Fourier Analysis: Discrete Series & Transform

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A user is seeking beginner-friendly resources on Fourier analysis, specifically focusing on the discrete series and transform for a project related to waves. They have a background in linear algebra and trigonometry but need foundational material. Recommendations include the classic text by Körner, though the user prefers downloadable internet sources in PDF format. Additional suggestions include a collection of eight books on Fourier analysis, some available in DjVu format, and links to video resources. The emphasis is on accessible materials that can be easily obtained online.
Omri
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Hello all,

I'm looking for a good textbook, tutorial or anything like that about Fourier analysis: the discrete series and the Transform (very important - for a project about waves). I don't know a lot about Fourier analysis, so this textbook should start quite from the beginning. What I do know pretty well that might be relevant is linear algebra and (obviously) trigonometry.

Thank you very much for your help! :-)
 
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The classic text I believe is Körner. But it is an analysis text.
 
Actually I meant internet sources, preferably ones that I can download to my computer, like PDF files.
 
Please? It's important to me...
 
Hope this helps.

Here are 8 books on Fourier analysis. Some are in DjVu format. To view those files, download DjVu reader.
Download from this http://rapidshare.com/files/60774362/Fourier_Analysis.zip.html.
Here are some http://video.google.com/videosearch?num=10&so=0&hl=en&q=fourier+analysis+duration%3Along&start=0 on Fourier analysis as well.
 

Thread 'Proving that convexity implies second order derivative being positive'

There are probably loads of proofs of this online, but I do not want to cheat. Here is my attempt: Convexity says that $$f(\lambda a + (1-\lambda)b) \leq \lambda f(a) + (1-\lambda) f(b)$$ $$f(b + \lambda(a-b)) \leq f(b) + \lambda (f(a) - f(b))$$ We know from the intermediate value theorem that there exists a ##c \in (b,a)## such that $$\frac{f(a) - f(b)}{a-b} = f'(c).$$ Hence $$f(b + \lambda(a-b)) \leq f(b) + \lambda (a - b) f'(c))$$ $$\frac{f(b + \lambda(a-b)) - f(b)}{\lambda(a-b)}...
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