Tagged Questions
2
votes
0answers
22 views
Mathematically inclined books on Signal Processing Theory
First off, i know this may seem off topic but i could not find help in signal processing communities so i was hoping there would be people here who both love mathematics and have interest in signal ...
4
votes
2answers
30 views
partially reconstruct information of function convoluted with boxcar kernel
the function (f) I want to reconstruct partially could look like this:
The following properties are known:
It consists only of alternating plateau (high/low).
So the first derivation is zero ...
1
vote
1answer
122 views
Is there an autocorrelation function with a constant integral whose absolute value integral diverges?
Suppose a function $g:\mathbb{R}\rightarrow\mathbb{R}$ such that:
$|g(x)|\leq g(0)$;
$g(x)=g(-x)$, i.e. $g(x)$ is even;
$\int_{-\infty}^{\infty}g(x)dx=C$;
There exists a Fourier transform
of ...
2
votes
0answers
159 views
An example of a “pathological” power-spectral density function?
Suppose that we are given a wide-sense stationary random process $X$ with autocorrelation function $R_X(t)$. Power spectral density $S_X(f)$ of $X$ is then given by the Fourier transform of $R_X(t)$, ...
1
vote
1answer
429 views
Hilbert transform of white noise
What is the Hilbert transform of a white noise $\xi(t)$?
By the Hilbert transform I mean:
http://mathworld.wolfram.com/HilbertTransform.html
Thank you.
6
votes
1answer
264 views
Qualitative interpretation of Hilbert transform
the well-known Kramers-Kronig relations state that for a function satisfying certain conditions, its imaginary part is the Hilbert transform of its real part.
This often comes up in physics, where ...
