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27 relations: Algebra over a field, Boxcar function, Constant function, Crenel function, Disjoint sets, Dynamical system (definition), Finite set, Floor and ceiling functions, Function (mathematics), Heaviside step function, Indicator function, Integral, Interval (mathematics), Lebesgue integration, Linear combination, Mathematics, Piecewise, Piecewise linear function, Real number, Rectangular function, Sigmoid function, Sign function, Signal, Simple function, Step detection, Step response, Union (set theory).
Algebra over a field
In mathematics, an algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product.
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Boxcar function
In mathematics, a boxcar function is any function which is zero over the entire real line except for a single interval where it is equal to a constant, A. The boxcar function can be expressed in terms of the uniform distribution as where f(a,b;x) is the uniform distribution of x for the interval and H(x) is the Heaviside step function.
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Constant function
In mathematics, a constant function is a function whose (output) value is the same for every input value.
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Crenel function
In mathematics, the crenel function is a periodic discontinuous function P(x) defined as 1 for x belonging to a given interval and 0 outside of it.
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Disjoint sets
In mathematics, two sets are said to be disjoint sets if they have no element in common.
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Dynamical system (definition)
The dynamical system concept is a mathematical formalization for any fixed "rule" which describes the time dependence of a point's position in its ambient space.
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Finite set
In mathematics, a finite set is a set that has a finite number of elements.
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Floor and ceiling functions
In mathematics and computer science, the floor function is the function that takes as input a real number x and gives as output the greatest integer less than or equal to x, denoted \operatorname(x).
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Function (mathematics)
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
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Heaviside step function
The Heaviside step function, or the unit step function, usually denoted by or (but sometimes, or), is a discontinuous function named after Oliver Heaviside (1850–1925), whose value is zero for negative argument and one for positive argument.
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Indicator function
In mathematics, an indicator function or a characteristic function is a function defined on a set X that indicates membership of an element in a subset A of X, having the value 1 for all elements of A and the value 0 for all elements of X not in A. It is usually denoted by a symbol 1 or I, sometimes in boldface or blackboard boldface, with a subscript specifying the subset.
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Integral
In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.
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Interval (mathematics)
In mathematics, a (real) interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set.
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Lebesgue integration
In mathematics, the integral of a non-negative function of a single variable can be regarded, in the simplest case, as the area between the graph of that function and the -axis.
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Linear combination
In mathematics, a linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of x and y would be any expression of the form ax + by, where a and b are constants).
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Piecewise
In mathematics, a piecewise-defined function (also called a piecewise function or a hybrid function) is a function defined by multiple sub-functions, each sub-function applying to a certain interval of the main function's domain, a sub-domain.
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Piecewise linear function
In mathematics, a piecewise linear function is a real-valued function defined on the real numbers or a segment thereof, whose graph is composed of straight-line sections.
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Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
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Rectangular function
The rectangular function (also known as the rectangle function, rect function, Pi function, gate function, unit pulse, or the normalized boxcar function) is defined as: 0 & \mbox |t| > \frac \\ \frac & \mbox |t|.
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Sigmoid function
A sigmoid function is a mathematical function having a characteristic "S"-shaped curve or sigmoid curve.
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Sign function
In mathematics, the sign function or signum function (from signum, Latin for "sign") is an odd mathematical function that extracts the sign of a real number.
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Signal
A signal as referred to in communication systems, signal processing, and electrical engineering is a function that "conveys information about the behavior or attributes of some phenomenon".
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Simple function
In the mathematical field of real analysis, a simple function is a real-valued function over a subset of the real line, similar to a step function.
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Step detection
In statistics and signal processing, step detection (also known as step smoothing, step filtering, shift detection, jump detection or edge detection) is the process of finding abrupt changes (steps, jumps, shifts) in the mean level of a time series or signal.
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Step response
The step response of a system in a given initial state consists of the time evolution of its outputs when its control inputs are Heaviside step functions.
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Union (set theory)
In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection.
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Piecewise constant, Piecewise constant function, Piecewise-constant, Stair function, Staircase function.
References
[1] https://en.wikipedia.org/wiki/Step_function
