processingsystems. Only recently have computers become fast enough to meet real-time requirements while performing non-trivialsignal processing.
and programmability means that the signal processing system can be easily changed. This flexibility has obvious appeal, andhas been widely accepted in the marketplace. Programmability means that we can perform signal processing operationsimpossible with analog systems (circuits). We will also discover that digital systems enjoy an algorithmic advantage that contributes to rapid processing speeds: Computations can be restructured innon-obvious ways to speed the processing. This flexibility comes at a price, a consequence of how computers work. How docomputers perform signal processing?

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Source:  OpenStax, Fundamentals of electrical engineering i. OpenStax CNX. Aug 06, 2008 Download for free at http://legacy.cnx.org/content/col10040/1.9
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