"Richard (Rick) Lyons" <r.lyons@ieee.org> writes:> On Friday, December 20, 2019 at 9:31:12 PM UTC-8, Randy Yates wrote: >> "Richard (Rick) Lyons" <r.lyons@ieee.org> writes: >> >> > On Monday, December 16, 2019 at 9:13:02 PM UTC-8, dbd wrote: >> >> >> >> The evangelists who wish to interpret the output of the DFT as samples of the Fourier Transform must assume that the input is periodic in the DFT size. >> >> >> >> Dale B Dalrymple >> > >> > Hi Dale (and Steve Pope). The notion of periodicity is much more >> > complicated than we first thought when we began to learn DSP >> > theory. College DSP textbooks say that an x(n) sequence has a >> > period of N samples if and only if: >> > >> > x[n+N] = x[n] for all n. >> > >> > But that equality is ONLY true for infinite-length sequences, and >> > infinite-length sequences do not exist in reality. >> >> Neither do numbers. >> -- >> Randy Yates > > Randy, ...you rapscallion!! Ha ha. > Now you're forcing me to decide if the number 3 exists.> I THOUGHT IT DID.(emphasis mine) Well now that's interesting. Can you show me the number "3" Rick? I don't mean one of a number of "representations" of the number "3," e.g., using Roman numerals written in blue ink pen on one of Ziggy's thank-you notes in your handwriting (possibly while slightly intoxicated), but: !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! THE ONE AND ONLY NUMBER "3." !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Betcha can't. In my book, that makes it abstract: only a concept; not existing in the real world. And that was my point: if you insist that one concept must be dismissed solely because it is abstract, you must dismiss them all, and this would lead to a total breakdown of science, physics, and mathematics as we know them today. So perhaps it would be good to rethink periodicity and infinite-length sequences.> [...] > Randy, does the musical note "middle C" exist?Well, it depends on what you mean by "middle C." If you mean a note with the exact frequency 440 * (2^(1/12))^3 Hz, then no (please, let's not get into temperaments!). If you mean the 3rd white note C from the lowest C on a piano, then yes (on most pianos). Finally, I must thank you for expanding my vocabulary: I don't remember ever hearing of the word "rapscallion" before this. Thank you! I am not sure if I'm OK with being referred to as one, but thanks for the word anyway! -- Randy Yates, DSP/Embedded Firmware Developer Digital Signal Labs http://www.digitalsignallabs.com
mirroring a signal before FFT - why?
Started by ●December 14, 2019
Reply by ●December 26, 20192019-12-26
Reply by ●December 29, 20192019-12-29
On Thursday, December 26, 2019 at 1:29:45 PM UTC-8, Randy Yates wrote:> > Well now that's interesting. Can you show me the number "3" Rick? I > don't mean one of a number of "representations" of the number "3," e.g., > using Roman numerals written in blue ink pen on one of Ziggy's thank-you > notes in your handwriting (possibly while slightly intoxicated), but: > > !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! > THE ONE AND ONLY NUMBER "3." > !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! > > Betcha can't. > > In my book, that makes it abstract: only a concept; not existing in the > real world.Hi Randy. Over the last few days I've been thinkin' about the question, "Does the number 3 exist?" My current opinion is: No. The number 3 does not exist. But this whole discussion troubles me because (don't laugh at me) I believe Santa Claus exists. So now you'll ask me, "How could Santa Claus exist but the number 3 does not exist?" I have to think more about all of this.> And that was my point: if you insist that one concept must be dismissed > solely because it is abstract, you must dismiss them all, and this would > lead to a total breakdown of science, physics, and mathematics as we > know them today.Wait, I didn't say that abstract ideas should be dismissed. The abstract notion of a perfect circle is a useful idea in math field of geometry. And the same can be said for the abstract notion of one of Euclid's lines having infinite length and zero thickness.> So perhaps it would be good to rethink periodicity and infinite-length > sequences.My main point was that the college textbook definition of "periodicity" does not apply to any discrete sequence that we will ever encounter (or ever generate) in practice.> Finally, I must thank you for expanding my vocabulary: I don't remember > ever hearing of the word "rapscallion" before this. Thank you! I am > not sure if I'm OK with being referred to as one, but thanks for > the word anyway!NO OFFENSE INTENDED. My guess is that the word "rapscallion" is a couple of hundred years old. To me the word means "a likeable guy who makes innocent trouble strictly for entertainment purposes", i.e., one who is playfully mischievous. (Huckleberry Finn, the boy created by Mark Twain, was a rapscallion. So, ha ha, you're in good company Randy!)
Reply by ●December 29, 20192019-12-29
"Richard (Rick) Lyons" <r.lyons@ieee.org> writes:> On Thursday, December 26, 2019 at 1:29:45 PM UTC-8, Randy Yates wrote: >> >> Well now that's interesting. Can you show me the number "3" Rick? I >> don't mean one of a number of "representations" of the number "3," e.g., >> using Roman numerals written in blue ink pen on one of Ziggy's thank-you >> notes in your handwriting (possibly while slightly intoxicated), but: >> >> !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! >> THE ONE AND ONLY NUMBER "3." >> !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! >> >> Betcha can't. >> >> In my book, that makes it abstract: only a concept; not existing in the >> real world. > > Hi Randy. Over the last few days I've been thinkin' about > the question, "Does the number 3 exist?" My current opinion > is: No. The number 3 does not exist. > > But this whole discussion troubles me because (don't laugh > at me) I believe Santa Claus exists. So now you'll ask me, > "How could Santa Claus exist but the number 3 does not exist?" > I have to think more about all of this. > >> And that was my point: if you insist that one concept must be dismissed >> solely because it is abstract, you must dismiss them all, and this would >> lead to a total breakdown of science, physics, and mathematics as we >> know them today. > > Wait, I didn't say that abstract ideas should be dismissed. > The abstract notion of a perfect circle is a useful idea in > math field of geometry. And the same can be said for the > abstract notion of one of Euclid's lines having infinite > length and zero thickness. > >> So perhaps it would be good to rethink periodicity and infinite-length >> sequences. > > My main point was that the college textbook definition > of "periodicity" does not apply to any discrete sequence > that we will ever encounter (or ever generate) in practice.Well, yeah, that's true. There are no infinite-length sequences in reality. There are no lines in reality. There are no circles in reality. There are no Dirac delta functions in reality. Sinusoids don't exist. Etc., etc. What of it? How is this fact pertinent to your point? In fact, color me thick, but I'm not exactly sure what your point even is. Can you please break it down to simple (but accurate) terms for me?>> Finally, I must thank you for expanding my vocabulary: I don't remember >> ever hearing of the word "rapscallion" before this. Thank you! I am >> not sure if I'm OK with being referred to as one, but thanks for >> the word anyway! > > NO OFFENSE INTENDED. > My guess is that the word "rapscallion" is a couple > of hundred years old. To me the word means "a likeable > guy who makes innocent trouble strictly for entertainment > purposes", i.e., one who is playfully mischievous. > (Huckleberry Finn, the boy created by Mark Twain, > was a rapscallion. So, ha ha, you're in good company Randy!)Gosh, I almost feel special now... :) -- Randy Yates, DSP/Embedded Firmware Developer Digital Signal Labs http://www.digitalsignallabs.com
Reply by ●January 27, 20202020-01-27
On Thursday, December 26, 2019 at 1:29:45 PM UTC-8, Randy Yates wrote: (sni, someone wrote)> > I THOUGHT IT DID.> (emphasis mine)> Well now that's interesting. Can you show me the number "3" Rick? I > don't mean one of a number of "representations" of the number "3," e.g., > using Roman numerals written in blue ink pen on one of Ziggy's thank-you > notes in your handwriting (possibly while slightly intoxicated), but:> !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! > THE ONE AND ONLY NUMBER "3." > !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!Reminds me of the proof that there is no least interesting number. 1: Assume that there is a least interesting number. 2: That number would be very interesting, as it has a property that no other number has. 3: So it isn't least interesting after all. And definitely it isn't the number 3.
Reply by ●January 27, 20202020-01-27
On Tuesday, December 17, 2019 at 5:36:07 AM UTC-8, Richard (Rick) Lyons wrote: (snip)> Hi Dale (and Steve Pope). The notion of periodicity is much more > complicated than we first thought when we began to learn DSP theory. > College DSP textbooks say that an x(n) sequence has a period of > N samples if and only if:> x[n+N] = x[n] for all n.> But that equality is ONLY true for infinite-length sequences, > and infinite-length sequences do not exist in reality. > An infinite-length sequence is an abstract idea, ...like a perfect > circle or one of Euclid's lines having infinite length and > zero thickness. What this means is that, based on the above > periodicity definition, we will never encounter, nor ever > be able to generate, a periodic sequence in our real world.This is bad, as much of physics, especially quantum mechanics, depends on Fourier transforms with t from -infinity to +infinity, or in higher dimension, over all space.
Reply by ●January 27, 20202020-01-27
On Sunday, December 15, 2019 at 8:31:26 PM UTC-8, Richard (Rick) Lyons wrote:> On Sunday, December 15, 2019 at 1:20:36 AM UTC-8, Christian Gollwitzer wrote: > > Am 15.12.19 um 03:44 schrieb hdre..@freenet.de:> > The FFT assumes that the input signal is periodic and > > repeats infinitely many times.> The unfortunately popular notion that "The FFT assumes its input > is periodic" must surely be the most profound misconception > in all of DSP. The FFT cannot make assumptions. Making an > assumption is a mental activity. Only a living creature with > a brain can make an assumption.I suppose so. But consider that the Fourier series is made up as a sum of periodic functions with the same period. Mathematically, the sum is also periodic with that period. So, who is making assumptions? There are transforms with other properties, but Fourier chose those functions when making the Fourier series. Does that move Fourier's assuming into the transform? Why can only living creatures with a brain make assumptions? Can robots with an electronic brain make assumptions? Or are the assumptions built-in by the designers and builders of the robot? Now consider a robot constructed to do some operation given some inputs, and maybe stretching it somewhat, the Fourier series is a robot that, given some input gives some other output. The assumptions that went into its design determine those outputs. To me, it isn't so hard to say that the robot makes assumptions based on the properties given to it by its designer. Even more, what is it that gives biochemical brains the ability to make assumptions but electronic ones don't have that ability? Both are built out of quantum-mechanical atoms and molecules, yet we give special properties to some, and not to others.
