I taught digital signal processing once to MS and PhD students without knowing the field. For what it's worth, I validate Ed's observations. (In my defense, I got very good student evaluations)
--- Frank C. Wimberly 140 Calle Ojo Feliz, Santa Fe, NM 87505 505 670-9918 Santa Fe, NM 87505 On Mon, Aug 15, 2022, 3:14 PM Angel Edward <[email protected]> wrote: > Sorry I missed the discussion. I was in Vancouver all week for SIGGRAPH. > > A few comments after looking at the two websites. I taught Fourier > transforms for many years both through digital signal processing and though > optics as part of a course on hybrid processing at the Institute of Optics > at Rochester. > > The main problem with these sites is that they fail to distinguish between > the continuous Fourier transform and the discrete Fourier transform, which > have major differences that affect what you see in the examples. In > particular, you need to talk about sampling and reconstruction to talk > about the DFT. The Nyqist sampling theorem is key to understanding the > effects of windowing in space or frequency, the uncertainty principle for > the transforms, the limits of displays and the artifacts due the windows. > In the transforms in the second site, I’m pretty certain that all the > dominant frequencies in the transforms are window artifacts and not due to > the data. At least the first site gives you the option of applying a > spatial window to the data although it doesn’t give you a way to understand > some of the displays you can generate with window applied to band limited > data. > > There is an Appendix in my books about the FT and I have some notes from a > summer short course at the Institute of Optics that cover these issues. > > Ed > __________ > > Ed Angel > > Founding Director, Art, Research, Technology and Science Laboratory (ARTS > Lab) > Professor Emeritus of Computer Science, University of New Mexico > > 1017 Sierra Pinon > Santa Fe, NM 87501 > 505-984-0136 (home) [email protected] > 505-453-4944 (cell) http://www.cs.unm.edu/~angel > > On Aug 12, 2022, at 2:09 PM, Stephen Guerin <[email protected]> > wrote: > > Jon, Mike and I were talking about fourier transforms on images, JPEG > compression and filtering at this morning's FRIAM. > > Here's a nice site that lets you load an image, and its fourier transform > (amplitude spectrum) in cartesian or log-polar. > https://www.djmannion.net/img_freq_web/ > > A menu allows you to pull up sample images, simple sine waves in various > frequencies and orientation and a live webcam image to see their point > dualities in fourier space. > > The lower panel lets you filter high and low cutoffs (much like jpeg > compression) to see the impact on the image. > > links related to compression: > > https://blog.demofox.org/2020/11/04/frequency-domain-image-compression-and-filtering/ > > https://micro.magnet.fsu.edu/primer/java/digitalimaging/processing/fouriertransform/ > > different but related use of fourier transform for finding epicycles in a > drawing: > > - https://www.jezzamon.com/fourier/ > - https://www.myfourierepicycles.com/ > > > -S > > > _______________________________________________________________________ > [email protected] <[email protected]> > CEO, https://www.simtable.com <http://www.simtable.com/> > 1600 Lena St #D1, Santa Fe, NM 87505 > office: (505)995-0206 mobile: (505)577-5828 > -. --- - / ...- .- .-.. .. -.. / -- --- .-. ... . / -.-. --- -.. . > FRIAM Applied Complexity Group listserv > Fridays 9a-12p Friday St. Johns Cafe / Thursdays 9a-12p Zoom > https://bit.ly/virtualfriam > to (un)subscribe http://redfish.com/mailman/listinfo/friam_redfish.com > FRIAM-COMIC http://friam-comic.blogspot.com/ > archives: 5/2017 thru present > https://redfish.com/pipermail/friam_redfish.com/ > 1/2003 thru 6/2021 http://friam.383.s1.nabble.com/ > > > -. --- - / ...- .- .-.. .. -.. / -- --- .-. ... . / -.-. --- -.. . > FRIAM Applied Complexity Group listserv > Fridays 9a-12p Friday St. Johns Cafe / Thursdays 9a-12p Zoom > https://bit.ly/virtualfriam > to (un)subscribe http://redfish.com/mailman/listinfo/friam_redfish.com > FRIAM-COMIC http://friam-comic.blogspot.com/ > archives: 5/2017 thru present > https://redfish.com/pipermail/friam_redfish.com/ > 1/2003 thru 6/2021 http://friam.383.s1.nabble.com/ >
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