On Sun, 17 Feb 2008 05:33:33 -0600, Richard Owlett <rowlett@atlascomm.net> wrote:>glen herrmannsfeldt wrote: >> Jerry Avins wrote: >> (snip) >> >>> The question is whether imaginary numbers and negative frequencies are >>> inherent qualities of the real world, or whether they are scaffolding >>> for the simplified mathematics that we use to describe it. I hold to >>> the latter alternative. >> >> >> Some of the time I agree. >> >> I was watching the usual car commercial where the (aliased) wheels >> are turning slowly backwards and realized that sometimes negative >> frequencies do exist. >> >> -- glen >> > >Never thought of stroboscopic effects in terms of sampling theory. Are >wheels going "backwards" and stop/slow motion effects generally really >an aliasing effect or artifact of not meeting a Nyquist related criterion?The wagon wheel effect has its own Wikipedia page: http://en.wikipedia.org/wiki/Wagon-wheel_effect It serves as a familiar example of temporal aliasing. Also see the Moir� pattern page: http://en.wikipedia.org/wiki/Moir%C3%A9_pattern which is a familiar example of 2-D spatial aliasing. Regards, Allan
Possibly unrelated questions
Started by ●February 15, 2008
Reply by ●February 17, 20082008-02-17
Reply by ●February 17, 20082008-02-17
Rune Allnor wrote:> On 17 Feb, 12:33, Richard Owlett <rowl...@atlascomm.net> wrote: > >>glen herrmannsfeldt wrote: > > >>>I was watching the usual car commercial where the (aliased) wheels >>>are turning slowly backwards and realized that sometimes negative >>>frequencies do exist. >> >>>-- glen >> >>Never thought of stroboscopic effects in terms of sampling theory. Are >>wheels going "backwards" and stop/slow motion effects generally really >>an aliasing effect or artifact of not meeting a Nyquist related criterion? > > > Sort of. >Love those definite precise answers ROFL Off to look at pages Alan mentions.> The human visual system can only take in so much information > per time, that's why we tend to see movies as 'flickering' > when there are less than 15 or so frames per second. > > In spatial sampling (like in antennas and arrays arrays) one > discrepancy is between forward and backward propagation; > another is between Direction of Arrival. But don't take the > analogy too far; in time domain it suffices to note that > one can not use the data unless Nyquist's criterion is met. > > Rune
Reply by ●February 17, 20082008-02-17
On 17 Feb, 15:11, Richard Owlett <rowl...@atlascomm.net> wrote:> Rune Allnor wrote: > > On 17 Feb, 12:33, Richard Owlett <rowl...@atlascomm.net> wrote:> >>Are > >>wheels going "backwards" and stop/slow motion effects generally really > >>an aliasing effect or artifact of not meeting a Nyquist related criterion? > > > Sort of. > > Love those definite precise answers ROFLGlad to be of help... If there existed a definite precise answer to your question avery textbook would contain it. In retrospect I can see that I developed my understanding of most abstract concepts by testing them against 'intuitive' or 'physical' analogies. Whatever insights I reached by that was caused by finding out where and why the analogies *failed* to describe the concept in question. Rune
Reply by ●February 17, 20082008-02-17
glen herrmannsfeldt wrote:> Jerry Avins wrote: > (snip) > >> The question is whether imaginary numbers and negative frequencies are >> inherent qualities of the real world, or whether they are scaffolding >> for the simplified mathematics that we use to describe it. I hold to >> the latter alternative. > > Some of the time I agree. > > I was watching the usual car commercial where the (aliased) wheels > are turning slowly backwards and realized that sometimes negative > frequencies do exist.Isn't what you saw an illusion? :-) Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●February 17, 20082008-02-17
Richard Owlett wrote:> glen herrmannsfeldt wrote: >> Jerry Avins wrote: >> (snip) >> >>> The question is whether imaginary numbers and negative frequencies >>> are inherent qualities of the real world, or whether they are >>> scaffolding for the simplified mathematics that we use to describe >>> it. I hold to the latter alternative. >> >> >> Some of the time I agree. >> >> I was watching the usual car commercial where the (aliased) wheels >> are turning slowly backwards and realized that sometimes negative >> frequencies do exist. >> >> -- glen >> > > Never thought of stroboscopic effects in terms of sampling theory. Are > wheels going "backwards" and stop/slow motion effects generally really > an aliasing effect or artifact of not meeting a Nyquist related criterion?Did you really mean 'or'? The wheels seeming to go backwards are an alias; a result of undersampling. Note that the apparent rotation is illusory. A five-spoke wheel and a six-spoke wheel of the same diameter will appear to have different speeds. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●February 17, 20082008-02-17
Rune Allnor wrote:> On 17 Feb, 15:11, Richard Owlett <rowl...@atlascomm.net> wrote: > >>Rune Allnor wrote: >> >>>On 17 Feb, 12:33, Richard Owlett <rowl...@atlascomm.net> wrote: > > >>>>Are >>>>wheels going "backwards" and stop/slow motion effects generally really >>>>an aliasing effect or artifact of not meeting a Nyquist related criterion? >> >>>Sort of. >> >>Love those definite precise answers ROFL > > > Glad to be of help... > > If there existed a definite precise answer to your question > avery textbook would contain it. In retrospect I can see that > I developed my understanding of most abstract concepts by > testing them against 'intuitive' or 'physical' analogies. > Whatever insights I reached by that was caused by finding > out where and why the analogies *failed* to describe the > concept in question. > > RuneAgreed, but you struck my funny bone ;)
Reply by ●February 17, 20082008-02-17
Jerry Avins wrote:> Richard Owlett wrote: > >> glen herrmannsfeldt wrote: >> >>> Jerry Avins wrote: >>> (snip) >>> >>>> The question is whether imaginary numbers and negative frequencies >>>> are inherent qualities of the real world, or whether they are >>>> scaffolding for the simplified mathematics that we use to describe >>>> it. I hold to the latter alternative. >>> >>> >>> >>> Some of the time I agree. >>> >>> I was watching the usual car commercial where the (aliased) wheels >>> are turning slowly backwards and realized that sometimes negative >>> frequencies do exist. >>> >>> -- glen >>> >> >> Never thought of stroboscopic effects in terms of sampling theory. Are >> wheels going "backwards" and stop/slow motion effects generally really >> an aliasing effect or artifact of not meeting a Nyquist related >> criterion? > > > Did you really mean 'or'?Yes. OOOPS ;)> The wheels seeming to go backwards are an > alias; a result of undersampling.It's easy to see, when stopping to think, that the reverse rotation is an artifact of under sampling. I don't think I've ever read other than 1. undersampling in the time domain *or* 2. aliasing in the frequency Except when using a spectrum analyzer, as a engineering tech I've never seen a observable in other than the time domain. Note that the apparent rotation is> illusory. A five-spoke wheel and a six-spoke wheel of the same diameter > will appear to have different speeds. > > Jerry
Reply by ●February 17, 20082008-02-17
On Sun, 17 Feb 2008 11:19:06 -0500, Jerry Avins <jya@ieee.org> wrote:>glen herrmannsfeldt wrote: >> Jerry Avins wrote: >> (snip) >> >>> The question is whether imaginary numbers and negative frequencies are >>> inherent qualities of the real world, or whether they are scaffolding >>> for the simplified mathematics that we use to describe it. I hold to >>> the latter alternative. >> >> Some of the time I agree. >> >> I was watching the usual car commercial where the (aliased) wheels >> are turning slowly backwards and realized that sometimes negative >> frequencies do exist. > >Isn't what you saw an illusion? :-) > >JerryIt's an illusion, but the "image" can have a negative frequency (i.e., rate of rotation). Actually, any rotation can if you need to have signed discrimination in rotation direction. The sign would be arbitrary, i.e., either CW or CCW could be positive, but the other direction would be negative. Eric Jacobsen Minister of Algorithms Abineau Communications http://www.ericjacobsen.org
Reply by ●February 17, 20082008-02-17
Richard Owlett wrote: ...> It's easy to see, when stopping to think, that the reverse rotation is > an artifact of under sampling. I don't think I've ever read other than > 1. undersampling in the time domain > *or* > 2. aliasing in the frequencynote that in fact it is 1. undersampling in the time domain *and* 2. aliasing in the frequency (Same thing, really. Id the clown standing upside down, or downside up?)> Except when using a spectrum analyzer, as a engineering tech I've never > seen a observable in other than the time domain.You remind me of a dirty trick I pulled on an arrogant lab instructor in my Rotating Machinery course. I took a pair of 3-phase 5-hp wound-rotor induction motors and connected the stators and rotors phase for phase. I started the motors with the rotors shorted, then removed the shorts. One motor was in a Prony brake, while the other was standing free with a strobe disk on it. The wiring arrangement ensured that the sum of the two speeds would be 7200 RPM with the shorts removed. When one was clamped in the brake and stopped, the other ran the full 7200 RPM by itself. (The rotor diameters were small enough so that centrifugal force wasn't a worry. At least, it didn't worry me. :-)) One of the gizmos we were supposed to learn to use was a stroboscope to measure speed. It worked with a black disk on the motor shaft that had a single white circle near the rim. If the circle appeared in more than one location, the strobe was flashing at the wrong rate, but there are many rates that will produce a single stationary spot. The trick is to find the right one and not be fooled by aliases. For example, if the disk turns at 3600 RPM and the strobe flashes 7200 times a second, there will be two spots diametrically opposed, while if the disk spins at 7200 RPM and the strobe flashes 3600 times a second, there will be a single spot (lit up every second turn). I called the TA over and said I was having trouble getting a good strobe reading. He quickly found 3600 RPM and though he was puzzled by the induction motor running at synchronous speed, he didn't look into why. I reset the strobe to 7200 RPM and behold! Still a single spot! Naturally, he went to try a different strobe and was really perplexed to see the same reading. When I suggested that the motor might actually be turning at 7200 RPM, he insisted that it was flatly impossible for a 60-Hz machine to run that fast. "There are no one-pole motors!" I shrugged. After the next classroom session, the professor called me aside and asked me what I had done. I told him and he grinned widely. "Let the jerk stew for a while," he said. "Maybe I'll tell him next week." So: is a strobe a time-domain device? It's calibrated in frequency. ... Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●February 17, 20082008-02-17
Eric Jacobsen wrote:> On Sun, 17 Feb 2008 11:19:06 -0500, Jerry Avins <jya@ieee.org> wrote: > >> glen herrmannsfeldt wrote: >>> Jerry Avins wrote: >>> (snip) >>> >>>> The question is whether imaginary numbers and negative frequencies are >>>> inherent qualities of the real world, or whether they are scaffolding >>>> for the simplified mathematics that we use to describe it. I hold to >>>> the latter alternative. >>> Some of the time I agree. >>> >>> I was watching the usual car commercial where the (aliased) wheels >>> are turning slowly backwards and realized that sometimes negative >>> frequencies do exist. >> Isn't what you saw an illusion? :-) >> >> Jerry > > It's an illusion, but the "image" can have a negative frequency (i.e., > rate of rotation). Actually, any rotation can if you need to have > signed discrimination in rotation direction. The sign would be > arbitrary, i.e., either CW or CCW could be positive, but the other > direction would be negative.We glibly liken negative frequency to retrograde rotation. Does that mean that time marches backward on the return leg of a journey? :-) Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
