# Tagged Questions

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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### 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 ...
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### 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 ...
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### 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 ...
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### Convolution with interpolated function

I have some problems to calculate in reasonable speed the convolution of an interpolated function with a Gauss function. I have here (ExampleData.txt, alternate Pastebin link) data which I ...
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### Sparse convolution of sparse arrays

The documentation for ListConvolve mentions that "ListConvolve works with sparse arrays", which is true. The result, however is never sparse, eg: ...
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### 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 ...
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### Speed up Mathematica code involving Convolve

I'm trying to plot the averaged autocorrelation function of a random wire profile $\xi(x)$ which is build from unitsteps which are each L units long. To calculate the average I'm generating nMax ...
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### 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 ...
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### How to fit data to a convolution equation

How to fit data to a convolution equation: ...
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### ListConvolve with Padding -> Fixed?

The built-in function ImageConvolve takes a Padding option that "specifies what padding to use when extending beyond the ...
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### 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 ...
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### 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 ...
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### How to make 3D object smooth?

This thread considers mathematical methods here to make the 3D object smooth but this question consider how to achieve the goal of smoothing a 3D object in Mathematica. I want to get smoother ...
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### 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 ...
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### 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 ...
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### 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: ...
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### Basic 2D convolution with mathematica

Can anyone tell me why the following keeps burning my CPU without ever producing the desired plot? ...
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### 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 ...
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### 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. ...
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### 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 ...
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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 ...
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### 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 ...
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### 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 ...
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### 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: <...
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### 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 ...
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### Plotting a convolution fails [closed]

i'm trying to plot a graph of a convolution and a discrete convolution, using Mathematica 8 ...
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### How to find this convolution?

How can I use Mathematica to find the convolution $f*f$ for ...
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### Convolution with modified indices

I want to perform convolution for a sequence but instead of having the indices cycle from the ends periodically, I want to apply a function, specifically Abs, to ...
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### 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 ...
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### 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 ...
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### Convolution of a denstity function having a point mass with itself

My density function is as follows: ...
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### 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, ...
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### Conditional Convolution

I was hoping to incorporate an If function into a Convolve operation, as in ...
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### 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, ...
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### 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. ...
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### 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. ...
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### 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 ...
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 ...