http://answers.yahoo.com/question/index?qid=1006051531250
The Fourier transform in nature not just time<>frequency domain
Started by ●March 6, 2009
Reply by ●March 6, 20092009-03-06
Reply by ●March 6, 20092009-03-06
"Rune Allnor" <allnor@tele.ntnu.no> wrote in message news:9ab6ef27-b5fc-4f4a-8af7-1abe088fcf47@p11g2000yqe.googlegroups.com... On 6 Mar, 18:37, makol...@yahoo.com wrote:> I was enlightened to read here the other day that the Fourier > Transform also describes the relationship in electromagnetics > between the current distribution and the far field radiation > pattern.!The next obvious step on your path to Nirvana (or the !looney bin, whichever is closer) is to investigate why[*] !2+2=4 in such diverse fields as ! !- Maths !- Physics !- Economy !- Medicine !- and so on. ! !In fact, it't hard to come up with a single case !where 2+2=/=4. Now, *that's* food for tought. !Preferably somebody else's, but still. It is a great pity when those who would be the pundits of this NG seek personal satisfaction by pooh-poohing the expressed sense of academic excitement of a newbie. Such excitement is to be encouraged and nurtured.
Reply by ●March 6, 20092009-03-06
Jerry Avins wrote:> makolber@yahoo.com wrote: >> The Fourier transform in nature not just time<>frequency domain >> >> Most everyone here knows that the FT describes the relationship >> between a waveform in the time domain and the frequency domain. >> >> I was enlightened to read here the other day that the Fourier >> Transform also describes the relationship in electromagnetics >> between the current distribution and the far field radiation >> pattern. Yep, they have sidelobes just like in waveforms... >> >> So ... >> >> I thought it would be fun and interesting to ask the group to come up >> with a list of other pairings in nature whose relationship can be >> described by the FT. > > Optics also involve EM fields. It is nevertheless interesting to note > that the image seen in a microscope eyepiece is the FT of another plane > in the microscope tube that is plainly visible if you know where to look > and have the tool to look there. > > JerryFor that matter, the image that you see when you point a telescope at a point source is the Fourier transform of the aperture of the telescope. (See Airy rings, which are the 'ringing' of the 2-D FT of a circle.) -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Do you need to implement control loops in software? "Applied Control Theory for Embedded Systems" gives you just what it says. See details at http://www.wescottdesign.com/actfes/actfes.html
Reply by ●March 6, 20092009-03-06
On Mar 6, 6:58�pm, "Alun" <no.spam.thank....@invalid.invalid> wrote:> "Rune Allnor" <all...@tele.ntnu.no> wrote in message > > news:9ab6ef27-b5fc-4f4a-8af7-1abe088fcf47@p11g2000yqe.googlegroups.com... > On 6 Mar, 18:37, makol...@yahoo.com wrote: > > > I was enlightened to read here the other day that the Fourier > > Transform also describes the relationship in electromagnetics > > between the current distribution and the far field radiation > > pattern. > > !The next obvious step on your path to Nirvana (or the > !looney bin, whichever is closer) is to investigate why[*] > !2+2=4 in such diverse fields as > ! > !- Maths > !- Physics > !- Economy > !- Medicine > !- and so on. > ! > !In fact, it't hard to come up with a single case > !where 2+2=/=4. Now, *that's* food for tought. > !Preferably somebody else's, but still. > > It is a great pity when those who would be the pundits of > this NG seek personal satisfaction by pooh-poohing > the expressed sense of academic excitement of a newbie. > > Such excitement is to be encouraged and nurtured.Personally I have been unhealthily fascinated by the FT of log-time- sampled signals and it's relationship to the Reimann Hypothesis (see ref below). http://sail.usc.edu/~georgiou/pdfs/0400077.pdf It has the additional motivating factor of a 1 million dollar reward for it's solution. Which, of course, I would immediately invest in the stock market. Bob
Reply by ●March 6, 20092009-03-06
Tim Wescott wrote:> Jerry Avins wrote: >> makolber@yahoo.com wrote: >>> The Fourier transform in nature not just time<>frequency domain >>> >>> Most everyone here knows that the FT describes the relationship >>> between a waveform in the time domain and the frequency domain. >>> >>> I was enlightened to read here the other day that the Fourier >>> Transform also describes the relationship in electromagnetics >>> between the current distribution and the far field radiation >>> pattern. Yep, they have sidelobes just like in waveforms... >>> >>> So ... >>> >>> I thought it would be fun and interesting to ask the group to come up >>> with a list of other pairings in nature whose relationship can be >>> described by the FT. >> >> Optics also involve EM fields. It is nevertheless interesting to note >> that the image seen in a microscope eyepiece is the FT of another >> plane in the microscope tube that is plainly visible if you know where >> to look and have the tool to look there. >> >> Jerry > > For that matter, the image that you see when you point a telescope at a > point source is the Fourier transform of the aperture of the telescope. > (See Airy rings, which are the 'ringing' of the 2-D FT of a circle.)I chose to be specific. The optics of a microscope and a telescope differ only in the focal length of the objective, and in matters of implementation detail (like mounting). What is true of one is true of the other. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●March 6, 20092009-03-06
cpshah99 wrote:> http://answers.yahoo.com/question/index?qid=1006051531250wrong answer in context 2 + 2 < 4
Reply by ●March 7, 20092009-03-07
On 7 Mar, 00:58, "Alun" <no.spam.thank....@invalid.invalid> wrote:> "Rune Allnor" <all...@tele.ntnu.no> wrote in message > > news:9ab6ef27-b5fc-4f4a-8af7-1abe088fcf47@p11g2000yqe.googlegroups.com... > On 6 Mar, 18:37, makol...@yahoo.com wrote: > > > I was enlightened to read here the other day that the Fourier > > Transform also describes the relationship in electromagnetics > > between the current distribution and the far field radiation > > pattern. > > !The next obvious step on your path to Nirvana (or the > !looney bin, whichever is closer) is to investigate why[*] > !2+2=4 in such diverse fields as > ! > !- Maths > !- Physics > !- Economy > !- Medicine > !- and so on. > ! > !In fact, it't hard to come up with a single case > !where 2+2=/=4. Now, *that's* food for tought. > !Preferably somebody else's, but still. > > It is a great pity when those who would be the pundits of > this NG seek personal satisfaction by pooh-poohing > the expressed sense of academic excitement of a newbie. > > Such excitement is to be encouraged and nurtured.I could agree with you in principle, but the timing is wrong. I would assume one is at least a couple of years into college or university levels before one gets to know the FT; let's assume students to be of age at least 20. By that time, it ought to be clear to students that mathemathichs is a universal too which does not depend on context. Problem formulations and boundary conditions vary, but maths doesn't. The fact that the OP apparently realizes this general validity of maths in the context of the FT - which means he has some 15 years of previos exposure to maths - is a sign that there is something seriously missing with his insights into the basic tools of engineering. Rune
Reply by ●March 7, 20092009-03-07
On Mar 7, 4:13�am, Rune Allnor <all...@tele.ntnu.no> wrote:> On 7 Mar, 00:58, "Alun" <no.spam.thank....@invalid.invalid> wrote: > > > > > > > "Rune Allnor" <all...@tele.ntnu.no> wrote in message > > >news:9ab6ef27-b5fc-4f4a-8af7-1abe088fcf47@p11g2000yqe.googlegroups.com... > > On 6 Mar, 18:37, makol...@yahoo.com wrote: > > > > I was enlightened to read here the other day that the Fourier > > > Transform also describes the relationship in electromagnetics > > > between the current distribution and the far field radiation > > > pattern. > > > !The next obvious step on your path to Nirvana (or the > > !looney bin, whichever is closer) is to investigate why[*] > > !2+2=4 in such diverse fields as > > ! > > !- Maths > > !- Physics > > !- Economy > > !- Medicine > > !- and so on. > > ! > > !In fact, it't hard to come up with a single case > > !where 2+2=/=4. Now, *that's* food for tought. > > !Preferably somebody else's, but still. > > > It is a great pity when those who would be the pundits of > > this NG seek personal satisfaction by pooh-poohing > > the expressed sense of academic excitement of a newbie. > > > Such excitement is to be encouraged and nurtured. > > I could agree with you in principle, but the timing is > wrong. I would assume one is at least a couple of years > into college or university levels before one gets to > know the FT; let's assume students to be of age at > least 20. > > By that time, it ought to be clear to students that > mathemathichs is a universal too which does not depend > on context. Problem formulations and boundary conditions > vary, but maths doesn't. > > The fact that the OP apparently realizes this general > validity of maths in the context of the FT - which means > he has some 15 years of previos exposure to maths - is > a sign that there is something seriously missing with > his insights into the basic tools of engineering. > > Rune- Hide quoted text - > > - Show quoted text -Hi Rune, YEP I'm an engineer and your estimate of my experience is off by a factor of 2, (I'll leave it to you to wonder which way). But no I'm not a mathematician.... to me, math is a useful but sometimes cumbersome tool to describe what happens in nature... I found it interesting that the natural behavior of EM fields mimics the natural behavior of waveforms in the frequency and time domain... I'm sorry if this was obvious to everyone else here. Interestingly, there are only a few other pairings mentioned so far... come on there must be more, maybe it's not so obvious after all... Mark
Reply by ●March 7, 20092009-03-07
makolber@yahoo.com wrote:> On Mar 7, 4:13 am, Rune Allnor <all...@tele.ntnu.no> wrote: >> On 7 Mar, 00:58, "Alun" <no.spam.thank....@invalid.invalid> wrote: >> >> >> >> >> >>> "Rune Allnor" <all...@tele.ntnu.no> wrote in message >>> news:9ab6ef27-b5fc-4f4a-8af7-1abe088fcf47@p11g2000yqe.googlegroups.com... >>> On 6 Mar, 18:37, makol...@yahoo.com wrote: >>>> I was enlightened to read here the other day that the Fourier >>>> Transform also describes the relationship in electromagnetics >>>> between the current distribution and the far field radiation >>>> pattern. >>> !The next obvious step on your path to Nirvana (or the >>> !looney bin, whichever is closer) is to investigate why[*] >>> !2+2=4 in such diverse fields as >>> ! >>> !- Maths >>> !- Physics >>> !- Economy >>> !- Medicine >>> !- and so on. >>> ! >>> !In fact, it't hard to come up with a single case >>> !where 2+2=/=4. Now, *that's* food for tought. >>> !Preferably somebody else's, but still. >>> It is a great pity when those who would be the pundits of >>> this NG seek personal satisfaction by pooh-poohing >>> the expressed sense of academic excitement of a newbie. >>> Such excitement is to be encouraged and nurtured. >> I could agree with you in principle, but the timing is >> wrong. I would assume one is at least a couple of years >> into college or university levels before one gets to >> know the FT; let's assume students to be of age at >> least 20. >> >> By that time, it ought to be clear to students that >> mathemathichs is a universal too which does not depend >> on context. Problem formulations and boundary conditions >> vary, but maths doesn't. >> >> The fact that the OP apparently realizes this general >> validity of maths in the context of the FT - which means >> he has some 15 years of previos exposure to maths - is >> a sign that there is something seriously missing with >> his insights into the basic tools of engineering. >> >> Rune- Hide quoted text - >> >> - Show quoted text - > > Hi Rune, > > YEP I'm an engineer and your estimate of my experience is off by a > factor of 2, (I'll leave it to you to wonder which way). > > But no I'm not a mathematician.... to me, math is a useful but > sometimes cumbersome tool to describe what happens in nature... > > I found it interesting that the natural behavior of EM fields mimics > the natural behavior of waveforms in the frequency and time domain... > I'm sorry if this was obvious to everyone else here. Interestingly, > there are only a few other pairings mentioned so far... come on there > must be more, maybe it's not so obvious after all...I think Rune expects too much of other people's intellect. I've been at this since the early 1950s and I'm always delighted to find new connections. I can explain dark-field microscopy in terms of Fourier transforms and also as the conversion of narrow-band FM to AM with a quadrature carrier shift. If you want to, you can use the FT to elucidate NBFM modulation. To answer your last question, Fourier did his transform work to describe heat flow in solids. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●March 7, 20092009-03-07
On 7 Mar, 14:34, makol...@yahoo.com wrote:> On Mar 7, 4:13�am, Rune Allnor <all...@tele.ntnu.no> wrote: > > > > > > > On 7 Mar, 00:58, "Alun" <no.spam.thank....@invalid.invalid> wrote: > > > > "Rune Allnor" <all...@tele.ntnu.no> wrote in message > > > >news:9ab6ef27-b5fc-4f4a-8af7-1abe088fcf47@p11g2000yqe.googlegroups.com... > > > On 6 Mar, 18:37, makol...@yahoo.com wrote: > > > > > I was enlightened to read here the other day that the Fourier > > > > Transform also describes the relationship in electromagnetics > > > > between the current distribution and the far field radiation > > > > pattern. > > > > !The next obvious step on your path to Nirvana (or the > > > !looney bin, whichever is closer) is to investigate why[*] > > > !2+2=4 in such diverse fields as > > > ! > > > !- Maths > > > !- Physics > > > !- Economy > > > !- Medicine > > > !- and so on. > > > ! > > > !In fact, it't hard to come up with a single case > > > !where 2+2=/=4. Now, *that's* food for tought. > > > !Preferably somebody else's, but still. > > > > It is a great pity when those who would be the pundits of > > > this NG seek personal satisfaction by pooh-poohing > > > the expressed sense of academic excitement of a newbie. > > > > Such excitement is to be encouraged and nurtured. > > > I could agree with you in principle, but the timing is > > wrong. I would assume one is at least a couple of years > > into college or university levels before one gets to > > know the FT; let's assume students to be of age at > > least 20. > > > By that time, it ought to be clear to students that > > mathemathichs is a universal too which does not depend > > on context. Problem formulations and boundary conditions > > vary, but maths doesn't. > > > The fact that the OP apparently realizes this general > > validity of maths in the context of the FT - which means > > he has some 15 years of previos exposure to maths - is > > a sign that there is something seriously missing with > > his insights into the basic tools of engineering. > > > Rune- Hide quoted text - > > > - Show quoted text - > > Hi Rune, > > YEP I'm an engineer and your estimate of my experience is off by a > factor of 2, (I'll leave it to you to wonder which way).You're a wonder kid? Switch schools. The sooner the better.> But no I'm not a mathematician.... to me, �math is a useful but > sometimes cumbersome tool to describe what happens in nature...That doesn't excuse you from learning how to use it.> I found it interesting that the natural behavior of EM fields �mimics > the natural behavior of waveforms in the frequency and time domain...Could the fact that EM fields actually *are* waves that can be analyzed in both time and frequency domains, have anything to do with this shocking insight...?> I'm sorry if this was obvious to everyone else here. �Interestingly, > there are only a few other pairings mentioned so far... �come on there > must be more, � maybe it's not so obvious after all...Right. Because *you* don't see the solution, none exists... A one-way ticket to the looney bin, if there ever was one. There is a Norwedian proverb that "one can't see the forest through the trees". Which is what you are up against: Everything is out there in front of your eyse, but you don't recognize it for what it is. The (generalized) Fourier transform is a standard tool for solving linear Differential Equations, which in turn are the backbone tools of mathematical physics. You'd know that if you paid attention in maths class. Your earth-shattering revelation that the FT can be used to describe several types of waves are caused by the fact - prepare yourself for a surprise - that they solve wave equations of the same form. Again, mathematics is generally useful and does not depend on context. So for your remaining time in High School and throughout college, pay attention when the teachers talk about abstract concepts. The concepts are abstracted because they apply generally, not only in specific contexts. It'a a part of the engineering training to be able to distill any given problem into its abstract form, and then find whatever standard solution for this abstract core problem. And vice versa. You have to know a set of standard problems and their solutions, so you have a standard 'language' which you can use to express problems so you don't have to derive e.g. the FT from scratch in every context where you encounter it. Rune
