Discrete-time 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 discrete integers. Each value in the sequence is called a sample.
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. When a discrete-time signal is a sequence corresponding to uniformly spaced times, it has an associated sampling rate; the sampling rate is not apparent in the data sequence, so may be associated as a separate data item.
Acquisition
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 accumulating a variable over time. For example, the number of people taking a certain elevator every day.
Digital signals
A digital signal is a discrete-time signal that takes on only a discrete set of values.
The process of converting a continuous-valued discrete-time signal to a digital (discrete-valued discrete-time) signal is known as quantization. This process, also known as analog-to-digital conversion, loses information (by truncating or rounding the sample values). That is, discrete-valued signals are always an approximation to the original continuous-valued 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
- Aliasing
- Anti-aliasing filter
- Digital-to-analog converter
- Digital control
- Digital frequency
- Nyquist–Shannon sampling theorem
- Whittaker–Shannon interpolation formula
- Sample (signal)
- Sampling (signal processing)
References
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