Tagged Questions
0
votes
1answer
78 views
Power spectrum for discrete signals.
If $x(t)$ is a real (aperiodic) power signal, i.e.
\begin{equation}
0<\lim_{T\rightarrow\infty} \frac{1}{T}\int_{-T/2}^{T/2}|x(t)|^2 dt<\infty
\end{equation}
$x_T (t)$ is a truncated version of ...
3
votes
1answer
81 views
Why is the Fourier Transform of a Lévy Process a continuous function? What about the inverse? (Bochners Theorem)
I was confronted with this question when reading "Stochastic Integration and Differential Equations" by Protter. Just after the definition of a Lévy process he says the following:
If $X_t$ is a ...
0
votes
0answers
117 views
Mixture of Normal distributions:Estimating variance& Fisher Information
I want to estimate the variances and the Fisher information of a countable mixture of Gaussians with assumed equal variance and identically spaced means. I thought that the Fourier transforms of an ...
1
vote
0answers
22 views
Fisher information of spectrum estimator
Perhaps someone could point me to a reference
I would like to calculate the Fisher information of a spectrum estimator. The spectrum estimator is a windowed Fourier transform of the data.
More ...
0
votes
1answer
115 views
Windowed Fourier transform of Gaussian distributed random time series
If I have a discrete time series $x(t_i)$, and each of the $x(t_{i})$ are normally distributed, i.e., come from a Gaussian distribution with mean zero and variance one, would a windowed finite Fourier ...
2
votes
0answers
69 views
Scale invariance and $1/f^2$ power spectrum
In the paper
Occlusion Models for Natural Images : A Statistical Study of a Scale-Invariant Dead Leaves Model; Lee, A. B. Mumford, D. B. Huang, J.; International Journal of Computer Vision
I read ...
