Signals and Systems in Biomedical Engineering pp 67-100 | Cite as

# Discrete Time Signals and Systems

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## Abstract

All the signals considered so far are *continuous-time* signals in the sense that they are defined for every possible value of time; in other words a function *x*(*t*)is defined for all real values of time. However, in order to subject signals to numerical analysis we must have finite lists of numbers, which can be obtained by *sampling* the continuous-time signal at a finite number of points in time. This means that the value of *x*(*t*) at discrete points in time is obtained. The resulting *discrete-time* signal, *x*[*n*], can be stored as a sequence of numbers in a computer and analyzed. In order to store *x*[*n*]as a sequence of numbers a finite resolution of representation must necessarily be chosen; this is the process of *quantization.* In practice sampling as well as quantization is done by electronic *analogue-to-digital* converter circuits. The two main considerations in analogue to digital (A/D) conversion are (i) the rate of data collection or the sampling frequency, and (ii) the resolution of data representation or quantization. During the theoretical analysis of discrete-time signals it is convenient to separate the issues of sampling and quantization. Since the effects of sampling are usually more critical we will primarily deal with the sampled signal, *x*[*n*], assuming that the effects of quantization are absent. Quantization, which on a digital computer depends on the number of digital bits used to represent the numbers, will be discussed briefly; but for most physiological signals it is found that 8 bits, 12 bits or 16 bits of data resolution is adequate for representing the signals.

## Keywords

Impulse Response Sinusoidal Signal Random Signal Clock Pulse Discrete Time Signal## Preview

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## References

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