Fourier analysis

mathematical transform that expresses a function of time as a function of frequency

the integral transform ∫₀^∞ d𝑠 𝑓(𝑡)⁢exp(−𝑠𝑡)

circle with radius one

function that repeats its values in regular intervals or periods

second order partial differential equation

pseudo-function δ such that an integral of δ(x-c)f(x) always takes the value of f(c)

thumb|400px|class=skin-invert-image|Visual comparison of convolution, cross-correlation, and [[autocorrelation. For the operations involving function f, and assuming the height of f is 1.0, the value of the result at 5 different points is indicated by the shaded area below each point. The symmetry of f is the reason f \star g and g*f are identical in this example. ]]

divergence of the gradient

families of solutions to related differential equations

branch of mathematics regarding periodic and continuous signals

technique representing data as sums of cosine functions

technique used in advanced mathematics

special function over the surface of a sphere

lowest frequency of a periodic waveform, such as sound

fourier transform of real-space lattices, important in solid-state physics

group that is a topological space with continuous group action

basis of a normed space consisting of mutually orthogonal elements of norm 1

relative importance of certain frequencies in a composite signal

theorem

Banach space of functions equipped with a norm that is a combination of Lᵖ-norms of the function itself and its weak derivatives up to a given order

discrete Fourier transform with short overlapping windows

particular kind of algebraic structure

type of infrared spectroscopy

function used in signal processing

duality for locally compact abelian groups

mathematical function

mathematical concept

change of basis applied in quantum computing

study of classical optics using Fourier transforms

problem of finding a function which solves a specified partial differential equation with prescribed boundary values

element of a basis for a function space

function space of all functions whose derivatives are rapidly decreasing

In probability theory and statistics, given a stochastic process, the autocovariance is a function that gives the covariance of the process with itself at pairs of time points. Autocovariance is closely related to the autocorrelation of the process in question.

Fourier analysis technique applied to sequences

function that "converges" to periodicity

variant Fourier transforms

spectroscopy based on time- or space-domain data

numerical analysis procedure

an integral transform closely related to the Fourier transform

signal (re-)construction algorithm

mathematical transform using in signal processing

Computation method named after Paul Peter Ewald

topological group with compact topology

linear transformation generalizing the Fourier transform, used in the area of harmonic analysis

particular representation of a signal

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technique of studying linear partial differential equations

generalization of Fourier transform to any ring

variant of the discrete Fourier transform

algorithm

an equation that relates the Fourier series coefficients of the periodic summation of a function to values of the function's continuous Fourier transform

Fourier-related mathematical transform

effect in signal processing

theorem

In signal processing, a periodogram is an estimate of the spectral density of a signal. The term was coined by Arthur Schuster in 1898. Today, the periodogram is a component of more sophisticated methods (see spectral estimation). It is the most common tool for examining the amplitude vs frequency characteristics of FIR filters and window functions. FFT spectrum analyzers are also implemented as a time-sequence of periodograms.

branch of analysis focusing on localisation not only with respect to location in the space, but also with respect to cotangent space directions at a given point under the Fourier transform

Method in signal processing

function gauging the uniform continuity of a function

discrete Fourier Transform expressed as a matrix