Faster access than browser!Similarities between Fourier series and Fourier transform
Fourier series and Fourier transform have 36 things in common (in Unionpedia): Almost everywhere, Closed-form expression, Compact space, Convolution, Dirac comb, Dirac delta function, Discrete Fourier transform, Discrete-time Fourier transform, Distribution (mathematics), Eigenfunction, Eigenvalues and eigenvectors, Euler's formula, Even and odd functions, Fast Fourier transform, Fourier inversion theorem, Function (mathematics), Harmonic analysis, Heat equation, Hertz, Hilbert space, Hyperbolic function, Integral, Joseph Fourier, Multidimensional transform, Orthonormality, Partial differential equation, Periodic function, Peter–Weyl theorem, Plancherel theorem, Quantum mechanics, ..., Riemann–Lebesgue lemma, Signal processing, Sine, Sine wave, Square-integrable function, Trigonometric functions. Expand index (6 more) »
Almost everywhere
In measure theory (a branch of mathematical analysis), a property holds almost everywhere if, in a technical sense, the set for which the property holds takes up nearly all possibilities.
Almost everywhere and Fourier series · Almost everywhere and Fourier transform ·
Closed-form expression
In mathematics, a closed-form expression is a mathematical expression that can be evaluated in a finite number of operations.
Closed-form expression and Fourier series · Closed-form expression and Fourier transform ·
Compact space
In mathematics, and more specifically in general topology, compactness is a property that generalizes the notion of a subset of Euclidean space being closed (that is, containing all its limit points) and bounded (that is, having all its points lie within some fixed distance of each other).
Compact space and Fourier series · Compact space and Fourier transform ·
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.
Convolution and Fourier series · Convolution and Fourier transform ·
Dirac comb
In mathematics, a Dirac comb (also known as an impulse train and sampling function in electrical engineering) is a periodic tempered distribution constructed from Dirac delta functions for some given period T. The symbol \operatorname(t), where the period is omitted, represents a Dirac comb of unit period.
Dirac comb and Fourier series · Dirac comb and Fourier transform ·
Dirac delta function
In mathematics, the Dirac delta function (function) is a generalized function or distribution introduced by the physicist Paul Dirac.
Dirac delta function and Fourier series · Dirac delta function and Fourier transform ·
Discrete Fourier transform
In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency.
Discrete Fourier transform and Fourier series · Discrete Fourier transform and Fourier transform ·
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.
Discrete-time Fourier transform and Fourier series · Discrete-time Fourier transform and Fourier transform ·
Distribution (mathematics)
Distributions (or generalized functions) are objects that generalize the classical notion of functions in mathematical analysis.
Distribution (mathematics) and Fourier series · Distribution (mathematics) and Fourier transform ·
Eigenfunction
In mathematics, an eigenfunction of a linear operator D defined on some function space is any non-zero function f in that space that, when acted upon by D, is only multiplied by some scaling factor called an eigenvalue.
Eigenfunction and Fourier series · Eigenfunction and Fourier transform ·
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.
Eigenvalues and eigenvectors and Fourier series · Eigenvalues and eigenvectors and Fourier transform ·
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.
Euler's formula and Fourier series · Euler's formula and Fourier transform ·
Even and odd functions
In mathematics, even functions and odd functions are functions which satisfy particular symmetry relations, with respect to taking additive inverses.
Even and odd functions and Fourier series · Even and odd functions and Fourier transform ·
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.
Fast Fourier transform and Fourier series · Fast Fourier transform and Fourier transform ·
Fourier inversion theorem
In mathematics, the Fourier inversion theorem says that for many types of functions it is possible to recover a function from its Fourier transform.
Fourier inversion theorem and Fourier series · Fourier inversion theorem and Fourier transform ·
Function (mathematics)
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
Fourier series and Function (mathematics) · Fourier transform and Function (mathematics) ·
Harmonic analysis
Harmonic analysis is a branch of mathematics concerned with the representation of functions or signals as the superposition of basic waves, and the study of and generalization of the notions of Fourier series and Fourier transforms (i.e. an extended form of Fourier analysis).
Fourier series and Harmonic analysis · Fourier transform and Harmonic analysis ·
Heat equation
The heat equation is a parabolic partial differential equation that describes the distribution of heat (or variation in temperature) in a given region over time.
Fourier series and Heat equation · Fourier transform and Heat equation ·
Hertz
The hertz (symbol: Hz) is the derived unit of frequency in the International System of Units (SI) and is defined as one cycle per second.
Fourier series and Hertz · Fourier transform and Hertz ·
Hilbert space
The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space.
Fourier series and Hilbert space · Fourier transform and Hilbert space ·
Hyperbolic function
In mathematics, hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions.
Fourier series and Hyperbolic function · Fourier transform and Hyperbolic function ·
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.
Fourier series and Integral · Fourier transform and Integral ·
Joseph Fourier
Jean-Baptiste Joseph Fourier (21 March 1768 – 16 May 1830) was a French mathematician and physicist born in Auxerre and best known for initiating the investigation of Fourier series and their applications to problems of heat transfer and vibrations.
Fourier series and Joseph Fourier · Fourier transform and Joseph Fourier ·
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.
Fourier series and Multidimensional transform · Fourier transform and Multidimensional transform ·
Orthonormality
In linear algebra, two vectors in an inner product space are orthonormal if they are orthogonal and unit vectors.
Fourier series and Orthonormality · Fourier transform and Orthonormality ·
Partial differential equation
In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives.
Fourier series and Partial differential equation · Fourier transform and Partial differential equation ·
Periodic function
In mathematics, a periodic function is a function that repeats its values in regular intervals or periods.
Fourier series and Periodic function · Fourier transform and Periodic function ·
Peter–Weyl theorem
In mathematics, the Peter–Weyl theorem is a basic result in the theory of harmonic analysis, applying to topological groups that are compact, but are not necessarily abelian.
Fourier series and Peter–Weyl theorem · Fourier transform and Peter–Weyl theorem ·
Plancherel theorem
In mathematics, the Plancherel theorem is a result in harmonic analysis, proven by Michel Plancherel in 1910.
Fourier series and Plancherel theorem · Fourier transform and Plancherel theorem ·
Quantum mechanics
Quantum mechanics (QM; also known as quantum physics, quantum theory, the wave mechanical model, or matrix mechanics), including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.
Fourier series and Quantum mechanics · Fourier transform and Quantum mechanics ·
Riemann–Lebesgue lemma
In mathematics, the Riemann–Lebesgue lemma, named after Bernhard Riemann and Henri Lebesgue, is of importance in harmonic analysis and asymptotic analysis.
Fourier series and Riemann–Lebesgue lemma · Fourier transform and Riemann–Lebesgue lemma ·
Signal processing
Signal processing concerns the analysis, synthesis, and modification of signals, which are broadly defined as functions conveying "information about the behavior or attributes of some phenomenon", such as sound, images, and biological measurements.
Fourier series and Signal processing · Fourier transform and Signal processing ·
Sine
In mathematics, the sine is a trigonometric function of an angle.
Fourier series and Sine · Fourier transform and Sine ·
Sine wave
A sine wave or sinusoid is a mathematical curve that describes a smooth periodic oscillation.
Fourier series and Sine wave · Fourier transform and Sine wave ·
Square-integrable function
In mathematics, a square-integrable function, also called a quadratically integrable function, is a real- or complex-valued measurable function for which the integral of the square of the absolute value is finite.
Fourier series and Square-integrable function · Fourier transform and Square-integrable function ·
Trigonometric functions
In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are functions of an angle.
Fourier series and Trigonometric functions · Fourier transform and Trigonometric functions ·
The list above answers the following questions
- What Fourier series and Fourier transform have in common
- What are the similarities between Fourier series and Fourier transform
Fourier series and Fourier transform Comparison
Fourier series has 129 relations, while Fourier transform has 248. As they have in common 36, the Jaccard index is 9.55% = 36 / (129 + 248).
References
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