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The math of noise
October 28, 2010 7:37 PM   Subscribe

Assuming a grasp of college algebra, what maths would one need to understand the entirety of the wikipedia entry on white noise. Which order would be the most advisable way to learn those maths and which books might be good for a self study on those topics?
posted by Drama Penguin to Technology (7 answers total) 8 users marked this as a favorite
 
1. Basic linear algebra (e.g., Axler, Lay, Strang, etc.).
2a. Harmonic analysis (e.g., this).
2b. Mathematical statistics (e.g., this).

This assumes some background in calculus.
posted by Nomyte at 7:49 PM on October 28, 2010 [1 favorite]


You should check out MIT's OpenCourseWare.

Start with single variable calculus. Then do multivariable calculus.

And after that check out vibrations and waves, statistical physics, and linear algebra.

That should do you.
posted by leslietron at 8:30 PM on October 28, 2010 [1 favorite]


What you're asking is how to learn the basics of stochastic processes & statistical signal processing, two areas that are central to the electrical engineering sub-field of signal processing. Algebra won't really cut it--you've gotta learn calculus, linear algebra, and differential equations.

Here are some books that are part of a basic curriculum to get you up to speed on these topics (beyond the fundamental engineering math topics).

First, start with Signals & Systems (O&W).
Then get up to speed on probability & stochastic processes (Ross, Papoulis).
Finally, statistical signal processing (Kay).
posted by scalespace at 8:38 PM on October 28, 2010 [1 favorite]


Also, to get a real deep appreciation & understanding--you've gotta implement & experiment with these concepts: get a book on digital signal processing (Oppenheim), which is a non-trivial extension of the basics of signals & systems. You will also want to get your hands on a copy & license for MATLAB to read in data, play with it (implement signal processing algorithms), and visualize what you've done. (Octave seems like a potentially viable open source stand-in but I've never personally dealt with it.)
posted by scalespace at 8:46 PM on October 28, 2010


Khan Academy has sections on statistics, calculus, linear algebra and differential equations. I can't recommend his site enough to get a layman's understanding of any topic that he covers. Everything is in 10 minute bursts and he walks you through detailed examples in a very casual, easy to understand way.
posted by empath at 9:02 PM on October 28, 2010


What they've all said above, but be aware that wikipedia's mathematical explanations are often written in a way that makes them difficult to understand even if you know the requisite math. They just want to get the facts down and make little effort to explain what they're talking about.
posted by Obscure Reference at 4:31 AM on October 29, 2010


I'm late here, but Nomyte mentions Strang for Linear Algebra, with which I totally agree. Leslietron then mentions Opencourseware. Strang's Linear Algebra course is actually on OCW in its entirety. It's a great Linear Algebra course, and it helped me pass my comps in grad school, (my background was all abstract algebra, but my PhD is in applied mathematics, so I needed to learn linear to pass my exams).

Also, as Obscure Reference mentions (eponytastically) Wikipedia math is often correct but difficult to read. In fast, some of it is exactly the same as what is on Wolfram's Mathworld, and I'm not sure which came first.
posted by monkeymadness at 10:38 AM on November 5, 2010


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