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Linear Algrebra and Signal Processing


scottyboy85

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I'm doing a project on Linear Algebra and Signal Processing, and I need to gather some sources for my proposal. Do you guys know any good books, websites, or people I could talk to to get a basic understanding of how this works? The project is just a 3 or 4 page paper and a presentaion, and it's for a Linear Algebra class (about half way up the "math ladder" in college). Any help you can give me, even if it's just a spurt about what you know, would be greatly appreciated. Thanks guys!

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Are you a math major or an engineering major? I'm wondering because of the viewpoint.

I'd say "Adaptive Filter Theory" by Simon Haykin. Either the 2nd or the 4th edition (3rd edition is full of extra blah stuff, but the 4th puts back in the good stuff that was in 2 but left out of 3)

I'll say that personally I didn't get much out of my first linear algebra class (and I didn't take the second cause it was an elective). Almost all of what I know of linear alegebra I learned from Haykin and my class on adaptive filters (my professor - he is really more of a mathematician, so he covered the background stuff really well)

Although the book is aimed at a graduate level course, it's very readable.

Some of the things you might want to consider are the use of a Psuedo Inverse as the Least Squares solution to a filtering problem, or the application of Singular Value Decomposition in Signal Processing. Or you could consider discuss finding the gradient vector of a N-dimensional cost-function (fun stuff, but stick to the basics and make sure it has only a global minimum ;)

Other books:

Golub and VanLoan is a very good Linear Algebra book, but not a SP book. Very dense too.

Proakis and Manolokis is an alternative for a DSP book to the Oppenheim and Schafer suggestion Sir HC had. O&S is a much better book and would stay on your bookshelf longer as an engineer, but P&M is a bit more accessible for the beginner (yeah, I have both. Loved P&M while it school, but always grab O&S now).

Feel free to PM me with any specific questions. I'm hopefully teaching a class on adaptive filters next spring, so I will be freshening up on all of this fairly soon (I was supposed to start in Sept, but you know how things go)

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Originally posted by ck3

Math scares me ... though it may be interesting to become acquainted with the fundamental elements of effects algorythm programming.
:thu:



No way, d00d! All thet tehcnical mumbo jumbo jus gets in the way of bein a artist! Fuk the man and his math! Just play with some sole, and forgit all thet structured crap.

P.S. I am a genus and my music is awsome, and if you dont like it, you are a idiot and have horrible taste! :mad:

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Originally posted by ck3

Math scares me ... though it may be interesting to become acquainted with the fundamental elements of effects algorythm programming.
:thu:



You can get buy with a little, but if you want to understand the Fourier transform you'll need a little complex alegebra and calculus. If you don't want to understand it, you can just use an FFT. :D

As for the fundamental elements, you could look for those Signal Processing books that Sir HC and myself recommended.


If you have any specific questions, go ahead and ask. I teach a course to EEs on the engineering aspects of music. We cover alot of things including simulating effects in MATLAB. Last time we simulated the following: compressor, ring modulator, tremolo, distortion, delay, flanger and chorus (actually the same as a flanger, but different input values).

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What I hated most about my Calc, Diff Eq, and other math classes is that they purposely tried to avoid useful things. Instead of using surface integrals to solve for flux and the like we did bs with spheres whose density varied with the radius.

Complex numbers rule.

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thanks a lot guys. i'm a math major, not engineering, but we do a lot of application and this project is designed to give us a taste of the different types of application that are out there--i just chose one that was relevent to me. I think i'm going to do something with fourier analysis and the FFT but please keep the suggestions coming.

thanks!

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Originally posted by scottyboy85

thanks a lot guys. i'm a math major, not engineering, but we do a lot of application and this project is designed to give us a taste of the different types of application that are out there--i just chose one that was relevent to me. I think i'm going to do something with fourier analysis and the FFT but please keep the suggestions coming.


thanks!

 

 

Fourier's a good place to go. Look for the linear alebra version using the "tiddle factor" (I'm not kidding, that's the name of the matrix - it's in O&S).

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I've got and read almost all of th aforementioned texts but I think you really need something on an introductory level. Haykin is real heavy stuff. Proakis, O&S, etc are fairly heavy as well.

A good intro text on Sig Proc is Lyons' "Understanding Digital Signal Processing".

DFT and FFT are covered thoroughly so it would suit your project nicely.

I've been thinking about writing a book on modern signal processing techniques as applied towards effects processing. I wonder if I could get someone to publish it. Hmmmm.

CC

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Originally posted by jcn37203

I was just reading some linear algebra last night. When I got to the part where it looked like x was about to be divided by the square root of i, I had to put it down.

 

 

oh man, thats just were it starts to get good. I went through highschool with out ever doing any homework or studying in math.... id just show up for the test and ace it. imaginary numbers were cool, because it actually made me think in math class for once.... i didnt have to do that again until i got to matracies.

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Originally posted by hoerni


If you have any specific questions, go ahead and ask. I teach a course to EEs on the engineering aspects of music. We cover alot of things including simulating effects in MATLAB. Last time we simulated the following: compressor, ring modulator, tremolo, distortion, delay, flanger and chorus (actually the same as a flanger, but different input values).

 

 

MATLAB!! *wipes drool*

 

I think I have to go change my shorts now...

 

That sounds like an awesome class! Where?

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The basics of dsp really are not that math heavy. I'm not so great at math and did fine in various signal processing courses and a grad level course.

I'll also second CliffC's recommendation for Lyon's book, which is light on math, but will give you the basics. O&S paired with Lyon's would be a good combo.

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Originally posted by fractal



MATLAB!! *wipes drool*


I think I have to go change my shorts now...


That sounds like an awesome class! Where?



Yeah, I love MATLAB too. It's been my main language for the past 12 years or so. Most of the SP work I do at my main job (wireless signal process) is in MATLAB, and it's really great for quickly prototyping audio stuff.

I teach at the Cooper Union in NYC.

I've looked around for other similar classes, but the only thing I found that was close was at Columbia (also NYC).

BTW, we also cover the following:
- basic music theory and how to build scales in just and equal temperament
- basics of guitar pickups, microphones and speakers
- audio amplifier basics: class A,AB,B and D and vacuum tubes (I once "threatened" the department head about teaching vacuum tubes and I finally got my chance)
- little bit of synthesis: additive subtractive, wave table, etc
- MIDI including reading the file format
- Digital recording basics
- Psycho acoustics and Lossy compression (the MPEG standards)

It's a really fun course and I've been please to see it evolve from it's first offering in 1998 to the current form in 2005. It's kinda my baby as I'm the one who created it and the only one whos taught it here.

I have one of my presentations online at

http://www.cooper.edu/~hoerni/teach/eemusic/Effects_v6_files/frame.htm

I recently wrote up a guest lecture on the basics of digital sampling. Unfortunately, I may have overshot the technical level of class it was intended for. :( Looks like I'll be able to give it to a class of engineers soon. I'll be posting that as soon as I get a chance, so watch for it. (currently low on server space)

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Originally posted by sirhcathome



I am a Geek dear sir. You can't be a geek without a double E.

 

 

I am Northwestern student, dear sir. You can't be a Wildcat without a double Major.

 

Translation: I am a nerd of sorts, as well.

 

PS - I apologize for the poor attempt at a parody post.

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