All Questions
Tagged with fourier-transform convolution
7 questions
2
votes
0
answers
141
views
Calculating convolution in R [closed]
I am struggling to get the correct answer for the simple calculation of convolution in R.
The convolution of $f(t) = e^{-t}$ and $g(t) = \sin(t)$ is:
$$
(f * g)(t) = 1/2 \left( e^{-t} + \sin(t) - \cos(...
- 705
2
votes
1
answer
212
views
Spectral Graph Convolutions: What are the spectral filters functions
I am trying to understand the mathematical meaning of one of the steps that appear in the Convolution Theorem (Step 4 here).
To give some context, this is related to applying the convolution theorem ...
- 298
2
votes
0
answers
492
views
How to define a loss function for discrete fourier series?
In each batch there are 8000 sample points, and I apply discrete Fourier transform on them. The original samples are real valued, so only the half of the result is needed. The end result is 4000 ...
- 123
4
votes
0
answers
291
views
Deconvolution of sum results in negative numbers
Given $T=G+A$ where $A$ and $G$ are independent random variables, I'd like to estimate the distribution of $G$ given empirical (measured) distributions of $T$ and $A$. Of note: all three random ...
- 1,721
6
votes
1
answer
146
views
Express product as convolution? Or, given $f(s)$, find $g$ satisfying $f(s)=\mathbb{E}[g(X)]$ where $X\sim \mathcal{N}(0,s^2)$
Given a function $f(\mu)$ (satisfying certain properties), it is possible to find a function $g(x)$ such that $f(\mu)=\int_{-\infty}^{\infty} g(x)\phi(x-\mu) dx $, where $\phi$ is the standard normal ...
- 285
3
votes
1
answer
2k
views
Standard deviations and confidence intervals (weighted) running average
My question is related to this one. I am calculating averages, actually as many as I have samples because I calculate a running average, and for equal weighting I know how to calculate the $95\%$ CI, ...
- 505
3
votes
1
answer
706
views
Deconvolution with fourier transform or characteristic function?
Let us consider the following model:
$$Y_j = X_j + \epsilon_j \hspace{15pt} j=1, ..., n$$
Where $Y_j$ is a noisy signal, $\epsilon_j$ is the noise which is independend from the signal $X_j$. We have ...
- 1,401