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# Digital signal (signal processing)

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 Title: Digital signal (signal processing) Author: World Heritage Encyclopedia Language: English Subject: Collection: Digital Signal Processing Publisher: World Heritage Encyclopedia Publication Date:

### Digital signal (signal processing)

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.[1] [2] [3] [4] [5]

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.[6]  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.

## References

1. ^ Smith, Steven W. (2002-11-06). "3". Digital Signal Processing: A Practical Guide for Engineers and Scientists. Demystifying Technology 1 (1 ed.).
2. ^ Harris, Frederic J. (2004-05-24). "1.1". Multirate Signal Processing for Communication Systems. Upper Saddle River, NJ: Prentice Hall PTR. p. 2.
3. ^ Vaseghi, Saeed V. (2009-03-02). "1.4". Advanced Digital Signal Processing and Noise Reduction (4 ed.). Chichester, West Suffix, United Kingdom: John Wiley & Sons. p. 23.
4. ^ Diniz, Paulo S. R.; Eduardo A. B. da Silva; Sergio L. Netto (2010-09-13). "1.1". Digital Signal Processing: System Analysis and Design (2 ed.). New York & UK: Cambridge University Press. p. 5.
5. ^ Manolakis, Dimitris G.; Vinay K. Ingle (2011-11-21). "1.1.1". Applied Digital Signal Processing: Theory and Practice. Cambridge, UK: Cambridge University Press. p. 5.
6. ^ Ingle, Vinay K.; John G. Proakis (2011-01-01). "1.1". Digital Signal Processing Using MATLAB (3 ed.). Stamford, CT: CL Engineering. p. 3.
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