Questions tagged [convolution]
For questions about applying convolutions to data. This can include the process of convolving two functions together or seeking a kernel matrix to convolve with a grid of data (often done in image processing).
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How to plan convoluted measurements
I have a physical function $f(x)$ which I intend to measure. Problem is that I cannot read it directly, but through a response function $g(x)$ which is known to me with great accuracy and any one ...
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82
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Convolution/weighted average of two arrays in Python
I have an equation that I need to calculate numerically, but I am having doubts about my approach. I am cross-posting this question from Stack Exchange, because I am not getting any responses.
This is ...
- 105
1
vote
1
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Computing convolution on non-uniform sample
How to efficiently convolve the function $h(t)=H(t)e^{-t}$ with a function $x(t)$ sampled non-uniformly, i.e. $\{x(t_0), x(t_1), ..., x(t_{N-1})\}$?
$H(t)$ is the Heaviside step function, and the ...
- 181
2
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1
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Padding length and error analysis of discrete convolution by FFT
The standard algorithm for discrete convolution of two vectors $x\in \mathbb{R}^{n}$ and $y \in \mathbb{R}^{m}$ is (in essence) a FFT of the two input vectors, multiplication of the two elementwise, ...
- 2,125
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Deconvolution of sinc function in spectrum calculation in FTS
In Fourier transform spectroscopy (FTS) I am calculating a broadband interferogram (e.m. frequency 190-300 GHz top-hat), then back-retrieving the spectrum by FT.
Here in the figure, you can see the ...
- 61
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3
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506
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Why not use the convolution theorem for explicit timestepping?
Consider the advection equation
\begin{equation}
\frac{\partial C}{\partial t} + u\frac{\partial C}{\partial x} + v\frac{\partial C}{\partial y} = 0
\end{equation}
I want to do a forward time, center ...
- 141
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378
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Numerical evaluation of Duhamel's integration
I am trying to numerically evaluate the following Duhamel's integration:
$$
x = \frac{-1}{\omega_d} \int_0^t \ddot{x}_g (\tau) e^{-\zeta \omega_n(t - \tau)} \sin{\left( \omega_d (t - \tau) \right)} d\...
- 465
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What's the relationship of machine learning and mechanical simulation?
What's the relationship of machine learning and mechanical simulation?
Particularly, machine learning is about learning from a large sample and predicting based on filters tuned on that.
Mechanical ...
- 427
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3
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Convolute a gaussian kernel with a large array of off-grid centroids without looping? (how to make "A Thousand (Gaussian) Points of Light" )
For a finite object size diffraction simulator, I need to generate arrays which are the sum of thousands of instances of a Gaussian (or other) 2D kernel at centroids that will not fall in any ...
- 1,016
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How to generate the convolution of f(x, y) with a parametric function g(t), x(t), y(t) in Python? (Something better than this brute-force sum)
The answer to Convolute a gaussian kernel with a large array of off-grid centroids without looping? (how to make "A Thousand (Gaussian) Points of Light" ) involves summing a 3D array over ...
- 1,016
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Compute efficiently a 1D function relying on a 2D convolution
Let $X = [0,1]$, $h$ the Gaussian function (i.e. $\forall x \in X, h(x) = e^{-\frac{x}{2}}$) and $p \in L^2(X^2)$
I would like to compute numerically the following function :
$$
\forall x \in X, \...
- 11
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0
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492
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How to take convolution of two arrays in Python by using NumPy?
Generally, we know that if we have this relation between Fourier transforms of three functions in frequency domain as:
$$\mathfrak{F}\{\mathsf{P}(t)\} = \mathfrak{F}\{\mathsf{Z}(t)\}\mathfrak{F}\{\...
- 2,322
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1
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Problem implementing convolutions exactly with the FFT
I'm trying to perform convolutions as defined mathematically $f \star g (\tau)= \int_{\mathcal{R}}f(t-\tau)g(t) dt$ in a numerical simulation. Hence, my signal is a sampling of points $f(x_i)$.
I ...
- 131
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Convolution in Python
I have an integral of a convolution between two functions. How can I calculate this in Python? It is a continuum convolution.
4
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Computation of triple nested loops as a convolution product?
I'm trying to compute efficiently the following
\begin{equation}
A_j = \sum_{l'=1}^{\infty}\sum_{k= 0}^{K-1} L_{l'}T_ke^{2\pi i \frac{k}{K}j}\epsilon_{l',k}
\end{equation}
for $j = 0,1, \ldots, K-2,K-...
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Levinson Recursion for Non Square Toeplitz Matrices
Given a rectangular Toeplitz Matrix $ H $, how could one solve:
$$ y = H x $$
For instance, $ H $ can be Linear Convolution Matrix of the filter $ h $:
$$ H = \begin{bmatrix}
{h}_{1} & 0 & ...
- 332
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0
answers
38
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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
$$
x_{i} = i \Delta x, i = 0, 1, 2\...
- 81
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49
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FFT convolution works only with certain domain length
in my quest to understand how I can use FFT to compute integrals (see my other question click, still no answer there), I came across the fact that a convolution of two functions can be calculated by ...
- 153
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1
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Accelerating Conjugate Gradients fitting for small localized kernel (like cubic B-spline)
Question:
Is there some pre-conditioner for Conjugate-Gradient (CG) cheap enough, that it is worth using even if my operator is very local (i.e. already has a low number of non-zero elements), as it ...
- 907
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1
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Calculating the Convolution Using DFT (FFT)
I have the following convolution as part of a numerical simulation.
$$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 ...
- 131