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Convolution

In mathematics (in particular, functional analysis), convolution is a mathematical operation on two functions f {\displaystyle f} and g {\displaystyle g} that produces a third function f ∗ g {\displaystyle f*g} , as the integral of the product of the two functions after one is reflected about the y-axis and shifted. The term convolution refers to both…

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Overview

Definition

Historical developments

Circular convolution

Discrete convolution

Domain of definition

Properties

Convolutions on groups

Convolution of measures

Infimal convolution

Bialgebras

Applications

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Convolution

Nodes196
Edges195
Triples287
Avg. degree1.99
Density0.010204
Components1

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Convolution

Top relations

related to Further reading · 142
Convolution → Abelian, Abstract, Academic Press Harcourt Brace, Addison, Advances, Alejandro, Alexdfar/origin-adn-history-of-convolution, An, Anal, Analysis, Andrzej, Appl, Applied Mathematics, Band, Barry, Beckenstein, Bedford MK43 OAL, Berlin, Bibcode, Boca Raton
has application · 20
Convolution → At, Convolutional, Doppler, For, Gaussian, Golay, In, In Fractional, In Smoothed-particle, Kernel, LES, Lorentzian, LTI, Often, Savitzky, The, They, Though, Voigt, When
related to External links · 20
Convolution → Alan PetersConvolution Kernel Mask, Another, Convolution/CI, FFT, Flash, Image Processing, Intuitive Guide, Java Applet, Java Applethttps, JavaScripthttps, JavaScriptLectures, Lecture, MathWorldFreeverb3 Impulse Response Processor, Opensource, Operation Interactive, Salman KhanExample, University CS, Vanderbilt University, Visual, VST
related to Integrable functions · 11
Convolution → L1, Lebesgue, Likewise, Lp, Rd, Stein, The, Theorem, This, Tonelli's, Weiss
is a · 9
Convolution → commutative associative algebra without identity, compact multiplication operator in this basis, continuous bilinear map between suitable Lp spaces, continuous bilinear mapping from Lp, imposition of a spectral or rhythmic structure on a sound, mathematical operation on two functions f, most general translation invariant operation, pointwise product of the Fourier transforms, product defined on the endomorphism algebra End
related to Fast convolution algorithms · 9
Convolution → Digital, Eq, For, Gathen, Gerhard, In, Knuth, N2, That
related to Functions of rapid decay · 8
Convolution → An, Combined, In, Properties, Schwartz, Stein, Theorem, Weiss
related to Bialgebras · 6
Convolution → End, Hopf, III, Kassel, Let, The
related to Convolutions on groups · 6
Convolution → Haar, Hausdorff, If, In, It, The
related to Infimal convolution · 6
Convolution → Fourier, Furthermore, In, It, Legendre, We

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Important terminology

functions function displaystyle fourier transform defined also isbn operation theorem two analysis product integrable measure continuous processing integral see group

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Convolutionis amathematical operation on two functions f0.90text
Convolutionis acontinuous bilinear map between suitable Lp spaces0.90text
Convolutionis acontinuous bilinear mapping from Lp0.90text
Convolutionis acommutative associative algebra without identity0.90text
Convolutionis amost general translation invariant operation0.90text
Convolutionis apointwise product of the Fourier transforms0.90text
Convolutionis acompact multiplication operator in this basis0.90text
Convolutionis aproduct defined on the endomorphism algebra End0.90text
Convolutionis aimposition of a spectral or rhythmic structure on a sound0.90text
the overlapinstance ofdecomposing the longer sequence into blocks and convolving each block allows for faster algorithms0.80text
adding blurring.In digital data processingIn analytical chemistryinstance ofThe photographic term for this is bokeh.In image processing applications0.80text
Savitzkyinstance ofThe photographic term for this is bokeh.In image processing applications0.80text

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