Questions tagged [convolution]
The convolution tag has no usage guidance.
8
questions
3
votes
1answer
60 views
Problem implementing convolutions exactly with the FFT
I'm trying to perform convolutions as defined mathematically $f \star g (\tau)= \int_{\mathcal{R}}f(t-\tau)g(t) dt$ in a numerical simulation. Hence, my signal is a sampling of points $f(x_i)$.
I ...
1
vote
2answers
58 views
Convolution in Python
I have an integral of a convolution between two functions. How can I calculate this in Python? It is a continuum convolution.
4
votes
1answer
121 views
Computation of triple nested loops as a convolution product?
I'm trying to compute efficiently the following
\begin{equation}
A_j = \sum_{l'=1}^{\infty}\sum_{k= 0}^{K-1} L_{l'}T_ke^{2\pi i \frac{k}{K}j}\epsilon_{l',k}
\end{equation}
for $j = 0,1, \ldots, K-2,K-...
3
votes
0answers
54 views
Levinson Recursion for Non Square Toeplitz Matrices
Given a rectangular Toeplitz Matrix $ H $, how could one solve:
$$ y = H x $$
For instance, $ H $ can be Linear Convolution Matrix of the filter $ h $:
$$ H = \begin{bmatrix}
{h}_{1} & 0 & ...
2
votes
0answers
33 views
Computing convolution of two characteristic function over a 1D Cartesian mesh
I am trying to compute the convolution of two characteristic functions over a Cartesian mesh. First, I define my Cartesian mesh of the interval $[0,1]$ as follows
$$
x_{i} = i \Delta x, i = 0, 1, 2\...
1
vote
0answers
36 views
FFT convolution works only with certain domain length
in my quest to understand how I can use FFT to compute integrals (see my other question click, still no answer there), I came across the fact that a convolution of two functions can be calculated by ...
1
vote
1answer
40 views
Accelerating Conjugate Gradients fitting for small localized kernel (like cubic B-spline)
Question:
Is there some pre-conditioner for Conjugate-Gradient (CG) cheap enough, that it is worth using even if my operator is very local (i.e. already has a low number of non-zero elements), as it ...
3
votes
1answer
93 views
Calculating the Convolution Using DFT (FFT)
I have the following convolution as part of a numerical simulation.
$$T(r)=\int \mathrm{d}^3r_2\, p(r_2)f(r_2)\alpha(r-r_2)\, .$$
My problem is that the analytical expressions for $f$ and $p$ do ...
