4
votes
1answer
105 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 ...
5
votes
2answers
87 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
207 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
1answer
215 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 $R_X(t)$, ...
2
votes
1answer
614 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
320 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 ...