Linked from

The 39 pages that link to Convolution, each with the reason it gives.

• Green's functionRelated: For translation-invariant problems, integrating a Green's function against a source becomes convolution.

• Generating functionRelated: Multiplying generating functions produces convolution of their coefficient sequences.

• Poisson's equationRelated: Translation-invariant Green's functions turn a source into a solution by convolution.

• Matrix multiplicationCompared with: Convolution can be implemented with matrix products, though its structure differs from a general product.

• Linear systemRelated: It computes outputs by combining an input with the system's impulse response.

• Digital signal processingRelated: It computes the output of a linear time-invariant system from its input and impulse response.

• Point spread functionRelated: Convolving an ideal scene with the PSF predicts the blurred image under linear, shift-invariant conditions.

• Signal processingRelated: It models linear filtering and the response of systems to changing inputs.

• Transfer functionRelated: An LTI system’s output is the convolution of its input with its impulse response.

• Dirac delta functionRelated: Convolving with a delta leaves a function unchanged, expressing the delta's identity role.

• Fubini's theoremRelated: Fubini justifies rearranging the integrals used to establish many convolution identities.

• Impulse responseRelated: Convolving an input with the impulse response gives an LTI system’s output.

• Fast Fourier transformRelated: The convolution theorem lets FFTs turn this costly operation into pointwise multiplication.

• Gaussian functionRelated: Convolving Gaussian functions produces another Gaussian, with variances adding.

• Hadamard productCompared with: Convolution mixes neighboring positions, while the Hadamard product acts independently at each position.

• Heaviside step functionRelated: Convolving a system’s impulse response with a step produces its step response.

• Convolutional neural networkNarrower topic: The network’s defining operation applies learned filters across input locations.

• Gaussian distributionRelated: Convolving Gaussian densities yields another Gaussian, with variances adding.

• Cauchy productNarrower topic: The Cauchy product is the discrete convolution of the two coefficient sequences.

• Fundamental solutionRelated: Convolving a fundamental solution with a source often constructs a solution to the corresponding equation.

• Haar measureRelated: Haar measure provides the invariant integration used to define group convolution.

• Image processingRelated: Image filters use convolution kernels to compute each output pixel from nearby input pixels.

• Poisson summation formulaRelated: Convolution with a lattice comb expresses periodization in distributional form.

• Dirac combRelated: Convolving a signal with the comb creates a periodic sum of shifted copies.

• Fourier inversion theoremRelated: Regularized Fourier inversion can be expressed as convolution with a smoothing kernel.

• Gamma distributionRelated: Convolving independent gamma variables with a shared scale adds their shape parameters.

• Integrable functionRelated: Integrable inputs support convolution estimates and many regularity results.

• Support (mathematics)Related: The support of a convolution is constrained by sums of the input supports.

• Wavelet transformRelated: The continuous transform can be computed as convolution with scaled wavelets.

• White noiseRelated: Passing white noise through a system produces an output shaped by its impulse response.

• Tonelli's theoremRelated: Tonelli can justify rearranging nonnegative integrals in convolution calculations.

• Linear dynamical systemRelated: It computes a linear time-invariant system’s output from its impulse response and input.

• Rectangular functionRelated: Convolving rectangular functions produces piecewise-linear or higher-order pulse shapes.

• Young's inequality for productsRelated: Its norm estimates use product bounds to establish Young's convolution inequality.

• Filter (signal processing)Related: It connects a filter’s impulse response to its output for any input signal.

• Hilbert transformNarrower topic: The transform is convolution with a singular reciprocal kernel, interpreted in the principal-value sense.

• Steinhaus theoremRelated: Convolving an indicator with its reflection measures overlap between a set and its translates.

• Cauchy's formula for repeated integrationRelated: Repeated integration can be written as convolution with a truncated power kernel.

• Fuglede's conjectureRelated: Convolutions of indicator functions express overlap counts in translation tilings.