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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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Issue with numerical convolution integral

I want to solve a convolution integral numerically: ...
Luigi's user avatar
  • 1,303
0 votes
0 answers
38 views

DiscreteDelta, DiscreteConvolve, PiecewiseExpand: odd behavior

I noticed something odd when trying DiscreteDelta, DiscreteConvolve and PiecewiseExpand for ...
user9716869 - supports Ukraine's user avatar
1 vote
1 answer
87 views

Trouble understanding the syntax and parameters of ListDeconvolve

I'd like to use the ListDeconvolve command to do the following task but I'm having a hard time understanding the description in the Wolfram Language Reference. ...
5-limit_JI's user avatar
2 votes
1 answer
133 views

Speeding a Manipulate illustrating convolution

I'd like to illustrate the mathematical process of convolution ($f(x) \star g(x)$) with an interactive Manipulate, but the evaluation is far too slow for a class ...
David G. Stork's user avatar
1 vote
1 answer
73 views

Is there an option for InverseLaplaceTransform to make Mathematica use the convolution theorem when feasible?

By default, it appears that Mathematica won't use the convolution theorem to write an inverse Laplace transform in the form of a convolution of two functions. For example, ...
Matt's user avatar
  • 453
3 votes
2 answers
119 views

Convolving using Integrate function [closed]

Convolving two UnitBox using the Convolve function gives accurate results as fig.1). However, when I try using Integrate function according to the document, the results are different as fig2. What ...
Soon's user avatar
  • 648
2 votes
1 answer
119 views

Convolution to regularize list

I try to regularize a given list of points, say f=Table[Exp[-a t],{t,0,100}], with some kernel $h_{\sigma}(t)=\frac{1}{\sqrt{2\pi \sigma}}e^{-\frac{t^2}{2\sigma ^2}}...
qising's user avatar
  • 43
4 votes
3 answers
224 views

Integration involving two DiracDelta with variable limit

I want to write a code to evaluate $$ \int_0^{t-1}\frac{\delta(z-1)}{z}\frac{\delta(t-z-1)}{t-z}dz$$ which should gives the answer $$\frac{\delta(t-2)}{t-1}.$$ I tried to write the code ...
Mohamed Mostafa's user avatar
2 votes
3 answers
164 views

DiscreteConvolution

I am not an expert in discrete Convolutions so perhaps there is a mathematical misunderstanding with me and or the options. But shouldn't convolve average over the two lists like in the continuous ...
Michael Fischer's user avatar
0 votes
1 answer
64 views

What's the expression of transformation T in area-based Image operations such as ImageFilter and ImageConvolve?

in the “tutorial/ImageProcessing”, as the following picture shows I just wonder what's the expression of the T in the area-based image operations such as ...
Aerterliusi's user avatar
3 votes
1 answer
67 views

How to align the dimensions of Deconvolution in neural-net?

I tried to implement a NetGraph similar to UNet in Mathematica, but I found an error in the dimension. ...
Life_Checkpoint's user avatar
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1 answer
67 views

Maximizing a stochastic function with Convolution distribution

I have a stochastic profit function where I want to maximize with respect to a variable "a". I have written the code like this ...
P Initiate's user avatar
2 votes
1 answer
132 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 ...
Carl's user avatar
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2 votes
2 answers
603 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: ...
Ajay Menon's user avatar
1 vote
0 answers
96 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(...
SaMaSo's user avatar
  • 231
0 votes
1 answer
89 views

The inverse Laplace transform alters parameter constraints

I have this Laplace transform: $$\left( w \frac{L}{L+s}+(1-w) \frac{Q}{Q+s}\right)^n \ for \ L>0, Q>0,0<w<1.\ (1)$$ ...
step-by-step's user avatar
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1 answer
54 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 $f(t,x_1,x_2)$ ...
Luke's user avatar
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1 answer
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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: ...
James Bowery's user avatar
3 votes
1 answer
197 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_\...
Student's user avatar
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0 answers
58 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 ...
James Bowery's user avatar
3 votes
1 answer
108 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 ...
khajiit's user avatar
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1 vote
0 answers
95 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 ...
Seyhmus Güngören's user avatar
1 vote
0 answers
92 views

Discrete Convolution Doesn’t Work for Simple Example

...
Seyhmus Güngören's user avatar
1 vote
2 answers
98 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.
pedro's user avatar
  • 11
5 votes
1 answer
351 views

Why does ImageDeconvolve not restore this image?

The ImageDeconvolve documentation page has many examples where ImageDeconvolve restores blurred images almost perfectly. I ...
Szabolcs's user avatar
  • 235k
1 vote
1 answer
150 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 ...
user13465718's user avatar
1 vote
2 answers
159 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? ...
Hans's user avatar
  • 179
2 votes
1 answer
215 views

Discrete Convolution, Mathematica [closed]

I can't find the discrete Convolution [1] in mathematica, neither DiscreteConvolve nor ListConvolve do "what I want", ...
Michael Fischer's user avatar
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) = ...
sonicboom's user avatar
  • 183
2 votes
0 answers
35 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 ...
C.S.'s user avatar
  • 121
5 votes
1 answer
387 views

Convolution and cross-correlation of two discrete signals

I have the following two discrete signals ...
VDF's user avatar
  • 453
1 vote
0 answers
92 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 ...
HeitorGalacian's user avatar
1 vote
0 answers
117 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
木子何's user avatar
3 votes
1 answer
509 views

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

I have an experimental data as shown bellow. ...
user14634's user avatar
  • 779
4 votes
1 answer
365 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 ...
TumbiSapichu's user avatar
  • 1,603
2 votes
0 answers
86 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 ...
Saja El Failali's user avatar
5 votes
2 answers
193 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 ...
Richard Burke-Ward's user avatar
0 votes
0 answers
93 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 ...
wuhanichina's user avatar
1 vote
0 answers
62 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 ...
Fidel I. Schaposnik's user avatar
3 votes
2 answers
149 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 ...
Robjobbob's user avatar
  • 361
0 votes
2 answers
50 views

convolution of two normal bivariate

i need to perform the convolution of two normal vibariate. I defined ...
Andrea Mazzolari's user avatar
1 vote
2 answers
403 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: ...
user27119's user avatar
  • 2,520
1 vote
3 answers
190 views

Writing a program to convolve two inputs [closed]

...
Noah's user avatar
  • 11
1 vote
0 answers
233 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 -...
dcydhb's user avatar
  • 615
2 votes
1 answer
135 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: ...
YoAn's user avatar
  • 35
4 votes
1 answer
116 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....
yarchik's user avatar
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1 vote
1 answer
454 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 ...
user3368447's user avatar
0 votes
1 answer
608 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 ...
SuperCiocia's user avatar
  • 1,472
2 votes
1 answer
893 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 ...
user27119's user avatar
  • 2,520
0 votes
1 answer
75 views

Convolve doesn't yeild expected answer, nor does integrate

I am convolving, or trying to, a Gaussian and a Lorentzian as follows: ...
user27119's user avatar
  • 2,520