Allan Herriman wrote:> 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.So, Shannon and Nyquist were just reinventing the wheel. :-) Steve
Possibly unrelated questions
Started by ●February 15, 2008
Reply by ●February 17, 20082008-02-17
Reply by ●February 17, 20082008-02-17
John E. Hadstate wrote:> > "Richard Owlett" <rowlett@atlascomm.net> wrote in message > news:13rg6q7a1esbs64@news.supernews.com... > >> 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. >>> >> 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? >> > > I slightly disagree with Rune's answer, "sort of". Assuming your > question is posed to need a Yes/No answer, I think the answer is > "absolutely". > > In other words, the flash of a strobe (or the wink of the camera) is > "sampling", regardless of what the eye does later with the stream of > images. It gets really interesting when a frames of film are re-sampled > for the TV frame rate. > > Note: your question could also be interpreted to require an answer of > "aliasing effect" vs. "artifact of not meeting a Nyquist related > criterion". I would point out that these two are the same thing, so a > Yes vs. No answer is appropriate. > >I gathered that from the other posts. But still haven't really wrapped my mind around aliasing and Nyquist being closely related. Night's sleep may help.
Reply by ●February 17, 20082008-02-17
Richard Owlett wrote:> John E. Hadstate wrote:...>> Note: your question could also be interpreted to require an answer of >> "aliasing effect" vs. "artifact of not meeting a Nyquist related >> criterion". I would point out that these two are the same thing, so a >> Yes vs. No answer is appropriate. >> >> > > I gathered that from the other posts. But still haven't really wrapped > my mind around aliasing and Nyquist being closely related. Night's sleep > may help.Maybe I can help. Aliases happen when the sampling rate is too low. When you say, "Nyquist rate," what do you mean? Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●February 18, 20082008-02-18
On Sun, 17 Feb 2008 15:50:42 -0500, Jerry Avins <jya@ieee.org> wrote:>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? :-) > >JerryOnly if the water starts running uphill. ;) Eric Jacobsen Minister of Algorithms Abineau Communications http://www.ericjacobsen.org
Reply by ●February 18, 20082008-02-18
Jerry Avins wrote:> glen herrmannsfeldt wrote:(snip)>> 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? :-)Yes, but seeing a rotating wheel in a sampled image is always an illusion. Our visual system prefers the assumption of the slowest absolute value rotation rate. I read recently that it was previously attributed to persistence of vision, but it seems that isn't really true. The psychology of vision of sampled images really isn't well understood. It is all an illusion. -- glen
Reply by ●February 18, 20082008-02-18
"Richard Owlett" <rowlett@atlascomm.net> wrote in message news:13rho7bd0thgu1d@news.supernews.com...> John E. Hadstate wrote: >> >> "Richard Owlett" <rowlett@atlascomm.net> wrote in message >> news:13rg6q7a1esbs64@news.supernews.com... >> >>> 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. >>>> >>> Never thought of stroboscopic effects >>> in terms of sampling theory. >> >> The flash of a strobe (or the wink of the camera) is >> "sampling".... >> > > But still haven't really wrapped my mind around aliasing and > Nyquist > being closely related.In the analog (continuous) world, there is a related effect called "heterodyning". When one multiplies two periodic signals, one generates sum and difference frequencies. Pointing a strobe at a rotating object causes the reflected light to be a product of the strobe's nearly "On-Off" illumination (multiplying by 0 or 1) and whatever is going on in the illuminated scene. When the strobe is synchronized with some periodic event in the scene, the "beat frequency" will be zero and the event will appear to be frozen in time. (The beat frequency is the difference frequency, I don't have a clue as to how to observe the sum frequency.) Another example of this phenomenon is found in the ancient technology of the "synchronizing lamp". Suppose we have two AC generators, one on-line and one in standby. We want to bring the standby generator to the same frequency and phase as the currently on-line generator so we can connect them in parallel. ("Whenever I connect them together she go 'boom'" -- you had to be there.) If we hook a sufficiently robust light bulb between the generators (assuming of course that they have a common ground), we will see this heterodyning take place as the speed of the stand-by generator is brought up to match the speed of the on-line generator. When the light bulb goes dark (phase match) and stays that way (frequency match), it's safe to connect the generators in parallel.
Reply by ●February 18, 20082008-02-18
Jerry Avins wrote:> Richard Owlett wrote: > >> John E. Hadstate wrote: > > > ... > >>> Note: your question could also be interpreted to require an answer of >>> "aliasing effect" vs. "artifact of not meeting a Nyquist related >>> criterion". I would point out that these two are the same thing, so >>> a Yes vs. No answer is appropriate. >>> >>> >> >> I gathered that from the other posts. But still haven't really wrapped >> my mind around aliasing and Nyquist being closely related. Night's >> sleep may help. > > > Maybe I can help. Aliases happen when the sampling rate is too low. When > you say, "Nyquist rate," what do you mean? > > JerryAfter a good night's sleep, while waiting for my computer to boot, I came to that conclusion. The _mental image_ of Nyquist I always used was how many points on a sinewave did I need to define it. The _mental image_ of aliasing was similar to folding spectrum around sample rate with the related emphasis on proper prefiltering. Just never made the connection.
Reply by ●February 18, 20082008-02-18
John E. Hadstate wrote:> > "Richard Owlett" <rowlett@atlascomm.net> wrote in message > news:13rho7bd0thgu1d@news.supernews.com... > >> John E. Hadstate wrote: >> >>> >>> "Richard Owlett" <rowlett@atlascomm.net> wrote in message >>> news:13rg6q7a1esbs64@news.supernews.com... >>> >>>> 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. >>>>> >>>> Never thought of stroboscopic effects >>>> in terms of sampling theory. >>> >>> >>> The flash of a strobe (or the wink of the camera) is "sampling".... >>> >> >> But still haven't really wrapped my mind around aliasing and Nyquist >> being closely related. > > > In the analog (continuous) world, there is a related effect called > "heterodyning".Now you're speaking my generation. My father once operated a _legal land based spark gap transmitter.> When one multiplies two periodic signals, one generates > sum and difference frequencies. Pointing a strobe at a rotating object > causes the reflected light to be a product of the strobe's nearly > "On-Off" illumination (multiplying by 0 or 1) and whatever is going on > in the illuminated scene. When the strobe is synchronized with some > periodic event in the scene, the "beat frequency" will be zero and the > event will appear to be frozen in time. (The beat frequency is the > difference frequency, I don't have a clue as to how to observe the sum > frequency.)That's easy. In fact I believe it was even used commercially in some double conversion superhet receivers. The first IF was above the station frequency.> > Another example of this phenomenon is found in the ancient technology of > the "synchronizing lamp". Suppose we have two AC generators, one > on-line and one in standby. We want to bring the standby generator to > the same frequency and phase as the currently on-line generator so we > can connect them in parallel. ("Whenever I connect them together she go > 'boom'" -- you had to be there.)You haven't lived until you have been ~10-15 feet from 13 kV feed to 1.5 MW switchgear.> > If we hook a sufficiently robust light bulb between the generators > (assuming of course that they have a common ground), we will see this > heterodyning take place as the speed of the stand-by generator is > brought up to match the speed of the on-line generator. When the light > bulb goes dark (phase match) and stays that way (frequency match), it's > safe to connect the generators in parallel. >
Reply by ●February 18, 20082008-02-18
glen herrmannsfeldt wrote:> Jerry Avins wrote: > >> glen herrmannsfeldt wrote: > > (snip) > >>> 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? :-) > > > Yes, but seeing a rotating wheel in a sampled image is > always an illusion. Our visual system prefers the assumption > of the slowest absolute value rotation rate. > > I read recently that it was previously attributed > to persistence of vision, but it seems that isn't really > true. The psychology of vision of sampled images > really isn't well understood. It is all an illusion. > > > -- glen >In the links from one of the Wikipedia articles mention previously, it was pointed out that there three distinct effects that come under the general classification of "persistence of vision".
Reply by ●February 18, 20082008-02-18
Steve Underwood wrote:> Allan Herriman wrote: >> 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. > > So, Shannon and Nyquist were just reinventing the wheel. :-)How about setting up the formal mathematical description? Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
