<html><head><meta http-equiv="Content-Type" content="text/html; charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class="">Sorry I missed the discussion. I was in Vancouver all week for SIGGRAPH.<div class=""><br class=""></div><div class="">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.</div><div class=""> </div><div class="">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.</div><div class=""><br class=""></div><div class="">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.</div><div class=""><br class=""></div><div class="">Ed</div><div class=""><div class="">
<div>__________<br class=""><br class="">Ed Angel<br class=""><br class="">Founding Director, Art, Research, Technology and Science Laboratory (ARTS Lab)<br class="">Professor Emeritus of Computer Science, University of New Mexico<br class=""><br class="">1017 Sierra Pinon<br class="">Santa Fe, NM 87501<br class="">505-984-0136 (home)<span class="Apple-tab-span" style="white-space: pre;"> </span> <span class="Apple-tab-span" style="white-space: pre;"> </span><a href="mailto:edward.angel@gmail.com" class="">edward.angel@gmail.com</a><br class="">505-453-4944 (cell) <span class="Apple-tab-span" style="white-space: pre;"> </span><span class="Apple-tab-span" style="white-space: pre;"> </span>http://www.cs.unm.edu/~angel<br class=""></div>
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<div><br class=""><blockquote type="cite" class=""><div class="">On Aug 12, 2022, at 2:09 PM, Stephen Guerin <<a href="mailto:stephen.guerin@simtable.com" class="">stephen.guerin@simtable.com</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><div dir="ltr" class="">Jon, Mike and I were talking about fourier transforms on images, JPEG compression and filtering at this morning's FRIAM.<div class=""><br class=""></div><div class="">Here's a nice site that lets you load an image, and its fourier transform (amplitude spectrum) in cartesian or log-polar.<br class=""> <a href="https://www.djmannion.net/img_freq_web/" class="">https://www.djmannion.net/img_freq_web/</a></div><div class=""><br class=""></div><div class=""> 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.<br class=""><br class="">The lower panel lets you filter high and low cutoffs (much like jpeg compression) to see the impact on the image.</div><div class=""><br class=""></div><div class="">links related to compression:<br class=""> <a href="https://blog.demofox.org/2020/11/04/frequency-domain-image-compression-and-filtering/" class="">https://blog.demofox.org/2020/11/04/frequency-domain-image-compression-and-filtering/</a><br class=""> <a href="https://micro.magnet.fsu.edu/primer/java/digitalimaging/processing/fouriertransform/" class="">https://micro.magnet.fsu.edu/primer/java/digitalimaging/processing/fouriertransform/</a></div><div class=""><br class=""></div><div class="">different but related use of fourier transform for finding epicycles in a drawing:<br class=""><ul class=""><li class=""><a href="https://www.jezzamon.com/fourier/" class="">https://www.jezzamon.com/fourier/</a> </li><li class=""><a href="https://www.myfourierepicycles.com/" class="">https://www.myfourierepicycles.com/</a><br class=""></li></ul></div><div class=""><br class=""></div><div class="">-S<br class=""><br class=""><br clear="all" class=""><div class=""><div dir="ltr" class="gmail_signature" data-smartmail="gmail_signature"><div dir="ltr" class=""><div dir="ltr" class=""><div dir="ltr" class="">_______________________________________________________________________<br class=""><a href="mailto:stephen.guerin@simtable.com" target="_blank" class="">Stephen.Guerin@Simtable.com</a><div class="">CEO, <a href="http://www.simtable.com/" target="_blank" class="">https://www.simtable.com</a><br class=""><div class="">1600 Lena St #D1, Santa Fe, NM 87505<div class=""><div class="">office: (505)995-0206 <span style="font-size:12.8px" class="">mobile: (505)577-5828</span></div><div class=""></div></div></div></div></div></div></div></div></div></div></div>
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