Discrete-time signal

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Discrete sampled signal
Digital signal

A discrete signal or discrete-time signal is a time series consisting of a sequence of quantities. In other words, it is a time series that is a function over a domain of integers.

Unlike a continuous-time signal, a discrete-time signal is not a function of a continuous argument; however, it may have been obtained by sampling from a continuous-time signal, and then each value in the sequence is called a sample. When a discrete-time signal obtained by sampling a sequence corresponding to uniformly spaced times, it has an associated sampling rate; the sampling rate is not apparent in the data sequence, and so needs to be associated as a characteristic unit of the system.


Discrete signals may have several origins, but can usually be classified into one of two groups:[1]

  • By acquiring values of an analog signal at constant or variable rate. This process is called sampling.[2]
  • By recording the number of events of a given kind over finite time periods. For example, this could be the number of people taking a certain elevator every day.

Digital signals[edit]

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.

A digital signal is a discrete-time signal for which not only the time but also the amplitude has been made discrete; 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.

The process of converting a continuous-valued discrete-time signal to a digital (discrete-valued discrete-time) signal is known as analog-to-digital conversion. It usually proceeds by replacing each original sample value by an approximation selected from a given discrete set (for example by truncating or rounding, but much more sophisticated methods exist), a process known as quantization. This process loses information, and so discrete-valued signals are only an approximation of the converted continuous-valued discrete-time signal, itself only an approximation of the original continuous-valued continuous-time signal.

Common practical digital signals are represented as 8-bit (256 levels), 16-bit (65,536 levels), 32-bit (4.3 billion levels), and so on, though any number of quantization levels is possible, not just powers of two.

See also[edit]


  1. ^ "Digital Signal Processing" Prentice Hall - Pages 11-12
  2. ^ "Digital Signal Processing: Instant access." Butterworth-Heinemann - Page 8

  • Gershenfeld, Neil A. (1999). The Nature of mathematical Modeling. Cambridge University Press. ISBN 0-521-57095-6. 
  • Wagner, Thomas Charles Gordon (1959). Analytical transients. Wiley.