Digital signal (signal processing)

This article was created from material in Digital signal, in anticipation of converting that article into a disambiguation page. See Talk:Digital signal#Two topics.

Digital signal (red) is the sampled and rounded representation of the grey analog signal

A digital signal (red) that is produced by sampling may be considered discrete in time as well as by value, and is equivalent to a series of numbers, 4,5,4,3,4,6, etc.

In the context of Digital signal processing (DSP), a digital signal is a discrete-time signal for which not only the time but also the amplitude has discrete values; in other words, its samples take on only values from a discrete set (a countable set that can be mapped one-to-one to a subset of integers). If that discrete set is finite, the discrete values can be represented with digital words of a finite width. Most commonly, these discrete values are represented as fixed-point words (either proportional to the waveform values or companded) or floating-point words.

File:Discrete cosine.svg

Discrete cosine waveform with frequency of 50 Hz and a sampling rate of 1000 samples/sec, easily satisfying the sampling theorem for reconstruction of the original cosine function from samples.

The process of analog-to-digital conversion produces a digital signal.  It can be thought of as two steps: (1) sampling, which produces a continuous-valued discrete-time signal, and (2) quantization, which replaces each sample value by an approximation selected from a given discrete set (for example by truncating or rounding). It can be shown that for signal frequencies strictly below the Nyquist limit that the original continuous-valued continuous-time signal can be almost perfectly reconstructed, down to the (often very low) limit set by the quantisation.

Common practical digital signals are represented as 8-bit (256 levels), 16-bit (65,536 levels), 32-bit (4.3 billion levels). But the number of quantization levels is not limited to powers of two.