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A discrete frequency domain is a frequency domain that is discrete rather than continuous. For example, the discrete Fourier transform maps a function having a discrete time domain into one having a discrete frequency domain.
To contrast, a discrete-time signal has a countable domain, like the natural numbers. 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 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.
Time domain refers to the analysis of mathematical functions, physical signals or time series of economic or environmental data, with respect to time. In the time domain, the signal or function's value is known for all real numbers, for the case of continuous time, or at various separate instants in the case of discrete time.
Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continuous functions). Objects studied in discrete mathematics include integers, graphs, and statements in logic.
The domain of discourse is usually identified in the preliminaries, so that there is no need in the further treatment to specify each time the range of the relevant variables. [1] Many logicians distinguish, sometimes only tacitly, between the domain of a science and the universe of discourse of a formalization of the science. [2]
Dichotomization is the special case of discretization in which the number of discrete classes is 2, which can approximate a continuous variable as a binary variable (creating a dichotomy for modeling purposes, as in binary classification). Discretization is also related to discrete mathematics, and is an important component of granular computing.
Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous.In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic [1] – do not vary smoothly in this way, but have distinct, separated values. [2]