Faster access than browser!
151 relations: Acronym, Alan V. Oppenheim, Aliasing, Arithmetic–geometric mean, Atan2, Bandlimiting, Bartlett's method, Binomial theorem, Carl Friedrich Gauss, Characteristic polynomial, Charles E. Leiserson, Chirp Z-transform, Circulant matrix, Cis (mathematics), Class function (algebra), Clifford Stein, Commutative property, Companion matrix, Complex conjugate, Complex number, Composite number, Computer, Convolution, Convolution theorem, Cooley–Tukey FFT algorithm, Coordinate vector, Cross-correlation, Cyclic group, Defective matrix, Determinant, DFT matrix, Digital electronics, Digital image processing, Digital signal processing, Dimension (vector space), Direct current, Dirichlet kernel, Discrete cosine transform, Discrete Fourier transform (general), Discrete Hartley transform, Discrete sine transform, Discrete transform, Discrete wavelet transform, Discrete-time Fourier transform, Discretization, Eigenvalues and eigenvectors, Entropic uncertainty, Entropy (information theory), Euler's formula, Fast Fourier transform, ..., FFTPACK, FFTW, Field (mathematics), Finite field, Finite Fourier transform, Finite group, Fourier analysis, Fourier series, Fourier transform, Fourier transform on finite groups, Fractional Fourier transform, Frequency, Frequency domain, Function (mathematics), Function composition, Gaussian function, Generalizations of Pauli matrices, Geometric progression, Geometric series, Hermite polynomials, Identity matrix, Integer, Introduction to Algorithms, Inverse trigonometric functions, Involution (mathematics), James Cooley, JPEG, JPEG 2000, Kravchuk polynomials, Kronecker delta, Linear differential equation, Linear independence, Linear map, List of Fourier-related transforms, Lossy compression, Matched filter, Mathematics, Matrix (mathematics), Matrix polynomial, Modified discrete cosine transform, Modular arithmetic, Multidimensional transform, Multiplication algorithm, Normal distribution, Numerical analysis, Nyquist frequency, Nyquist rate, Orthogonal basis, Orthogonality, Orthonormal basis, Orthonormality, Overlap–add method, Overlap–save method, Parity (mathematics), Parseval's theorem, Partial differential equation, Periodic sequence, Periodic summation, Periodogram, Pixel, Plancherel theorem, Plane wave, Pointer (computer programming), Probability mass function, Quantum Fourier transform, Rader's FFT algorithm, Radio, Raster graphics, Real number, Representation theory, Representation theory of finite groups, Ron Rivest, Ronald W. Schafer, Root of unity, Sampling (signal processing), Sequence, Sign convention, Signal, Sinc function, Sine wave, Sound, Spectral density estimation, Spectral leakage, Spectral method, Spectrogram, Temperature, Theta function, Time–frequency analysis, Trigonometric interpolation, Uncertainty principle, Unitary matrix, Unitary operator, Unitary transformation, Vandermonde matrix, Variance, Wavelet, Wavelet transform, Welch's method, Window function, Z-transform, Zak transform. Expand index (101 more) »
Acronym
An acronym is a word or name formed as an abbreviation from the initial components in a phrase or a word, usually individual letters (as in NATO or laser) and sometimes syllables (as in Benelux).
New!!: Discrete Fourier transform and Acronym · See more »
Alan V. Oppenheim
Alan Victor Oppenheim as a member of National Academy of Engineering in Electronics, Communication & Information Systems Engineering and Computer Science & Engineering for innovative research, writing of pioneering textbooks, and inspired teaching in the field of digital signal processing.
New!!: Discrete Fourier transform and Alan V. Oppenheim · See more »
Aliasing
In signal processing and related disciplines, aliasing is an effect that causes different signals to become indistinguishable (or aliases of one another) when sampled.
New!!: Discrete Fourier transform and Aliasing · See more »
Arithmetic–geometric mean
In mathematics, the arithmetic–geometric mean (AGM) of two positive real numbers and is defined as follows: Call and and: \end Then define the two interdependent sequences and as \end where the square root takes the principal value.
New!!: Discrete Fourier transform and Arithmetic–geometric mean · See more »
Atan2
The function \operatorname (y,x) or \operatorname (y,x) is defined as the angle in the Euclidean plane, given in rad, between the positive x-axis and the ray to the Points in the upper half-plane deliver values in points with.
New!!: Discrete Fourier transform and Atan2 · See more »
Bandlimiting
Bandlimiting is the limiting of a signal's frequency domain representation or spectral density to zero above a certain finite frequency.
New!!: Discrete Fourier transform and Bandlimiting · See more »
Bartlett's method
In time series analysis, Bartlett's method (also known as the method of averaged periodograms), is used for estimating power spectra.
New!!: Discrete Fourier transform and Bartlett's method · See more »
Binomial theorem
In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.
New!!: Discrete Fourier transform and Binomial theorem · See more »
Carl Friedrich Gauss
Johann Carl Friedrich Gauss (Gauß; Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields, including algebra, analysis, astronomy, differential geometry, electrostatics, geodesy, geophysics, magnetic fields, matrix theory, mechanics, number theory, optics and statistics.
New!!: Discrete Fourier transform and Carl Friedrich Gauss · See more »
Characteristic polynomial
In linear algebra, the characteristic polynomial of a square matrix is a polynomial which is invariant under matrix similarity and has the eigenvalues as roots.
New!!: Discrete Fourier transform and Characteristic polynomial · See more »
Charles E. Leiserson
Charles Eric Leiserson is a computer scientist, specializing in the theory of parallel computing and distributed computing, and particularly practical applications thereof.
New!!: Discrete Fourier transform and Charles E. Leiserson · See more »
Chirp Z-transform
The Chirp Z-transform (CZT) is a generalization of the discrete Fourier transform.
New!!: Discrete Fourier transform and Chirp Z-transform · See more »
Circulant matrix
In linear algebra, a circulant matrix is a special kind of Toeplitz matrix where each row vector is rotated one element to the right relative to the preceding row vector.
New!!: Discrete Fourier transform and Circulant matrix · See more »
Cis (mathematics)
is a less commonly used mathematical notation defined by, where is the cosine function, is the imaginary unit and is the sine.
New!!: Discrete Fourier transform and Cis (mathematics) · See more »
Class function (algebra)
In mathematics, especially in the fields of group theory and representation theory of groups, a class function is a function on a group G that is constant on the conjugacy classes of G. In other words, it is invariant under the conjugation map on G.
New!!: Discrete Fourier transform and Class function (algebra) · See more »
Clifford Stein
Clifford Seth Stein (born December 14, 1965), a computer scientist, is a professor of industrial engineering and operations research at Columbia University in New York, NY, where he also holds an appointment in the Department of Computer Science.
New!!: Discrete Fourier transform and Clifford Stein · See more »
Commutative property
In mathematics, a binary operation is commutative if changing the order of the operands does not change the result.
New!!: Discrete Fourier transform and Commutative property · See more »
Companion matrix
In linear algebra, the Frobenius companion matrix of the monic polynomial p(t).
New!!: Discrete Fourier transform and Companion matrix · See more »
Complex conjugate
In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign.
New!!: Discrete Fourier transform and Complex conjugate · See more »
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.
New!!: Discrete Fourier transform and Complex number · See more »
Composite number
A composite number is a positive integer that can be formed by multiplying together two smaller positive integers.
New!!: Discrete Fourier transform and Composite number · See more »
Computer
A computer is a device that can be instructed to carry out sequences of arithmetic or logical operations automatically via computer programming.
New!!: Discrete Fourier transform and Computer · See more »
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.
New!!: Discrete Fourier transform and Convolution · See more »
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.
New!!: Discrete Fourier transform and Convolution theorem · See more »
Cooley–Tukey FFT algorithm
The Cooley–Tukey algorithm, named after J. W. Cooley and John Tukey, is the most common fast Fourier transform (FFT) algorithm.
New!!: Discrete Fourier transform and Cooley–Tukey FFT algorithm · See more »
Coordinate vector
In linear algebra, a coordinate vector is a representation of a vector as an ordered list of numbers that describes the vector in terms of a particular ordered basis.
New!!: Discrete Fourier transform and Coordinate vector · See more »
Cross-correlation
In signal processing, cross-correlation is a measure of similarity of two series as a function of the displacement of one relative to the other.
New!!: Discrete Fourier transform and Cross-correlation · See more »
Cyclic group
In algebra, a cyclic group or monogenous group is a group that is generated by a single element.
New!!: Discrete Fourier transform and Cyclic group · See more »
Defective matrix
In linear algebra, a defective matrix is a square matrix that does not have a complete basis of eigenvectors, and is therefore not diagonalizable.
New!!: Discrete Fourier transform and Defective matrix · See more »
Determinant
In linear algebra, the determinant is a value that can be computed from the elements of a square matrix.
New!!: Discrete Fourier transform and Determinant · See more »
DFT matrix
In applied mathematics, a DFT matrix is an expression of a discrete Fourier transform (DFT) as a transformation matrix, which can be applied to a signal through matrix multiplication.
New!!: Discrete Fourier transform and DFT matrix · See more »
Digital electronics
Digital electronics or digital (electronic) circuits are electronics that operate on digital signals.
New!!: Discrete Fourier transform and Digital electronics · See more »
Digital image processing
In computer science, Digital image processing is the use of computer algorithms to perform image processing on digital images.
New!!: Discrete Fourier transform and Digital image processing · See more »
Digital signal processing
Digital signal processing (DSP) is the use of digital processing, such as by computers or more specialized digital signal processors, to perform a wide variety of signal processing operations.
New!!: Discrete Fourier transform and Digital signal processing · See more »
Dimension (vector space)
In mathematics, the dimension of a vector space V is the cardinality (i.e. the number of vectors) of a basis of V over its base field.
New!!: Discrete Fourier transform and Dimension (vector space) · See more »
Direct current
Direct current (DC) is the unidirectional flow of electric charge.
New!!: Discrete Fourier transform and Direct current · See more »
Dirichlet kernel
In mathematical analysis, the Dirichlet kernel is the collection of functions e^.
New!!: Discrete Fourier transform and Dirichlet kernel · See more »
Discrete cosine transform
A discrete cosine transform (DCT) expresses a finite sequence of data points in terms of a sum of cosine functions oscillating at different frequencies.
New!!: Discrete Fourier transform and Discrete cosine transform · See more »
Discrete Fourier transform (general)
In mathematics, the discrete Fourier transform over an arbitrary ring generalizes the discrete Fourier transform of a function whose values are complex numbers.
New!!: Discrete Fourier transform and Discrete Fourier transform (general) · See more »
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.
New!!: Discrete Fourier transform and Discrete Hartley transform · See more »
Discrete sine transform
In mathematics, the discrete sine transform (DST) is a Fourier-related transform similar to the discrete Fourier transform (DFT), but using a purely real matrix.
New!!: Discrete Fourier transform and Discrete sine transform · See more »
Discrete transform
In signal processing, discrete transforms are mathematical transforms, often linear transforms, of signals between discrete domains, such as between discrete time and discrete frequency.
New!!: Discrete Fourier transform and Discrete transform · See more »
Discrete wavelet transform
In numerical analysis and functional analysis, a discrete wavelet transform (DWT) is any wavelet transform for which the wavelets are discretely sampled.
New!!: Discrete Fourier transform and Discrete wavelet transform · See more »
Discrete-time Fourier transform
In mathematics, the discrete-time Fourier transform (DTFT) is a form of Fourier analysis that is applicable to the uniformly-spaced samples of a continuous function.
New!!: Discrete Fourier transform and Discrete-time Fourier transform · See more »
Discretization
In mathematics, discretization is the process of transferring continuous functions, models, variables, and equations into discrete counterparts.
New!!: Discrete Fourier transform and Discretization · See more »
Eigenvalues and eigenvectors
In linear algebra, an eigenvector or characteristic vector of a linear transformation is a non-zero vector that changes by only a scalar factor when that linear transformation is applied to it.
New!!: Discrete Fourier transform and Eigenvalues and eigenvectors · See more »
Entropic uncertainty
In quantum mechanics, information theory, and Fourier analysis, the entropic uncertainty or Hirschman uncertainty is defined as the sum of the temporal and spectral Shannon entropies.
New!!: Discrete Fourier transform and Entropic uncertainty · See more »
Entropy (information theory)
Information entropy is the average rate at which information is produced by a stochastic source of data.
New!!: Discrete Fourier transform and Entropy (information theory) · See more »
Euler's formula
Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function.
New!!: Discrete Fourier transform and Euler's formula · See more »
Fast Fourier transform
A fast Fourier transform (FFT) is an algorithm that samples a signal over a period of time (or space) and divides it into its frequency components.
New!!: Discrete Fourier transform and Fast Fourier transform · See more »
FFTPACK
FFTPACK is a package of Fortran subroutines for the fast Fourier transform.
New!!: Discrete Fourier transform and FFTPACK · See more »
FFTW
The Fastest Fourier Transform in the West (FFTW) is a software library for computing discrete Fourier transforms (DFTs) developed by Matteo Frigo and Steven G. Johnson at the Massachusetts Institute of Technology.
New!!: Discrete Fourier transform and FFTW · See more »
Field (mathematics)
In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined, and behave as when they are applied to rational and real numbers.
New!!: Discrete Fourier transform and Field (mathematics) · See more »
Finite field
In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements.
New!!: Discrete Fourier transform and Finite field · See more »
Finite Fourier transform
In mathematics the finite Fourier transform may refer to either.
New!!: Discrete Fourier transform and Finite Fourier transform · See more »
Finite group
In abstract algebra, a finite group is a mathematical group with a finite number of elements.
New!!: Discrete Fourier transform and Finite group · See more »
Fourier analysis
In mathematics, Fourier analysis is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions.
New!!: Discrete Fourier transform and Fourier analysis · See more »
Fourier series
In mathematics, a Fourier series is a way to represent a function as the sum of simple sine waves.
New!!: Discrete Fourier transform and Fourier series · See more »
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.
New!!: Discrete Fourier transform and Fourier transform · See more »
Fourier transform on finite groups
In mathematics, the Fourier transform on finite groups is a generalization of the discrete Fourier transform from cyclic to arbitrary finite groups.
New!!: Discrete Fourier transform and Fourier transform on finite groups · See more »
Fractional Fourier transform
In mathematics, in the area of harmonic analysis, the fractional Fourier transform (FRFT) is a family of linear transformations generalizing the Fourier transform.
New!!: Discrete Fourier transform and Fractional Fourier transform · See more »
Frequency
Frequency is the number of occurrences of a repeating event per unit of time.
New!!: Discrete Fourier transform and Frequency · See more »
Frequency domain
In electronics, control systems engineering, and statistics, the frequency domain refers to the analysis of mathematical functions or signals with respect to frequency, rather than time.
New!!: Discrete Fourier transform and Frequency domain · See more »
Function (mathematics)
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
New!!: Discrete Fourier transform and Function (mathematics) · See more »
Function composition
In mathematics, function composition is the pointwise application of one function to the result of another to produce a third function.
New!!: Discrete Fourier transform and Function composition · See more »
Gaussian function
In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the form: for arbitrary real constants, and.
New!!: Discrete Fourier transform and Gaussian function · See more »
Generalizations of Pauli matrices
In mathematics and physics, in particular quantum information, the term generalized Pauli matrices refers to families of matrices which generalize the (linear algebraic) properties of the Pauli matrices.
New!!: Discrete Fourier transform and Generalizations of Pauli matrices · See more »
Geometric progression
In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
New!!: Discrete Fourier transform and Geometric progression · See more »
Geometric series
In mathematics, a geometric series is a series with a constant ratio between successive terms.
New!!: Discrete Fourier transform and Geometric series · See more »
Hermite polynomials
In mathematics, the Hermite polynomials are a classical orthogonal polynomial sequence.
New!!: Discrete Fourier transform and Hermite polynomials · See more »
Identity matrix
In linear algebra, the identity matrix, or sometimes ambiguously called a unit matrix, of size n is the n × n square matrix with ones on the main diagonal and zeros elsewhere.
New!!: Discrete Fourier transform and Identity matrix · See more »
Integer
An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").
New!!: Discrete Fourier transform and Integer · See more »
Introduction to Algorithms
Introduction to Algorithms is a book by Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein.
New!!: Discrete Fourier transform and Introduction to Algorithms · See more »
Inverse trigonometric functions
In mathematics, the inverse trigonometric functions (occasionally also called arcus functions, antitrigonometric functions or cyclometric functions) are the inverse functions of the trigonometric functions (with suitably restricted domains).
New!!: Discrete Fourier transform and Inverse trigonometric functions · See more »
Involution (mathematics)
In mathematics, an involution, or an involutory function, is a function that is its own inverse, for all in the domain of.
New!!: Discrete Fourier transform and Involution (mathematics) · See more »
James Cooley
James William Cooley (born 1926, died June 29, 2016) was an American mathematician.
New!!: Discrete Fourier transform and James Cooley · See more »
JPEG
JPEG is a commonly used method of lossy compression for digital images, particularly for those images produced by digital photography.
New!!: Discrete Fourier transform and JPEG · See more »
JPEG 2000
JPEG 2000 (JP2) is an image compression standard and coding system.
New!!: Discrete Fourier transform and JPEG 2000 · See more »
Kravchuk polynomials
Kravchuk polynomials or Krawtchouk polynomials (also written using several other transliterations of the Ukrainian name "Кравчу́к") are discrete orthogonal polynomials associated with the binomial distribution, introduced by.
New!!: Discrete Fourier transform and Kravchuk polynomials · See more »
Kronecker delta
In mathematics, the Kronecker delta (named after Leopold Kronecker) is a function of two variables, usually just non-negative integers.
New!!: Discrete Fourier transform and Kronecker delta · See more »
Linear differential equation
In mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where,..., and are arbitrary differentiable functions that do not need to be linear, and are the successive derivatives of an unknown function of the variable.
New!!: Discrete Fourier transform and Linear differential equation · See more »
Linear independence
In the theory of vector spaces, a set of vectors is said to be if one of the vectors in the set can be defined as a linear combination of the others; if no vector in the set can be written in this way, then the vectors are said to be.
New!!: Discrete Fourier transform and Linear independence · See more »
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.
New!!: Discrete Fourier transform and Linear map · See more »
List of Fourier-related transforms
This is a list of linear transformations of functions related to Fourier analysis.
New!!: Discrete Fourier transform and List of Fourier-related transforms · See more »
Lossy compression
In information technology, lossy compression or irreversible compression is the class of data encoding methods that uses inexact approximations and partial data discarding to represent the content.
New!!: Discrete Fourier transform and Lossy compression · See more »
Matched filter
In signal processing, a matched filter is obtained by correlating a known signal, or template, with an unknown signal to detect the presence of the template in the unknown signal.
New!!: Discrete Fourier transform and Matched filter · See more »
Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
New!!: Discrete Fourier transform and Mathematics · See more »
Matrix (mathematics)
In mathematics, a matrix (plural: matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.
New!!: Discrete Fourier transform and Matrix (mathematics) · See more »
Matrix polynomial
In mathematics, a matrix polynomial is a polynomial with square matrices as variables.
New!!: Discrete Fourier transform and Matrix polynomial · See more »
Modified discrete cosine transform
The modified discrete cosine transform (MDCT) is a lapped transform based on the type-IV discrete cosine transform (DCT-IV), with the additional property of being lapped: it is designed to be performed on consecutive blocks of a larger dataset, where subsequent blocks are overlapped so that the last half of one block coincides with the first half of the next block.
New!!: Discrete Fourier transform and Modified discrete cosine transform · See more »
Modular arithmetic
In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value—the modulus (plural moduli).
New!!: Discrete Fourier transform and Modular arithmetic · See more »
Multidimensional transform
In mathematical analysis and applications, multidimensional transforms are used to analyze the frequency content of signals in a domain of two or more dimensions.
New!!: Discrete Fourier transform and Multidimensional transform · See more »
Multiplication algorithm
A multiplication algorithm is an algorithm (or method) to multiply two numbers.
New!!: Discrete Fourier transform and Multiplication algorithm · See more »
Normal distribution
In probability theory, the normal (or Gaussian or Gauss or Laplace–Gauss) distribution is a very common continuous probability distribution.
New!!: Discrete Fourier transform and Normal distribution · See more »
Numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics).
New!!: Discrete Fourier transform and Numerical analysis · See more »
Nyquist frequency
The Nyquist frequency, named after electronic engineer Harry Nyquist, is half of the sampling rate of a discrete signal processing system.
New!!: Discrete Fourier transform and Nyquist frequency · See more »
Nyquist rate
In signal processing, the Nyquist rate, named after Harry Nyquist, is twice the bandwidth of a bandlimited function or a bandlimited channel.
New!!: Discrete Fourier transform and Nyquist rate · See more »
Orthogonal basis
In mathematics, particularly linear algebra, an orthogonal basis for an inner product space is a basis for whose vectors are mutually orthogonal.
New!!: Discrete Fourier transform and Orthogonal basis · See more »
Orthogonality
In mathematics, orthogonality is the generalization of the notion of perpendicularity to the linear algebra of bilinear forms.
New!!: Discrete Fourier transform and Orthogonality · See more »
Orthonormal basis
In mathematics, particularly linear algebra, an orthonormal basis for an inner product space V with finite dimension is a basis for V whose vectors are orthonormal, that is, they are all unit vectors and orthogonal to each other.
New!!: Discrete Fourier transform and Orthonormal basis · See more »
Orthonormality
In linear algebra, two vectors in an inner product space are orthonormal if they are orthogonal and unit vectors.
New!!: Discrete Fourier transform and Orthonormality · See more »
Overlap–add method
In signal processing, the overlap–add method (OA, OLA) is an efficient way to evaluate the discrete convolution of a very long signal x with a finite impulse response (FIR) filter h: \begin y.
New!!: Discrete Fourier transform and Overlap–add method · See more »
Overlap–save method
Overlap–save is the traditional name for an efficient way to evaluate the discrete convolution between a very long signal x and a finite impulse response (FIR) filter h: where h.
New!!: Discrete Fourier transform and Overlap–save method · See more »
Parity (mathematics)
In mathematics, parity is the property of an integer's inclusion in one of two categories: even or odd.
New!!: Discrete Fourier transform and Parity (mathematics) · See more »
Parseval's theorem
In mathematics, Parseval's theorem usually refers to the result that the Fourier transform is unitary; loosely, that the sum (or integral) of the square of a function is equal to the sum (or integral) of the square of its transform.
New!!: Discrete Fourier transform and Parseval's theorem · See more »
Partial differential equation
In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives.
New!!: Discrete Fourier transform and Partial differential equation · See more »
Periodic sequence
In mathematics, a periodic sequence (sometimes called a cycle) is a sequence for which the same terms are repeated over and over: The number p of repeated terms is called the period (period).
New!!: Discrete Fourier transform and Periodic sequence · See more »
Periodic summation
In signal processing, any periodic function, s_P(t) with period P, can be represented by a summation of an infinite number of instances of an aperiodic function, s(t), that are offset by integer multiples of P. This representation is called periodic summation: When s_P(t) is alternatively represented as a complex Fourier series, the Fourier coefficients are proportional to the values (or "samples") of the continuous Fourier transform, S(f) \ \stackrel \ \mathcal\, at intervals of 1/P.
New!!: Discrete Fourier transform and Periodic summation · See more »
Periodogram
In signal processing, a periodogram is an estimate of the spectral density of a signal. The term was coined by Arthur Schuster in 1898.
New!!: Discrete Fourier transform and Periodogram · See more »
Pixel
In digital imaging, a pixel, pel, dots, or picture element is a physical point in a raster image, or the smallest addressable element in an all points addressable display device; so it is the smallest controllable element of a picture represented on the screen.
New!!: Discrete Fourier transform and Pixel · See more »
Plancherel theorem
In mathematics, the Plancherel theorem is a result in harmonic analysis, proven by Michel Plancherel in 1910.
New!!: Discrete Fourier transform and Plancherel theorem · See more »
Plane wave
In the physics of wave propagation, a plane wave (also spelled planewave) is a wave whose wavefronts (surfaces of constant phase) are infinite parallel planes.
New!!: Discrete Fourier transform and Plane wave · See more »
Pointer (computer programming)
In computer science, a pointer is a programming language object that stores the memory address of another value located in computer memory.
New!!: Discrete Fourier transform and Pointer (computer programming) · See more »
Probability mass function
In probability and statistics, a probability mass function (pmf) is a function that gives the probability that a discrete random variable is exactly equal to some value.
New!!: Discrete Fourier transform and Probability mass function · See more »
Quantum Fourier transform
In quantum computing, the quantum Fourier transform (for short: QFT) is a linear transformation on quantum bits, and is the quantum analogue of the discrete Fourier transform.
New!!: Discrete Fourier transform and Quantum Fourier transform · See more »
Rader's FFT algorithm
Rader's algorithm (1968), named for Charles M. Rader of MIT Lincoln Laboratory, is a fast Fourier transform (FFT) algorithm that computes the discrete Fourier transform (DFT) of prime sizes by re-expressing the DFT as a cyclic convolution (the other algorithm for FFTs of prime sizes, Bluestein's algorithm, also works by rewriting the DFT as a convolution).
New!!: Discrete Fourier transform and Rader's FFT algorithm · See more »
Radio
Radio is the technology of using radio waves to carry information, such as sound, by systematically modulating properties of electromagnetic energy waves transmitted through space, such as their amplitude, frequency, phase, or pulse width.
New!!: Discrete Fourier transform and Radio · See more »
Raster graphics
In computer graphics, a raster graphics or bitmap image is a dot matrix data structure that represents a generally rectangular grid of pixels (points of color), viewable via a monitor, paper, or other display medium.
New!!: Discrete Fourier transform and Raster graphics · See more »
Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
New!!: Discrete Fourier transform and Real number · See more »
Representation theory
Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures.
New!!: Discrete Fourier transform and Representation theory · See more »
Representation theory of finite groups
The representation theory of groups is a part of mathematics which examines how groups act on given structures.
New!!: Discrete Fourier transform and Representation theory of finite groups · See more »
Ron Rivest
Ronald Linn Rivest (born May 6, 1947) is a cryptographer and an Institute Professor at MIT.
New!!: Discrete Fourier transform and Ron Rivest · See more »
Ronald W. Schafer
Ronald W. Schafer (born February 17, 1938) is an electrical engineer notable for his contributions to digital signal processing.
New!!: Discrete Fourier transform and Ronald W. Schafer · See more »
Root of unity
In mathematics, a root of unity, occasionally called a de Moivre number, is any complex number that gives 1 when raised to some positive integer power.
New!!: Discrete Fourier transform and Root of unity · See more »
Sampling (signal processing)
In signal processing, sampling is the reduction of a continuous-time signal to a discrete-time signal.
New!!: Discrete Fourier transform and Sampling (signal processing) · See more »
Sequence
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed.
New!!: Discrete Fourier transform and Sequence · See more »
Sign convention
In physics, a sign convention is a choice of the physical significance of signs (plus or minus) for a set of quantities, in a case where the choice of sign is arbitrary.
New!!: Discrete Fourier transform and Sign convention · See more »
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".
New!!: Discrete Fourier transform and Signal · See more »
Sinc function
In mathematics, physics and engineering, the cardinal sine function or sinc function, denoted by, has two slightly different definitions.
New!!: Discrete Fourier transform and Sinc function · See more »
Sine wave
A sine wave or sinusoid is a mathematical curve that describes a smooth periodic oscillation.
New!!: Discrete Fourier transform and Sine wave · See more »
Sound
In physics, sound is a vibration that typically propagates as an audible wave of pressure, through a transmission medium such as a gas, liquid or solid.
New!!: Discrete Fourier transform and Sound · See more »
Spectral density estimation
In statistical signal processing, the goal of spectral density estimation (SDE) is to estimate the spectral density (also known as the power spectral density) of a random signal from a sequence of time samples of the signal.
New!!: Discrete Fourier transform and Spectral density estimation · See more »
Spectral leakage
The Fourier transform of a function of time, s(t), is a complex-valued function of frequency, S(f), often referred to as a frequency spectrum.
New!!: Discrete Fourier transform and Spectral leakage · See more »
Spectral method
Spectral methods are a class of techniques used in applied mathematics and scientific computing to numerically solve certain differential equations, potentially involving the use of the Fast Fourier Transform.
New!!: Discrete Fourier transform and Spectral method · See more »
Spectrogram
A spectrogram is a visual representation of the spectrum of frequencies of sound or other signal as they vary with time.
New!!: Discrete Fourier transform and Spectrogram · See more »
Temperature
Temperature is a physical quantity expressing hot and cold.
New!!: Discrete Fourier transform and Temperature · See more »
Theta function
In mathematics, theta functions are special functions of several complex variables.
New!!: Discrete Fourier transform and Theta function · See more »
Time–frequency analysis
In signal processing, time–frequency analysis comprises those techniques that study a signal in both the time and frequency domains simultaneously, using various time–frequency representations.
New!!: Discrete Fourier transform and Time–frequency analysis · See more »
Trigonometric interpolation
In mathematics, trigonometric interpolation is interpolation with trigonometric polynomials.
New!!: Discrete Fourier transform and Trigonometric interpolation · See more »
Uncertainty principle
In quantum mechanics, the uncertainty principle (also known as Heisenberg's uncertainty principle) is any of a variety of mathematical inequalities asserting a fundamental limit to the precision with which certain pairs of physical properties of a particle, known as complementary variables, such as position x and momentum p, can be known.
New!!: Discrete Fourier transform and Uncertainty principle · See more »
Unitary matrix
In mathematics, a complex square matrix is unitary if its conjugate transpose is also its inverse—that is, if where is the identity matrix.
New!!: Discrete Fourier transform and Unitary matrix · See more »
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.
New!!: Discrete Fourier transform and Unitary operator · See more »
Unitary transformation
In mathematics, a unitary transformation is a transformation that preserves the inner product: the inner product of two vectors before the transformation is equal to their inner product after the transformation.
New!!: Discrete Fourier transform and Unitary transformation · See more »
Vandermonde matrix
In linear algebra, a Vandermonde matrix, named after Alexandre-Théophile Vandermonde, is a matrix with the terms of a geometric progression in each row, i.e., an m × n matrix 1 & \alpha_1 & \alpha_1^2 & \dots & \alpha_1^\\ 1 & \alpha_2 & \alpha_2^2 & \dots & \alpha_2^\\ 1 & \alpha_3 & \alpha_3^2 & \dots & \alpha_3^\\ \vdots & \vdots & \vdots & \ddots &\vdots \\ 1 & \alpha_m & \alpha_m^2 & \dots & \alpha_m^ \end, or for all indices i and j. (Some authors use the transpose of the above matrix.) The determinant of a square Vandermonde matrix (where m.
New!!: Discrete Fourier transform and Vandermonde matrix · See more »
Variance
In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its mean.
New!!: Discrete Fourier transform and Variance · See more »
Wavelet
A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases, and then decreases back to zero.
New!!: Discrete Fourier transform and Wavelet · See more »
Wavelet transform
In mathematics, a wavelet series is a representation of a square-integrable (real- or complex-valued) function by a certain orthonormal series generated by a wavelet.
New!!: Discrete Fourier transform and Wavelet transform · See more »
Welch's method
In physics, engineering, and applied mathematics, Welch's method, named after P.D. Welch, is used for estimating the power of a signal at different frequencies: that is, it is an approach to spectral density estimation.
New!!: Discrete Fourier transform and Welch's method · See more »
Window function
In signal processing, a window function (also known as an apodization function or tapering function) is a mathematical function that is zero-valued outside of some chosen interval.
New!!: Discrete Fourier transform and Window function · See more »
Z-transform
In mathematics and signal processing, the Z-transform converts a discrete-time signal, which is a sequence of real or complex numbers, into a complex frequency domain representation.
New!!: Discrete Fourier transform and Z-transform · See more »
Zak transform
In mathematics, the Zak transform is a certain operation which takes as input a function of one variable and produces as output a function of two variables.
New!!: Discrete Fourier transform and Zak transform · See more »
Redirects here:
Centered DFT, Circular convolution theorem, Cross-correlation theorem, DTFS, Discrete Fourier Transform, Discrete fourier transform, Generalized discrete Fourier transform, Inverse discrete Fourier transform, Offset DFT, Shifted DFT.
References
[1] https://en.wikipedia.org/wiki/Discrete_Fourier_transform
