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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2answers
87 views

n fold convolution of a function via a recursion function

I wanted to write a recursion function to calculate the n-th convolution of a function f[x_]. I wrote the function ...
2
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1answer
86 views

Why is DiscreteConvolve incorrect?

Let $h[n]=(\frac{1}{2})^n u[n]-3(\frac{1}{2})^{n-1}u[n-1]$ $g[n]=3^n u[n]-\frac{1}{2}3^{n-1}u[n-1]$ I convolved $h[n]$ and $g[n]$ in Mathematica and obtained the following result: ...
1
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2answers
95 views

How to convolve the unit box function and the modified Bessel function of the second kind in 2D?

In 1D the convolution of the unit box function and the modified Bessel function of the second kind $K_0(x)$ works very well. ...
1
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1answer
83 views

Using ListDeconvolve to find velocity distrbution

Consider a Distribution of Particles correspondent with the NormalDistribution: PDF[NormalDistribution[], x] The Particles also have a velocity distribution: ...
0
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1answer
60 views

InverseFourierTransform very slow

I determined a distribution dist = SmoothKernelDistribution[ListOfValues];. Then I determined the FT of the PDF, which is the ...
5
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1answer
180 views

How to fit data to a convolution equation

How to fit data to a convolution equation: ...
4
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1answer
83 views

Is it possible to recover the efficiency of ListConvolve when generalizing the convolution?

I've noticed that, while ListConvolve is very fast, it becomes much slower when you use anything but the standard Times,Plus as ...
2
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1answer
111 views

Basic 2D convolution with mathematica

Can anyone tell me why the following keeps burning my CPU without ever producing the desired plot? ...
1
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2answers
147 views

Is there a way to do a cyclic convolution analytically in Mathematica?

Let's say I want to convolve a Gaussian function Pulse[t_] = Exp[-(t - Mid)^2/(2 sig^2)]; with an exponential broadening function ...
0
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1answer
53 views

Convolution of interpolated data with function doesn't work

I need to convolve one function with interpolated data: function: av1 = 1.3888*(12/20)*10^8; bv1 = 2.5; tr5[t_] = Exp[-(av1*t-bv1)^2]; Data: ...
1
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0answers
40 views

Speedup ListCorrelation when using generalized correlation function

ImageCorrelation provides several general function that can be used to replace the default Dot function. For example, in the documentation of ImageCorrelation, ...
5
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1answer
86 views

ListConvolve with Padding -> Fixed?

The built-in function ImageConvolve takes a Padding option that "specifies what padding to use when extending beyond the ...
7
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2answers
149 views

Good coding for a tricky expansion with convolutions, limits, substitutions

I am attempting to generate a power series in $v$ as $v\rightarrow0$ for $$g(x,v)\equiv \ln\int_{-\infty}^{\infty}e^{-y\left(z\right)}N\left(x-z,v\right)\,\mathrm{d}z $$ where ...
12
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1answer
171 views

Why do singularities disappear when performing convolutions with the Dirac Delta function?

I am attempting to perform a convolution involving the Dirac Delta function: $\int_{-\infty}^{\infty} \frac{1}{t+1} \cdot \delta(t+1)\ dt$ I would expect that the result of this integral is ...
2
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0answers
293 views

How can estimate the PSF function to deblur an image of plate licence of a car [duplicate]

I want to deblur an image of a licence plate of a car. I have used the ImageDeconvolve[] function and Sharpen[] but the problem ...
2
votes
1answer
230 views

Challenge: deblurring images [duplicate]

My friend came back from holidays, where he took lots of pictures. Unfortunately, the camera was set on manual focus and most pictures are blurry. It got me thinking that mathematica showed how to ...
5
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0answers
134 views
0
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0answers
417 views

Extracting parameters from a fitted function

Let's say I have written a function which performs convolution and returns value calculated for the time, t. ...
12
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1answer
192 views

ListConvolve Memory Hemorrhage

Bug introduced in 10.0.0 and fixed in 10.2.0. I wrote a routine that convolves an impulse response array with a test array and checks for the RMS difference between that convolution and a data ...
3
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0answers
74 views

Analytical Fourier Transforms with convolution rule [closed]

The task is the following, how to extend Mathematica's FourierTransform command in order to be able to analytically deal with non-linear differential equations. To do so it should be able to deal with ...
2
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0answers
109 views

Performing a convolution for smoothing a function

I want to smooth a one-dimensional oscillating function by convolving it with another function that I'll call the screening function. This screening function should have a trapezoidal form and go to ...
0
votes
1answer
584 views

n-fold convolution

I am trying to calculate n-fold convolution of a function as $G^{*n}(x)$ where $G(x)=1-a*exp(-b)+b*ln(b)$. I tried this function, Convolve[G[x], G[x]^{n - 1}, x, x] but it didn't give any answer. ...
3
votes
1answer
2k views

Convolution of two distribution functions

I have two functions; f[x_] = (1/k) Exp[-x/k] ; g[x_] = (1/p) Exp[-x/p] ; How I can convolve them? In Mathematica for convolving two functions we have this ...
6
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1answer
1k views

Convolving/integrating problems

Let's say I want to convolve two functions (f and g), a gaussian with a breit-wigner: ...
6
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2answers
449 views

Convolve does not get the correct answer

Convolve[Sinc[x], Exp[-x^2], x, X] (* E^-X^2 π *) is obviously false, but why? Any suggestions ?
0
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0answers
72 views

Solving a nonlinear equation involving convolution

I consider the following functional : $\psi(u,v)= -u(1-v)(1-\alpha k * v) + \epsilon v (\alpha k * v)$, where $k(x)$ is a smooth kernel with $\int |k| = 1$ and $\int k_+ = \alpha \in ]0,1[$, $u(x), ...
0
votes
2answers
331 views

Convolution of a piecewise function

I want to find the convolute the the functions in the Convolve command ...
1
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2answers
118 views

Conditional Convolution

I was hoping to incorporate an If function into a Convolve operation, as in ...
1
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0answers
237 views

Crosscorrelation for nonperiodic signals

I want to detect patterns (of an absorption spectrum which is nonperiodic) with Mathematica automaticly. I have found CorrelationFuncion but as far as I understand, ...
1
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0answers
296 views

Mathematica does not calculate inverse fourier transformation or the convolution of two functions

I am trying to take convolution of a Gaussian function with an exponential function. Mathematica couldn't calculate it. ...
1
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0answers
185 views

Derivatives of Convolutions with Integration by Parts and Delta Functions

I am not even certain how to approach this problem. f[x] is a pdf: positive definite, normalized, and approaching 0 at +/- Infinity p[x] is f[x] convolved to a normal dist of mean = 0, variance = v. ...
0
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0answers
37 views

different values of integral with/without bogus assumptions

I do not understand why I get different answers for the following two identical integrals. ...
2
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0answers
101 views

Gradient Filter Function

I am trying to understand EXACTLY what the GradientFilter function in Mathematica is doing. As far as I can tell, it appears to be doing a convolution of a first derivative of a Gaussian with the ...
2
votes
2answers
139 views

Improving the speed/efficiency of multiple (finite range) convolutions for a causal response plot

So I am looking at modelling the response of a system that is excited by multiple pulses over a period of time. The way to find the response at time t is to take the convolution between the impulse ...
1
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1answer
649 views

Convolving data set with gaussian profile

I have a spectrum looking like List, and I want to convole it with a gaussian of the form PDF[NormalDistribution[μ, σ], x] (where σ also depends on x). The raw ...
0
votes
0answers
112 views

Complex Convolution

I am attempting to integrate a convolution variable using the following code. However, the program is taking too long to complete the integration. Does anybody have any coding tips that may make ...
2
votes
1answer
118 views

Remove singularity at zero from $-((i^{-n} (-1 + i^n)^2)/(n^2 π^2))$

The expression h[n_] = -((I^-n (-1 + I^n)^2)/(n^2 π^2)) is real for all integers n. Although indeterminate at ...
2
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0answers
197 views

Partial convolution of random variables in random vectors

Suppose $(X_1,Y_1)$ is a bivariate random vector with a given distribution and let $X_2$ be a univariate random variable with the same distribution as $X_1$ but independent of $(X_1,Y_1)$. I want to ...
0
votes
1answer
211 views

Calculate expected value of custom pdf

I've a custom pdf in the sense that it's the convolution of several other PDFs p[t_] := Convolve[p1[x],p2[x],x,t]; Now I want to calculate the expected value of ...
1
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0answers
453 views

Convolve two sets of (x,y) data sets

I have two sets of data in the form a={{.1,2},{.2,3},{.3,4},{.5,6}} b={{0,8},{.1,4},{.2,7},{.3,1},{.5,10},{.6,3}} Both data sets have even spacing, although ...
8
votes
3answers
2k views

Discrete Convolution

Ask to compute the convolution of 2 lists, I managed to do so, with what I feel is rather heavy : Let my 2 lists be : a = {1,2,3,4} b = {1,1,1,1,1,1}; The below function adds 0s on each part of ...
5
votes
3answers
2k views

cross-correlation with time lag

I have two lists with some data. a={1,2,3,4,5} b={5,4,3,2,1} Now I want to compute the cross correlation of the two lists with a time lag of 1, like it is ...
3
votes
1answer
786 views

How do you use fourier transforms to perform a deconvolution

I've been trying to teach myself about deconvolution through fourier transforms, but I seem to be missing something simple, as my results are garbage. I start by defining a test function and a window ...
4
votes
2answers
304 views

Graphing convolutions of user defined functions

I am a statistician who is very new to Mathematica. Ultimately I would like to be able to graph convolutions of arbitrary user defined functions. But I can't as yet obtain values of such ...
0
votes
1answer
397 views

Image convolution, motion blur

I define my degradation function as $$H(x,y;a,b,t)=\frac{T}{z}\sin z~e^{-jz}$$ where $$z=\pi(ax+by)$$ So I write ...
-2
votes
1answer
2k views

Convolution of two dirac delta functions

Why mathematica doesnt produce any answer to the following integral? Integrate[0.040608386793220284*DiracDelta[w]*DiracDelta[-w + x], {w, -2, 2}] and how can I ...
5
votes
3answers
1k views

recursive integration

I am trying to do multiple integrations recursively. For instance, I would like to do the following equation for arbitrary integer $n$: $\displaystyle R_n(t) = \int_0^t \mathrm dt' R_0(t-t') ...
1
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1answer
234 views

Plotting a convolution fails [closed]

i'm trying to plot a graph of a convolution and a discrete convolution, using Mathematica 8 ...
24
votes
3answers
2k views

How to find the center of a circular pattern?

I am writing an algorithm that finds the center of 500 x 500 pixels images coming from a live feed from a camera at 50 Hz. So it has to be quick! The images are images of an optical field which looks ...