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A signal of continuous amplitude and time is known as a continuous-time signal or an analog signal. This (a signal ) will have some value at every instant of time. The electrical signals derived in proportion with the physical quantities such as temperature, pressure, sound etc. are generally continuous signals.
The term discrete-time refers to the fact that the transform operates on discrete data, often samples whose interval has units of time. From uniformly spaced samples it produces a function of frequency that is a periodic summation of the continuous Fourier transform of the original continuous function.
A digital signal is a signal that represents data as a sequence of discrete values; at any given time it can only take on, at most, one of a finite number of values. [1] [2] [3] This contrasts with an analog signal, which represents continuous values; at any given time it represents a real number within a continuous range of values.
When the DFT is used for signal spectral analysis, the {} sequence usually represents a finite set of uniformly spaced time-samples of some signal (), where represents time. The conversion from continuous time to samples (discrete-time) changes the underlying Fourier transform of () into a discrete-time Fourier transform (DTFT), which generally ...
For example, the discrete-time Fourier transform and the Z-transform, from discrete time to continuous frequency, and the Fourier series, from continuous time to discrete frequency, are outside the class of discrete transforms. Classical signal processing deals with one-dimensional discrete transforms.
The Nyquist–Shannon sampling theorem is a theorem in the field of signal processing which serves as a fundamental bridge between continuous-time signals and discrete-time signals. It establishes a sufficient condition for a sample rate that permits a discrete sequence of samples to capture all the information from a continuous-time signal of ...
Discrete-time signal processing is for sampled signals, defined only at discrete points in time, and as such are quantized in time, but not in magnitude. Analog discrete-time signal processing is a technology based on electronic devices such as sample and hold circuits, analog time-division multiplexers , analog delay lines and analog feedback ...
Signals can be classified as continuous or discrete time. In the mathematical abstraction, the domain of a continuous-time signal is the set of real numbers (or some interval thereof), whereas the domain of a discrete-time (DT) signal is the set of integers (or other subsets of real numbers). What these integers represent depends on the nature ...