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DTSTART:20070311T020000
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DTSTAMP:20260307T204322
DTSTART;TZID=America/Detroit:20260330T160000
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SUMMARY:Workshop / Seminar:GLNT: How you think on a function defined on 0\,1\,…\,N-1?
DESCRIPTION:Abstract: Between thousand to million times per day\, your cellphone calculates the Fourier Transform (FT) of certain complex valued functions defined on 0\,1\,…\,N-1\, with N large (order of magnitude of thousands and more). \nThe calculation is done using the Fast Fourier Transform (FFT) - discovered by Cooley--Tukey in 1965 and by Gauss in 1805. \n\nIn the lecture I want to advertise a beautiful way—due to Auslander-Tolimieri—to obtain the FFT as a natural consequence of an answer to the following:\n\nQuestion: How to think on the space of functions on the set 0\,1\,…\,N-1?                              \n\nEngineers tell us that there are two answers for this question:\n\n(A) as functions on that set\, where 0\,1\,…\,N-1 regarded as times\; and\,\n\n(B) as functions on that set\, where 0\,1\,…\,N-1 regarded frequencies\;\n\nand then the FT is an operator translating between the two spaces. \n\nIn the lecture\, I will explain that there is another answer\, i.e.\, a not so well-known third space (C)\, of arithmetic nature\, that also gives an answer to the above question\, and then the FFT appears simply as the composition of two operators: \nthe one translating between spaces (A) and (C)\, and the one that translates (C) to (B).\n\nRemark: The lecture is prepared to be understood by undergraduate students (from any department) who took basic course in linear algebra.
UID:143323-21892902@events.umich.edu
URL:https://events.umich.edu/event/143323
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 4096
CONTACT:
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