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Everything about Convolution theorem
Theorem in mathematics
In mathematics, the convolution theorem states that under suitable conditions the Fourier transform of a convolution of two functions is the product of their Fourier transforms. More generally, convolution in one domain equals point-wise multiplication in the other domain. Other versions of the convolution theorem are applicable to various Fourier-related transforms. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Convolution theoremA 5-minute orientation
- Skim a recent paper: Convolution Theorem Associated with the QWFRFTInfluential work since 2022
- Pick up a classic book: Limit theorems for convolutionsThe most-reprinted book on the subject
- Read the landmark paper: Application of the Convolution Theorem to Rayleigh’s Integral FormulasCited 108 times
- Go sideways: Discrete-time Fourier transformA closely related topic
- Go sideways: ConvolutionA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
Application of the Convolution Theorem to Rayleigh’s Integral Formulas
A matrix theory proof of the discrete convolution theorem
Generalized convolution theorem associated with fractional Fourier transform
The convolution theorem for the continuous wavelet tranform
The Central Limit Theorem for Free Additive Convolution
A General Geometric Fourier Transform Convolution Theorem
Applications of a Convolution Theorem to Jacobi Polynomials
Non-parametric applications of an infinite dimensional convolution theorem
🆕 Influential since 2022
Convolution Theorem Associated with the QWFRFT
The Convolution Theorem Involving Windowed Free Metaplectic Transform
Quantum multiplication algorithm based on the convolution theorem
Holographic Lens Resolution Using the Convolution Theorem
Convolution theorem for the windowed linear canonical transform
📚 Books worth reading
- 📕Limit theorems for convolutionsHarald Bergström · 1963
- 📕The remainder in Wiener's Tauberian theoremTord H. Ganelius · 1962
- 📕Probabilistic and analytical aspects of the umbral calculusAlessandro Di Bucchianico · 1997
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Discrete-time Fourier transform In mathematics, the discrete-time Fourier transform (DTFT) is a form of Fourier analysis that is applicable to a sequence of discrete values. The DTFT…
- Convolution In mathematics (in particular, functional analysis), convolution is a mathematical operation on two functions f and g that produces a third function f∗g…
- Hilbert transform In mathematics and signal processing, the Hilbert transform is a specific singular integral that takes a function, u(t) of a real variable and produces…
- Discrete Fourier transform In mathematics, the discrete Fourier transform (DFT) is a discrete version of the Fourier transform that converts a finite sequence of numbers into another…
- Circular convolution Circular convolution, also known as cyclic convolution, is a special case of periodic convolution, which is the convolution of two periodic functions that…
- Linear time-invariant system In system analysis, among other fields of study, a linear time-invariant (LTI) system is a system that produces an output signal from any input signal…
- Fourier analysis In mathematics, the sciences, and engineering, Fourier analysis (/ˈfʊrieɪ, -iər/) is the study of the way general functions on the real line, circle, integers…
- Poisson summation formula In mathematics, the Poisson summation formula is an equation that relates the Fourier series coefficients of the periodic summation of a function to values…