30 lectures on Fourier transforms and not one mention of the Fourier transform over compact groups? (Which is arguably the most generalized/abstract formulation of the concept of a Fourier transform.) A lot of recent research has been done on FFTs over groups like the rotation group and the symmetric group, and this work has lead to significant progress on problems that were previously considered intractable.
The Fourier Transform and its Applications
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Re: The Fourier Transform and its Applications
#12I 'took' the stanford NLP course online it was great. Doing this one now. Funny - I did Fourier in Comp. Eng. - but it was jammed together with so many other things, I felt overwhelmed by all of it, I did enough to do decently on the exam, but I feel a lot of it was lost on me, and I forgot much of it. Using fourier in most computer applications is very rare! I'm excited to have a project I need to use it for - and w…
The prof noted that it's almost all EE folks, with a few others, but didn't mention Comp Sci. Can anyone comment on why there were seemingly no Comp Sci people in this class? Wouldn't this be 'core' to Comp Sci?
Not in this detail, no. And I bet there many are CS curricula where fourier transforms aren't in the core courses (or even not explicitly present at all).
It's only relevant for some application domains (and has no "pure" CS use case I can think of), so a basic idea what it does, as a single lecture in a maths course or so, is probably enough in many cases. If you go in an field that uses it, you hopefully learn it in more detail there (or go googling for resources like this...).
Re: The Fourier Transform and its Applications
#1330 lectures on Fourier transforms and not one mention of the Fourier transform over compact groups? (Which is arguably the most generalized/abstract formulation of the concept of a Fourier transform.) A lot of recent research has been done on FFTs over groups like the rotation group and the symmetric group, and this work has lead to significant progress on problems that were previously considered intractable.
Do you know of a link that does host such mentions?
Re: The Fourier Transform and its Applications
#14In case this is useful to anyone else: There's probably an easier way to do it, but if you want to get faster playback (2x is about as fast as I can comprehend this lecturer at), this line seems to do the trick: document.getElementById("myElement").querySelector("video").playbackRate = 2
document.getElementsByTagName('video')[0].playbackRate = 2;
Re: The Fourier Transform and its Applications
#15Web page didn't work for me on my Safari. YouTube works fine:
https://www.youtube.com/watch?v=gZNm7L96pfY
Re: The Fourier Transform and its Applications
#16This is an exceptional course. In my CS undergrad days, some 7 years ago, when I wanted to make sense of Fourier Series and Transform, this course was my savior. The mathematics text book had a dry and unintuitive treatment of the topics and electrical engineering, physics and computer science books mostly relegated the topics to a few pages in an appendix. I found this course and printed out the PDF of the lecture n…
> electrical engineering, physics and computer science books mostly relegated the topics to a few pages in an appendix.
Out of curiosity, is this really true? Perhaps I misunderstand you, but I have always been under the impression that Fourier Transform was a fundamental building block covered extensively in all EE curriculum?
I took Computer Engineering with some classes shared between Comp. Eng. and EE students. I probably had 2 full-semester classes dedicated to signal processing and fourier transforms. Additionally I took a math course that covered Fourier and Laplace transforms.
Re: The Fourier Transform and its Applications
#17There is this hard question that is often glossed over in a first course on Fourier analysis: We learn that the Fourier transform of f(t) is an integral of exp(iwt)f(t) over all t. But when we look at a table of Fourier transform pairs, we find things like the Fourier transform of a constant function (is the Dirac delta). Integral does not converge? WTF?
I really think Prof. Osgood hits a sweet spot of not sweeping this under the carpet, and not becoming a course on functional/integration theory. I'm a postdoc in theoretical physics, and use these transforms regularly, and I have yet to find a more honest but still useful introduction (although I understand that real mathematicians cringe at my abuse of mathematics.. :)
edit: typo
Re: The Fourier Transform and its Applications
#18This is an exceptional course. In my CS undergrad days, some 7 years ago, when I wanted to make sense of Fourier Series and Transform, this course was my savior. The mathematics text book had a dry and unintuitive treatment of the topics and electrical engineering, physics and computer science books mostly relegated the topics to a few pages in an appendix. I found this course and printed out the PDF of the lecture n…
> electrical engineering, physics and computer science books mostly relegated the topics to a few pages in an appendix. Out of curiosity, is this really true? Perhaps I misunderstand you, but I have always been under the impression that Fourier Transform was a fundamental building block covered extensively in all EE curriculum? I took Computer Engineering with some classes shared between Comp. Eng. and EE students. I…
He probably didn't study electrical engineering, or switched out of it before signals and systems.
Re: The Fourier Transform and its Applications
#19This is an exceptional course. In my CS undergrad days, some 7 years ago, when I wanted to make sense of Fourier Series and Transform, this course was my savior. The mathematics text book had a dry and unintuitive treatment of the topics and electrical engineering, physics and computer science books mostly relegated the topics to a few pages in an appendix. I found this course and printed out the PDF of the lecture n…
I think oppenheim's book, and the 6.007 mitocw course explains fourier analysis pretty well
Re: The Fourier Transform and its Applications
#20I 'took' the stanford NLP course online it was great. Doing this one now. Funny - I did Fourier in Comp. Eng. - but it was jammed together with so many other things, I felt overwhelmed by all of it, I did enough to do decently on the exam, but I feel a lot of it was lost on me, and I forgot much of it. Using fourier in most computer applications is very rare! I'm excited to have a project I need to use it for - and w…
The prof noted that it's almost all EE folks, with a few others, but didn't mention Comp Sci. Can anyone comment on why there were seemingly no Comp Sci people in this class? Wouldn't this be 'core' to Comp Sci?
Maybe at Carneigie Mellon, or the better universities. In a typical uni comp sci is a programming monkey degree (at least in Australia...)