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Hartley transform

Index Hartley transform

In mathematics, the Hartley transform (HT) is an integral transform closely related to the Fourier transform (FT), but which transforms real-valued functions to real-valued functions. [1]

28 relations: Angular frequency, Cis (mathematics), Complex number, Convolution, Convolution theorem, Discrete Hartley transform, Even and odd functions, Fourier optics, Fourier transform, Function (mathematics), Imaginary unit, Integral transform, Involution (mathematics), Journal of the Optical Society of America, Linear map, List of Fourier-related transforms, Mathematics, McGraw-Hill Education, Orthogonal matrix, Oxford University Press, Proceedings of the IEEE, Ralph Hartley, Real number, Ronald N. Bracewell, Self-adjoint operator, Symmetric matrix, Trigonometry, Unitary operator.

Angular frequency

In physics, angular frequency ω (also referred to by the terms angular speed, radial frequency, circular frequency, orbital frequency, radian frequency, and pulsatance) is a scalar measure of rotation rate.

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Cis (mathematics)

is a less commonly used mathematical notation defined by, where is the cosine function, is the imaginary unit and is the sine.

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Complex number

A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.

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Convolution

In mathematics (and, in particular, functional analysis) convolution is a mathematical operation on two functions (f and g) to produce a third function, that is typically viewed as a modified version of one of the original functions, giving the integral of the pointwise multiplication of the two functions as a function of the amount that one of the original functions is translated.

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Convolution theorem

In mathematics, the convolution theorem states that under suitable conditions the Fourier transform of a convolution is the pointwise product of Fourier transforms.

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Discrete Hartley transform

A discrete Hartley transform (DHT) is a Fourier-related transform of discrete, periodic data similar to the discrete Fourier transform (DFT), with analogous applications in signal processing and related fields.

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Even and odd functions

In mathematics, even functions and odd functions are functions which satisfy particular symmetry relations, with respect to taking additive inverses.

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Fourier optics

Fourier optics is the study of classical optics using Fourier transforms (FTs), in which the wave is regarded as a superposition of plane waves that are not related to any identifiable sources; instead they are the natural modes of the propagation medium itself.

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Fourier transform

The Fourier transform (FT) decomposes a function of time (a signal) into the frequencies that make it up, in a way similar to how a musical chord can be expressed as the frequencies (or pitches) of its constituent notes.

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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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Imaginary unit

The imaginary unit or unit imaginary number is a solution to the quadratic equation.

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Integral transform

In mathematics, an integral transform maps an equation from its original domain into another domain where it might be manipulated and solved much more easily than in the original domain.

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Involution (mathematics)

In mathematics, an involution, or an involutory function, is a function that is its own inverse, for all in the domain of.

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Journal of the Optical Society of America

The Journal of the Optical Society of America is a peer-reviewed scientific journal of optics, published by The Optical Society.

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Linear map

In mathematics, a linear map (also called a linear mapping, linear transformation or, in some contexts, linear function) is a mapping between two modules (including vector spaces) that preserves (in the sense defined below) the operations of addition and scalar multiplication.

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List of Fourier-related transforms

This is a list of linear transformations of functions related to Fourier analysis.

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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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McGraw-Hill Education

McGraw-Hill Education (MHE) is a learning science company and one of the "big three" educational publishers that provides customized educational content, software, and services for pre-K through postgraduate education.

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Orthogonal matrix

In linear algebra, an orthogonal matrix is a square matrix whose columns and rows are orthogonal unit vectors (i.e., orthonormal vectors), i.e. where I is the identity matrix.

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Oxford University Press

Oxford University Press (OUP) is the largest university press in the world, and the second oldest after Cambridge University Press.

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Proceedings of the IEEE

The Proceedings of the IEEE is a monthly peer-reviewed scientific journal published by the Institute of Electrical and Electronics Engineers (IEEE).

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Ralph Hartley

Ralph Vinton Lyon Hartley (November 30, 1888 – May 1, 1970) was an electronics researcher.

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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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Ronald N. Bracewell

Ronald Newbold Bracewell AO (22 July 1921 – 12 August 2007) was the Lewis M. Terman Professor of Electrical Engineering of the Space, Telecommunications, and Radioscience Laboratory at Stanford University.

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Self-adjoint operator

In mathematics, a self-adjoint operator on a finite-dimensional complex vector space V with inner product \langle\cdot,\cdot\rangle is a linear map A (from V to itself) that is its own adjoint: \langle Av,w\rangle.

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Symmetric matrix

In linear algebra, a symmetric matrix is a square matrix that is equal to its transpose.

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Trigonometry

Trigonometry (from Greek trigōnon, "triangle" and metron, "measure") is a branch of mathematics that studies relationships involving lengths and angles of triangles.

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Unitary operator

In functional analysis, a branch of mathematics, a unitary operator is a surjective bounded operator on a Hilbert space preserving the inner product.

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CAS (mathematics), Cas (function), Cas (mathematics), Cas (symbol), Cas function, Cas(t), Cas(x), Cas(θ), Continuous Hartley Transform, Continuous Hartley transform, Cosine and sine, Cosine-and-sine, Hartley Transform, Hartley kernel, Optical Hartley Transform, Optical Hartley transform.

References

[1] https://en.wikipedia.org/wiki/Hartley_transform

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