Questions tagged [convolution]

Tags for questions about convolution, including the Mathematica functions Convolve, DiscreteConvolve, ListConvolve, DirichletConvolve, ImageConvolve, and convolutions using Fourier, FourierTransform, or LaplaceTransform.

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2 votes
1 answer
100 views

Mean not working with Gamma convolution distribution

Using v 13.01 or 13.1: bug in integrate, see accepted answer below. First off, the distribution ...
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2 votes
2 answers
321 views

How do I implement convolution integrals symbolically (not numerically)? [closed]

I'm working to symbolically solve convolution integrals i.e., using symbolic equations and not numerical methods of integration. The general form of the convolution I'm working to solve is as follows: ...
1 vote
0 answers
71 views

Numerical solution for multi-step PDEs

I am trying to numerically solve the following PDEs in MMA (v12.0) $$\partial_u f(x,u) = \left\{\begin{matrix}&-a f(x,u) + b \, \partial_x^2 f(x,u), & 0<u<T\\ &r(x;\alpha_1) \, f(...
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0 votes
1 answer
74 views

The inverse Laplace transform alters parameter constraints

I have this Laplace transform: $$\left( w \frac{L}{L+s}+(1-w) \frac{Q}{Q+s}\right)^n \ for \ L>0, Q>0,0<w<1.\ (1)$$ ...
0 votes
1 answer
42 views

Convolution theorem if one function depends on the reciprocal space in a non-trivial way

I would like to write the following integral in terms of a convolution: \begin{equation} H(x_1,x_2) = \int dt e^{\mathrm{i} t (x_1+x_2)/2} f(t,x_1,x_2) g(t), \end{equation} where $f(t,x_1,x_2)$ ...
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0 votes
1 answer
68 views

Symbolic Evaluation of Convolve Between DiracDeltas Where the Variable Appears In a Sqrt

This notebook's Convolve won't symbolically evaluate this one dimensional convolution in tau: ...
2 votes
1 answer
105 views

plot mollifier of a function in mathematica

My goal is the compute and plot the mollifier of a function $f(x)=(1-x^2)^{-1/4}\chi_{(-1,1)}.$ Given an approximation of the identity $\rho$, the mollifier is defined as $$f_\epsilon(x)=\int \rho_\...
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0 votes
0 answers
27 views

Deconvolution To Solve For Radial Dirac Delta Expression By Laplacian, Division and Inverse Fourier?

An answer to the question "Laplacian and DiracDelta" (about a radial DiracDelta) involves taking the Laplacian of a ...
0 votes
0 answers
40 views

Axial Convolution of Plane and Spherical DiracDelta?

I'd like to evaluate this convolution to a function of r, z and r0 giving a density for the resulting region: $\boldsymbol{\pi}(z) \ast \delta(r-r0)$ WHERE $\boldsymbol{\pi}(z)$ is an xy planar region ...
3 votes
1 answer
100 views

Density of two independent uniform random variables in Mathematica

I've tried the following: d1 = UniformDistribution[{0, W}]; d2 = UniformDistribution[{0, S}]; CDF[d1 + d2, x] But I can't get it to work. I understand that the ...
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1 vote
0 answers
55 views

How to calculate generalized discrete convolution without using DiscreteConvolve

I want to find the discrete convolution of two functions which potentially do not share a common domain. For example I have ...
0 votes
0 answers
47 views

Discrete Convolution Doesn’t Work for Simple Example

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1 vote
2 answers
92 views

Im trying to write this in Mathematica. It is a recurrence relation for convolution [duplicate]

I have tried many things, the relation is in the following picture, x' is a dummy variable.
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5 votes
1 answer
243 views

Why does ImageDeconvolve not restore this image?

The ImageDeconvolve documentation page has many examples where ImageDeconvolve restores blurred images almost perfectly. I ...
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1 vote
1 answer
118 views

PDF of sum of (1/(1+uniform distribution)) and a normal distribution

I have a continuous uniform random variable $P∼U(0,1)$ and a normal random variable $X∼N(0,σ)$. If $Z$ is given by $Z=\frac{1}{1+P}+X$ where $X$ and $P$ are independent variables, how can I calculate ...
1 vote
2 answers
75 views

How to compute a multi-round convolution? [duplicate]

I am trying to do a n-round of convolution of a function. The code is posted as below. But it is not working. Is there a solution? ...
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2 votes
1 answer
147 views

Discrete Convolution, Mathematica [closed]

I can't find the discrete Convolution [1] in mathematica, neither DiscreteConvolve nor ListConvolve do "what I want", ...
0 votes
1 answer
35 views

Evaluating $T(x,y) = ((K_h*K_g - K_g)*(K_h*K_g - K_g))(x-y)$?

Define $K_h$ as$$ K_h(x) = \dfrac{1}{h}K\bigg(\dfrac{x}{h}\bigg), $$ where $K$ is the Gaussian function$$ K(x) = \frac{1}{\sqrt{2\pi}}e^{-\frac{1}{2}x^2}. $$ Define the function $T(x,y)$ by$$ T(x,y) = ...
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2 votes
0 answers
34 views

Convolution for large arrays went wrong [closed]

I am trying to use ListConvolve[a, b, {1, -1}, 0] for large arrays a and b (1024 length) to ...
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5 votes
1 answer
246 views

Convolution and cross-correlation of two discrete signals

I have the following two discrete signals ...
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0 votes
0 answers
61 views

Convolution integral taking too long

I am a beginner in Wolfram Mathematica. I am working on a problem in Quantum Optics which concerns obtaining the lineshape. Basically, I have to consider the convolution of a Doppler profile with ...
1 vote
0 answers
90 views

How to convolve two audio signal?

Can we obtain reverb effect by convolve two audio signal? Here are some example. https://www.bilibili.com/video/BV1vE411h7W2
3 votes
1 answer
291 views

How to perform fitting with convolution of two functions in Mathematica?

I have an experimental data as shown bellow. ...
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4 votes
1 answer
259 views

How to get the class of neighbors in a 2D periodic matrix?

I'm trying to analyze the spatial structure of some rectangular arrays by counting the number and class/type of neighboring points around every point in the arrays, with periodic boundaries. For ...
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1 vote
0 answers
83 views

how to find convolution between two functions?

I have some problems with the convolution between two functions. i want to find the convolution of two models. The two models are given by gd and ...
5 votes
2 answers
163 views

How does `DirichletConvolve` relate to Dirichlet convolution?

Mathematica's Help documentation on DirichletConvolve is economical, to say the least. It claims the function "gives the Dirichlet convolution of the ...
0 votes
0 answers
78 views

How to add a multiplier in the convolution function?

I shall write my questions first: 1. Is there any other simple and efficient method in Mathematica that can compute the convolution of two or more random variables with correlation? 2. How to modify ...
1 vote
0 answers
51 views

How to define more general boundary conditions for ConvolutionLayer?

In Mathematica 12, I only see the option to define "PaddingSize" for a ConvolutionLayer in order to get Dirichlet boundary ...
3 votes
2 answers
140 views

I cannot get the convolution of Jacobsthal(n) and 3^n using Convolve[], DiscreteConvolve[] or ListConvolve[]

I am working on a problem where I found that the system I am working with follows OEIS A094705 which is the: "Convolution of Jacobsthal(n) and 3^n". So I have tried using the recursive formula ...
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0 votes
2 answers
41 views

convolution of two normal bivariate

i need to perform the convolution of two normal vibariate. I defined ...
1 vote
2 answers
264 views

Using Convolve with functions that contain error functions, and iterative convolutions

I need to produce convolutions of convolutions to study some probability distributions. My starting distribution is the Rayleigh distribution, which I convolve with itself as: ...
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1 vote
3 answers
128 views

Writing a program to convolve two inputs [closed]

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1 vote
0 answers
198 views

How to solve ode with convolution?

my question is as this and i want to get the solution of this ode x(t) $ ({M_{33}}{\rm{ + }}{{\rm{m}}_{33}})x''(t) + \int\limits_{ - \infty }^t {x'(tau){K_{33}}(t -...
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2 votes
1 answer
111 views

How to include measurement error in FindDistributionParameters (using maximum likelihood)?

I am trying to fit a non-standard PDF to data using FindDistributionParameters. My custom distribution is defined like this: ...
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4 votes
1 answer
114 views

Result of Convolve is affected by the GenerateCondition

It is very puzzling to observe that the results of Convolve depend on the GenerateCondition option and on the names of variables....
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1 vote
1 answer
322 views

Convolution integrals

I want to calculate the following integral $$\int_{-\infty}^{\infty} d \omega f(\omega) g(\omega'\pm\omega)$$ where $f$ has the form $$f(\omega)=\frac{a}{\omega- \omega_0\pm i \eta}$$ and $g$ has a ...
0 votes
1 answer
446 views

Discrete fourier transform and convolution -- scaling factor?

I am trying to convolve a square wave (a diffraction grating phgrating with slits size \[CapitalLambda]) with a point spread ...
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1 vote
1 answer
640 views

Numerically convolve lists in mathematica

I have a function $$\chi(x) = \frac{a^2}{a^2 + \left(\frac{d^{2}}{x} + x\left( \frac{ab}{x^{2} - c^2} - 1 \right) \right)^{2}}$$ which I would like to convolve with the Fourier transform of the ...
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0 votes
1 answer
62 views

Convolve doesn't yeild expected answer, nor does integrate

I am convolving, or trying to, a Gaussian and a Lorentzian as follows: ...
  • 2,366
1 vote
2 answers
238 views

Getting Convolve to behave in preparation for NonlinearModelFit

New information added at bottom of post This is an outgrowth of this earlier question. Let us suppose that we have an instrumental response function given here: ...
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0 votes
1 answer
111 views

Convolve gives inconsistent results if performed symbolically and numerically

Response from Wolfram Technical Support at end. Suppose that I have an instrument response function of the form: ...
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0 votes
1 answer
96 views

Arrays, Mapping, and Convolutions

I'm trying to create a function that convolutes a 3D Normal Distribution to the points listed below. However, I think I'm going about it in the wrong way. When I try and convolve it with the points, ...
2 votes
1 answer
145 views

Switch Function Is Not Working Properly

I'd like to select between the Tent and Hat function to convolve, but my switch function produces an error. I don't exactly need the initial plots. But I would like to plot the two that I select. <...
1 vote
1 answer
182 views

Convolution in Fourier domain

I am computing the convolution of a disk Img in 2D numerical matrix form with a kernel Ker in the Fourier domain but the output ...
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2 votes
1 answer
410 views

Analog of MATLAB's conv2 in Mathematica?

I have a matlab code filter = 1; F = conv2(double([1 2 1]),double([1 2 1]'))/16; for i=1:some_integer filter = conv2(double(filter),double(F)); end In the ...
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3 votes
1 answer
180 views

How to prove a numerical identity?

Let be a function power function f[s_, r_] := Piecewise[{{s^r, s >= 0}, {0, True}}]; And its convolution ...
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7 votes
2 answers
757 views

Does Mathematica reuse previous computations?

I am doing an analysis of experimental results in which I need to repeat the same GaussianFilter hundred of times on different data. As explained in the ...
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3 votes
1 answer
238 views

Rewrite the power sum in terms of convolution

Let be an identity $$n^{2m+1}=\sum_{r=0}^{m}A_{m,r}\sum_{k=0}^{n-1}k^r(n-k)^r,$$ where $A_{m,r}$ are real coefficients, see A302971 for numerators and formula of $A_{m,r}$. Here we can notice that $\...
  • 171
0 votes
2 answers
104 views

Convolve application

How to define the function $$f_m(s)=\begin{cases} s^m, \quad s\in[0,n]\\ 0, \quad otherwise \end{cases}$$ And to get its value of discrete self-convolution in $s=n$ by means of ...
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1 vote
0 answers
79 views

Convolve and Plotting

I want to convolute my equation with Gaussian function.I used following code for it but it does not give the output? How do I correct it ...
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