/sci/ - Science & Math » Thread #14353346

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Anonymous Fri 01 Apr 02:09:26 2022 No.14353346 View Reply Original Report

Quoted By: >>14355661 >>14357858

Does stochastic calculus/SDEs have any applications in signal processing/communications/DSP? I rarely see the topic discussed outside of quantitative finance and physics.

Anonymous

Anonymous Fri 01 Apr 2022 19:09:09 No.14355581 Report

Quoted By:

Bump sounds interesting

Anonymous

Anonymous Fri 01 Apr 2022 19:38:48 No.14355661 Report

Quoted By: >>14356683

>>14353346
Yes, look here https://en.m.wikipedia.org/wiki/Spectral_density

Anonymous

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Anonymous Sat 02 Apr 2022 01:46:29 No.14356683 Report

Quoted By:

>>14355661
…I’m aware of PSDs and the role they play in stochastic analysis and signal processing. I was more interested in more advanced applications of SDEs like Ito Calculus, Brownian Motion, martingales and the like

Anonymous

Anonymous Sat 02 Apr 2022 03:24:33 No.14356889 Report

Quoted By: >>14358015

Anon, what do I read for signal processing? I thought I could start with "systems and signals" but that listed fourier analysis as a prerequisite. I realize I don't even know a lot of the electrical stuff. I am mostly interested in the software side so all of this stuff may not be necessary beyond "hypotenuse of i and q is amplitude".

Anonymous

Anonymous Sat 02 Apr 2022 14:21:05 No.14357858 Report

Quoted By: >>14358015

>>14353346
it is surely possible to use the framework of SDEs but usually the signal processing theory is done without them (also without sacrificing much rigour). SDEs are fairly complex, you will not find them in the usual treatment of signal processing.

Anonymous

Anonymous Sat 02 Apr 2022 15:38:07 No.14358015 Report

Quoted By: >>14360155

>>14356889
A background in Fourier analysis or electrical systems isn’t really necessary. If you don’t have a strong math background, then dspguide.com would be where I would start. If you have a solid background in math ie linear algebra then Foundations of Signal Processing by Vetterli would be my pick.
>>14357858
I figured as much. I know there’s been a lot of research in applying SDEs to controls and I was hoping that the same was true for signal processing applications.

Anonymous

Anonymous Sun 03 Apr 2022 07:11:47 No.14360155 Report

Quoted By:

>>14358015
Even in controls SDEs are pretty specialized. In theory every dynamical system (diffyq) with stochastic influence (noise) could be subject to an SDE analysis, but for that you need to know how to deal with SDEs in the first place and this is rarely a part of a standard curriculum. Oddly enough when looking at Kalman filters and other parts of controls we can safely get away without utilizing SDEs though be aware that you may as well use them. I figure it is much more difficult though (stochastic optimal control).

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