discrete and continuous systems

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Systems by which signals are recorded, communicated, or displayed may represent the data in discrete form (e.g. as integers) or in continuous form (as “real” numbers). An important classification results from the choice of discrete or continuous representation of the amplitude, and of discrete or continuous representation of the time at which the amplitude occurred. Analog computers employ physical quantities that are approximations to continuous representations. Discrete representations of both time and amplitude are required by digital computers.

The question of whether the signal (or its source) is intrinsically discrete or intrinsically continuous is unresolvable: any experiment to determine this would require infinite bandwidth (or infinite time) and infinite signal-to-noise ratio, and so would be impossible in practice. All that is in question is whether a discrete or continuous representation is more convenient, or useful, or appealing.

Signals that appear intuitively to be continuous-time or continuous-amplitude, but for which a discrete-time or discrete-amplitude representation is preferred, are said to have been time-quantized or amplitude-quantized. Time quantization is either adequate or inadequate according to Nyquist's criterion. Time-quantized signals are said to be sampled, and the systems that handle them are called sampled-data systems. Amplitude quantization worsens the signal-to-noise ratio, an effect describable as the introduction of quantization noise.

Time and amplitude must both be quantized for processing by digital computers (or by other digital devices), which operate at finite speeds on finite amounts of data held to finite precisions. The same physical constraints operate, although in a different way, to limit the extent to which analog computers (or other analog devices) can approximate to the continuous representation of signals.

See also quantization.

Subjects: Computing.

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