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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0answers
31 views

Discrete Convolution Doesn’t Work for Simple Example

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28 views

Convolution layer input size error

I have network which I want to take in a $6 \times 2761$ 'image' and output into one of three classifications. I have 240 of these images that I would like to train with. My training list therefore ...
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2answers
87 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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1answer
189 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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1answer
97 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 ...
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2answers
64 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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1answer
112 views

Discrete Convolution, Mathematica [closed]

I can't find the discrete Convolution [1] in mathematica, neither DiscreteConvolve nor ListConvolve do "what I want", ...
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1answer
32 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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31 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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1answer
138 views

Convolution and cross-correlation of two discrete signals

I have the following two discrete signals ...
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0answers
46 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 ...
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55 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
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1answer
132 views

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

I have an experimental data as shown bellow. ...
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1answer
169 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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80 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 ...
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2answers
144 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 ...
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67 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 ...
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41 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 ...
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2answers
135 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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2answers
33 views

convolution of two normal bivariate

i need to perform the convolution of two normal vibariate. I defined ...
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2answers
204 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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3answers
88 views

Writing a program to convolve two inputs [closed]

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169 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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1answer
100 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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1answer
113 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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1answer
200 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 ...
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1answer
338 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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1answer
501 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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1answer
60 views

Convolve doesn't yeild expected answer, nor does integrate

I am convolving, or trying to, a Gaussian and a Lorentzian as follows: ...
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2answers
178 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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1answer
108 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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1answer
92 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, ...
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1answer
129 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. <...
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1answer
159 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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1answer
377 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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1answer
150 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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2answers
747 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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1answer
215 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 $\...
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2answers
97 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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0answers
74 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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0answers
127 views

Convolution of an Image with Gaussian sigma = 1

I'm new to image processing and I've been testing out different Gaussian blur filters. Out of curiosity, I generated an object that is a 2D Gaussian with sigma = 1. I convolved this object with a ...
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1answer
25 views

Table of convolutes

Inputs Start with a vector $x\in\mathbb{R}^{n}$, and a vector-valued function $f:\mathbb{R}^{n}\mapsto\mathbb{R}^{n}$. Output Given some $k\in\mathbb{Z}^{+}$, what are elegant ways to produce the ...
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353 views

Deconvolution using Fourier transforms

I have a 2D signal in the form of a function $g(x_m,y_m)$ given as $$ \begin{aligned} g(x_m,y_m) = \ & \int^{\infty}_{-\infty} \mathrm{d}x_o \ \mathrm{d}y_o \ \frac{1}{\varepsilon^2} P(x_o - x_m,...
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65 views

Convolve taking too long and producing error message Integrate::idiv:

The following functions do not produce an output."f1" is a convolution of Gaussian function and my model. It took too much time and gave an error message. I have attached that error message also. How ...
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1answer
88 views

Fitting complex equation

I used the following code for fitting but it does not produce an output.I kept it nearly 3 to 4 hours but it does not give any output. How should I make it correct?I have used two equation(f1,f2).I ...
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0answers
40 views

Convolve[...] behaves differently to that of Integrate[...] when numerically integrating the result

I am performing a convolution between two functions, and then I want to numerically integrate the result. If I go: ...
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1answer
332 views

Convolve and fitting

I want to convolve two equation, then I want to find the parameters. But it doesn't give the answer and Takes too much time. What is the wrong with my code? ...
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0answers
38 views

Help with Plot excluding parts of a curve even with "Exclusions" option set to "None" and speed up of code

I modeled a system mathematically. When the model is ideal, I can plot the results and export the plotted points. Everything works fine. Now, I started to model some imperfections of the system, but ...
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0answers
116 views

Use List convolve for aligning images

I am trying to align images of point spread functions using a convolution. Before doing it on real data, I wanted to try on simulated data. I have no problem with the 1-D case where I create 2 ...
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3answers
375 views

Can I use ListDeconvolve or any other functions to get the original kernel?

I have seen an example in the help document: data1 = {0., 0., 1., 2., 1., 2., 1., 0., 0., 0.}; ker = {1/3, 1/3, 1/3}; conv = ListConvolve[ker, data1, 2] my question ...