Questions tagged [convolution]
Tags for questions about convolution, including the Mathematica functions Convolve, DiscreteConvolve, ListConvolve, DirichletConvolve, ImageConvolve, and convolutions using Fourier, FourierTransform, or LaplaceTransform.
153
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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 ...
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0
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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, ...
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2
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108
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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 ...
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2
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1
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105
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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}}...
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3
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218
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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
...
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1
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3
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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 ...
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57
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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 ...
- 343
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64
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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.
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1
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62
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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
...
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2
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1
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129
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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
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2
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536
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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:
...
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93
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Numerical solution for multi-step PDEs
I am trying to numerically solve the following PDEs in MMA (v12.0)
$$\partial_u f(x,u) =
\left\{\begin{matrix}&-a f(x,u) + b \, \partial_x^2 f(x,u), & 0<u<T\\ &r(x;\alpha_1) \, f(...
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87
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The inverse Laplace transform alters parameter constraints
I have this Laplace transform:
$$\left( w \frac{L}{L+s}+(1-w) \frac{Q}{Q+s}\right)^n \ for \ L>0, Q>0,0<w<1.\ (1)$$
...
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Convolution theorem if one function depends on the reciprocal space in a non-trivial way
I would like to write the following integral in terms of a convolution:
\begin{equation}
H(x_1,x_2) = \int dt e^{\mathrm{i} t (x_1+x_2)/2} f(t,x_1,x_2) g(t),
\end{equation}
where $f(t,x_1,x_2)$ ...
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Symbolic Evaluation of Convolve Between DiracDeltas Where the Variable Appears In a Sqrt
This notebook's Convolve won't symbolically evaluate this one dimensional convolution in tau:
...
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plot mollifier of a function in mathematica
My goal is the compute and plot the mollifier of a function $f(x)=(1-x^2)^{-1/4}\chi_{(-1,1)}.$ Given an approximation of the identity $\rho$, the mollifier is defined as
$$f_\epsilon(x)=\int \rho_\...
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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 ...
- 103
3
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1
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106
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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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87
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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
...
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88
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2
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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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328
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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
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144
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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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137
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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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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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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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0
answers
35
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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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1
answer
358
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Convolution and cross-correlation of two discrete signals
I have the following two discrete signals
...
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85
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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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115
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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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454
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How to perform fitting with convolution of two functions in Mathematica?
I have an experimental data as shown bellow.
...
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342
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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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86
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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
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178
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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 ...
- 2,141
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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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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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149
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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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convolution of two normal bivariate
i need to perform the convolution of two normal vibariate. I defined
...
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2
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382
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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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183
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1
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0
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224
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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 -...
- 605
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130
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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
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1
answer
115
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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
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423
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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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572
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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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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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72
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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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2
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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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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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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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