# Tagged Questions

Tags for questions about convolution, including the Mathematica functions Convolve, DiscreteConvolve, ListConvolve, DirichletConvolve, ImageConvolve, and convolutions using Fourier, FourierTransform, or LaplaceTransform.

44 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, ...
32 views

### Convolution of a Dirac impulse with a periodic signal [migrated]

I have to do a convolution of a periodic signal with a Dirac impulse. $\quad \quad x(t)=\sin(π\, t)(u(t)−u(t−2))$ $\quad \quad h(t)=u(t−1)−u(t−3)$ The first is a periodic signal that intersects the ...
80 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. ...
97 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. ...
21 views

### different values of integral with/without bogus assumptions

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

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 ...
80 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 ...
125 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 ...
120 views

### How can estimate the PSF function to deblur an image of plate licence of a car

I want to deblur a blurred image of a plate licence of a car. I need to deblured it. I have used the ImageDeconvolve[] function and Sharpen but the problem is still difficult because I need to ...
94 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 ...
106 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 ...
138 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 ...
190 views

### How to use the function ImageCorrelate? [closed]

I am a beginner in using Mathematica, know little about optics. However, I would like to know how to understand the function ImageCorrelate, since the ...
91 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 ...
226 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 ...
708 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 ...
325 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 ...
175 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 ...
221 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 ...
643 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 ...
133 views

### Convolution of a denstity function having a point mass with itself

My density function is as follows: ...
922 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 ...
640 views

### Convolving/integrating problems

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

### Plotting a convolution fails [closed]

i'm trying to plot a graph of a convolution and a discrete convolution, using Mathematica 8 ...
1k 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 ...
348 views

### 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 ...
49 views

### MATLAB-like convolution and derivation using Mathematica [duplicate]

Possible Duplicate: Discrete Convolution I would like to be able to convolve two functions of two variables in Mathematica, and then plot derivatives (or functions of derivatives) of the ...
319 views

### How to find this convolution?

How can I use Mathematica to find the convolution $f*f$ for ...
588 views

### 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: ...
163 views

### Error in Compiled function at runtime in spatial competition model

I just did a model of spatial competition between two species with different competitive ability & dispersal rates on a lattice with variables nrs of individuals per site. To speed it up I tried ...
304 views

### Use of Cellular Automaton or Discrete Convolution to calculate Potts Energy of a 2D Matrix

In a project of Monte Carlo Modelling of Grain Growth (Link) one of the most costly subroutines is the calculation of the Potts-Energy of an Monte Carlo Grid cell by comparing the center cell value ...
1k views

### 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 ...
924 views

### How to plot the convolution of dirac delta series with a sine function [closed]

I am new to mathematica. I do the convolution of dirac delta :(DiracDelta(x-10)" with "sine(t),t=0-pi". How to plot the output ? Theoretically, the full wave should appear at the location of the ...
725 views

### 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 ...
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') ...