
The Fourier Transform and its Applications - bsilvereagle
http://see.stanford.edu/see/courseInfo.aspx?coll=84d174c2-d74f-493d-92ae-c3f45c0ee091
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pling
Finest resource of Fourier transforms here:
[http://betterexplained.com/articles/an-interactive-guide-
to-...](http://betterexplained.com/articles/an-interactive-guide-to-the-
fourier-transform/)

This is the one that made me get it in the end.

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jonahx
Thanks for the link. His website is terrific. He offers some perspectives for
gaining intuition about complex numbers that I'd never heard before, even
after all these years. This should be required reading for HS math students.

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j2kun
Brad Osgood's lectures are phenomenal. He was trained as a mathematician, so
his explanations are crystal clear in terms of definitions and where
physicists sweep mathematical formalisms under the rug. After watching his
entire lecture for this course, and spending a lot of time reading the course
reader, I learned a lot about how to decrypt the kind of mathematical nonsense
that physicists tend to say (as well as learning about the real foundations,
c.f. tempered distributions and others).

That being said, a lot of these lectures can be summarized in a few sentences
if you already have a strong foundation in linear algebra. For example, the
fact that complex exponentials form an orthonormal basis for periodic
functions is the content of the first handful of lectures, and deriving the
Fourier transform is only slightly messier to explain in terms of linear
algebra (this is not because of the linear algebra but because Fourier
transforms are inherently a little messy).

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sliverstorm
The Fourier transform is possibly my favorite mathematical function, and the
closest I've ever been to "Whoa, math is beautiful". Ironically enough, I
reached this conclusion in a signal analysis class, not a math class.

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dalacv
Laplace transform is better. So nannynannybooboo

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zwieback
FT goes from -inf to +inf, LT only 0 to +inf. So, FT is twice as good as LT.

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flpgr
The Fourier Transform is just a special case of the bilateral LT. Laplace wins
=)

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mjcohen
Come to me my Mellin-choly baby!

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jbert
I'm interested in understanding more about the use of the transform in
discrete signal processing. I wish I had the time to try and absorb 30 50min
lectures, but I probably don't.

Can anyone recommend a more limited course or tutorial focussing on that, or
should I try and extract particular lectures from this course?

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badsock
Maybe try this:
[http://www.dspguide.com/ch8.htm](http://www.dspguide.com/ch8.htm)

Really great book in any case.

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jbert
Looks good. Thanks!

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cedias
If anyone is looking for a quick intro to FT this was posted on HN a few month
ago: [http://nautil.us/blog/the-math-trick-behind-mp3s-jpegs-
and-h...](http://nautil.us/blog/the-math-trick-behind-mp3s-jpegs-and-homer-
simpsons-face)

~~~
bdevine
Yes, I remember that well. Seeing the animated graphics linked within that
article really was an 'ah ha!' moment for me; I'd definitely recommend it as
an introductory intuitive motivation.

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dfan
In the same sequence, Stephen Boyd's course Introduction to Linear Dynamical
Systems
([http://see.stanford.edu/see/courseinfo.aspx?coll=17005383-19...](http://see.stanford.edu/see/courseinfo.aspx?coll=17005383-19c6-49ed-9497-2ba8bfcfe5f6))
is also excellent. The title sounds pretty specific but it is really about a
wide range of applied linear algebra. Boyd's lecture style is a little
idiosyncratic but he's great about constantly emphasizing how to gain an
intuitive qualitative sense of what everything means.

He also has a couple of courses on convex optimization that cover the theory
behind a lot of machine learning.

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quarterwave
These are excellent lectures! I saw Chap 4, and it was very satisfying to
watch the introduction to convergence, L2 norm, inner product etc.
Technically, Fourier transform requires only the L1 norm (the 'Manhattan
distance') to be finite, but L2 intersection L1 is a superb way to motivate
distributions. These lectures must be made required viewing for all students
of engineering and mathematical sciences.

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juanre
I took a class from Stanford with this name many years ago and it was an eye-
opener. Bracewell's book of the same name is wonderful as well
([http://www.amazon.com/Fourier-Transform-Its-
Applications/dp/...](http://www.amazon.com/Fourier-Transform-Its-
Applications/dp/0070070156/)).

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EpiMath
Also from Stanford, from longer ago... The Fourier Transform and its
Applications by Bracewell. McGraw-Hill. Extremely well written with great
examples and some fascinating problems. I highly recommend it. Discrete
transforms are a bit of an afterthought in a final chapter, but enough to dig
in and see how the FFT works.

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feelix
After spending hours searching, I ended up finding the way I wish I'd seen it
explained in the beginning:
[http://www.altdevblogaday.com/2011/05/17/understanding-
the-f...](http://www.altdevblogaday.com/2011/05/17/understanding-the-fourier-
transform/)

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autokad
thanks stanford, and thanks ycombinator, i really look forward to going over
these lessons

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jokoon
isn't DSL internet an application from this theorem ?

