# Tagged Questions

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

33 views

### single slit diffraction numerical simulation

I'm trying to simulate the Fraunhoffer diffraction at slits(single,double,triple) with Mathematica. In the picture, the red one is analytical result and the green one is numerical result. The ...
159 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. ...
876 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 ...
503 views

535 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. ...
194 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 ...
85 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 ...
121 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 ...
652 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. ...
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 ...
1k views

### Convolving/integrating problems

Let's say I want to convolve two functions (f and g), a gaussian with a breit-wigner: ...
474 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 ?
365 views

### Convolution of a piecewise function

I want to find the convolute the the functions in the Convolve command ...
125 views

### Conditional Convolution

I was hoping to incorporate an If function into a Convolve operation, as in ...
261 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, ...
314 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. ...
191 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. ...
40 views

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

I do not understand why I get different answers for the following two identical integrals. ...
107 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 ...
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 ...
763 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 ...
115 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 ...
120 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 ...
202 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 ...
218 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 ...
468 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 ...
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 ...
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 ...
316 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 ...
411 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 ...
163 views

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

My density function is as follows: ...
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') R_{n-1}(...