Digital signal (signal processing)

Last updated
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] The conversion process can be thought of as occurring in 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), 24-bit (16.8 million levels) and 32-bit (4.3 billion levels). But the number of quantization levels is not necessarily limited to powers of two. A floating point representation is used in many DSP applications.

References

  1. Smith, Steven W. (2002-11-06). "3". Digital Signal Processing: A Practical Guide for Engineers and Scientists. Demystifying Technology. 1 (1 ed.). Newnes. pp. 35–39. ISBN   075067444X.
  2. Harris, Frederic J. (2004-05-24). "1.1". Multirate Signal Processing for Communication Systems. Upper Saddle River, NJ: Prentice Hall PTR. p. 2. ISBN   0131465112.
  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. ISBN   0470754060.
  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. ISBN   0521887755.
  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. ISBN   0521110025.
  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. ISBN   1111427372.