Eric Jacobsen wrote:> > On Wed, 20 Aug 2003 22:06:40 -0400, Jerry Avins <jya@ieee.org> wrote: >> > ... The nonlinearity that Clay wrote of > > -- I hadn't thought of it explicitly before, but its tickling > >was the reason I started this thread -- is that the magnitude of the > >pitch shift from a moving source is different for the same speeds to and > >away. > > > >Jerry > > I'm not sure if that's really a nonlinearity, since the cases are > different. Writing the expression as you did with the terms for the > emitter and receiver separated clarifies the issue, I think. >I think it is nonlinearity because the Doppler shift isn't proportional to speed. Had you thought of that? (I hadn't either until now.) Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Is the Doppler effect really linear?
Started by ●August 19, 2003
Reply by ●August 21, 20032003-08-21
Reply by ●August 21, 20032003-08-21
In article 3F45198E.351FEA2C@ieee.org, Jerry Avins at jya@ieee.org wrote on 08/21/2003 15:12:> Eric Jacobsen wrote: >> >> On Wed, 20 Aug 2003 22:06:40 -0400, Jerry Avins <jya@ieee.org> wrote: >> > >>> ... The nonlinearity that Clay wrote of >>> -- I hadn't thought of it explicitly before, but its tickling >>> was the reason I started this thread -- is that the magnitude of the >>> pitch shift from a moving source is different for the same speeds to and >>> away. >>> >>> Jerry >> >> I'm not sure if that's really a nonlinearity, since the cases are >> different. Writing the expression as you did with the terms for the >> emitter and receiver separated clarifies the issue, I think. >> > I think it is nonlinearity because the Doppler shift isn't proportional > to speed. Had you thought of that? (I hadn't either until now.)Jerry, perhaps this is just semantic, but why do you say that the Doppler shift "operator" ain't linear? doesn't superposition apply? it ain't time-invariant, that's for sure, but ain't it linear?
Reply by ●August 21, 20032003-08-21
Stan Pawlukiewicz <stanp@nospam_mitre.org> wrote in message news:<bi30ll$ldt$1@newslocal.mitre.org>...> Eric Jacobsen wrote: > > On Wed, 20 Aug 2003 22:06:40 -0400, Jerry Avins <jya@ieee.org> wrote: > > > > > >>Raymond Toy wrote: > >> > >> ... > >> > >>>So, if I were blindfolded, I could tell if I were in a train moving > >>>towards a whistle instead of the whistle moving towards me? > >>> > >> > >>Only if you knew the original pitch and the speed very accurately. Let's > >>say that the train is moving at Mach .2 (fast, but possible) and its > >>whistle has a frequency of f. when the train is approaching, its > >>whistle's frequency sounds like f/(1 - .2), or 1.25f. If the train is in > >>the station and you are on another approaching it at Mach .2, the pitch > >>you would hear would be f(1 + .2) or 1.2f. The nonlinearity that Clay > >>wrote of -- I hadn't thought of it explicitly before, but its tickling > >>was the reason I started this thread -- is that the magnitude of the > >>pitch shift from a moving source is different for the same speeds to and > >>away. > >> > >>Jerry > > > > > > I'm not sure if that's really a nonlinearity, since the cases are > > different. Writing the expression as you did with the terms for the > > emitter and receiver separated clarifies the issue, I think. > > > > There's actually a lot of information about the situation that can be > > obtained merely by observing the Doppler history of things moving > > around you (this was the topic of my MS thesis). Back in the day I > > set out to show that one could even determine how far away the emitter > > was by the Doppler history observed at a single sensor (i.e., > > microphone). After some initial failed attempts I told my advisor > > that I was going to drop that parameter from my analysis, and he > > emphatically replied in his Korean accent, "No! Must do range!" I > > then set out to prove that range could not be determined in this > > manner and after a weekend hunched over a pad of engineering paper I > > had an algorithm for determining range from the Doppler observation. > > It worked pretty well. > > > > So my effort to prove that it couldn't be done failed, too. > > > > > > Eric Jacobsen > > Minister of Algorithms, Intel Corp. > > My opinions may not be Intel's opinions. > > http://www.ericjacobsen.org > > There's a derivation in Quinn and Hannan's "The Estimation and Tracking > of Frequency"Eh... what's the trick? Assuming a stationary reciever, the Doppler history would show some atan type of behaviour. If you observe for long enough (and conditions otherwise allow), you will get the asymptotic boundaries of the frequency, which means you can determine the time of the Closest Point of Approach and thus the emitted frequency. So far so good. If you want to estimate CPA range, you need to know the target velocity as well. You don't know that, do you? Or maybe the velocity is given by the asymptotics of the atan? Rune
Reply by ●August 21, 20032003-08-21
robert bristow-johnson wrote:> > In article 3F45198E.351FEA2C@ieee.org, Jerry Avins at jya@ieee.org wrote on > 08/21/2003 15:12: > > > Eric Jacobsen wrote: > >> > >> On Wed, 20 Aug 2003 22:06:40 -0400, Jerry Avins <jya@ieee.org> wrote: > >> > > > >>> ... The nonlinearity that Clay wrote of > >>> -- I hadn't thought of it explicitly before, but its tickling > >>> was the reason I started this thread -- is that the magnitude of the > >>> pitch shift from a moving source is different for the same speeds to and > >>> away. > >>> > >>> Jerry > >> > >> I'm not sure if that's really a nonlinearity, since the cases are > >> different. Writing the expression as you did with the terms for the > >> emitter and receiver separated clarifies the issue, I think. > >> > > I think it is nonlinearity because the Doppler shift isn't proportional > > to speed. Had you thought of that? (I hadn't either until now.) > > Jerry, perhaps this is just semantic, but why do you say that the Doppler > shift "operator" ain't linear? doesn't superposition apply? it ain't > time-invariant, that's for sure, but ain't it linear?For a stationary observer, f' = f/(1 - s/c). Delta(f) = f - f' isn't proportional to s. Do you call it linear anyway? (f'/f isn't proportional either.) Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●August 21, 20032003-08-21
allnor@tele.ntnu.no (Rune Allnor) wrote in message news:<f56893ae.0308211233.3eea105d@posting.google.com>...> Or maybe the velocity is given by > the asymptotics of the atan?Of course it is. That's the whole starting point of this thread. It's another of those "seeing-the-answer-the-very-instant-after- having-submitted-the-question" incidents. Rune
Reply by ●August 21, 20032003-08-21
In article 3F453609.571AA6E5@ieee.org, Jerry Avins at jya@ieee.org wrote on 08/21/2003 17:13:> robert bristow-johnson wrote: >> >> In article 3F45198E.351FEA2C@ieee.org, Jerry Avins at jya@ieee.org wrote on >> 08/21/2003 15:12: >> >>> Eric Jacobsen wrote: >>>> >>>> On Wed, 20 Aug 2003 22:06:40 -0400, Jerry Avins <jya@ieee.org> wrote: >>>> >>> >>>>> ... The nonlinearity that Clay wrote of >>>>> -- I hadn't thought of it explicitly before, but its tickling >>>>> was the reason I started this thread -- is that the magnitude of the >>>>> pitch shift from a moving source is different for the same speeds to and >>>>> away. >>>>> >>>>> Jerry >>>> >>>> I'm not sure if that's really a nonlinearity, since the cases are >>>> different. Writing the expression as you did with the terms for the >>>> emitter and receiver separated clarifies the issue, I think. >>>> >>> I think it is nonlinearity because the Doppler shift isn't proportional >>> to speed. Had you thought of that? (I hadn't either until now.) >> >> Jerry, perhaps this is just semantic, but why do you say that the Doppler >> shift "operator" ain't linear? doesn't superposition apply? it ain't >> time-invariant, that's for sure, but ain't it linear? > > For a stationary observer, f' = f/(1 - s/c). Delta(f) = f - f' isn't > proportional to s. Do you call it linear anyway? (f'/f isn't > proportional either.)okay, the frequency shift is not linear with speed. fine. what i was thinking about when i would say that some box or "effect" or whatever is not linear is that there are cases when the superposition does not hold. that is does Doppler{x(t) + y(t)} = Doppler{x(t)} + Doppler{y(t)} ? There are a lot of LTV systems that change the frequency of an input (imagine DC going into an amp and someone wiggling the volume control at 1 Hz, lot'sa multiples on 1 Hz coming out and DC going in). it may not be time-invariant, but it's linear. i think i understand what you were saying, but we have a different semantic. r b-j
Reply by ●August 22, 20032003-08-22
Rune Allnor wrote:> Stan Pawlukiewicz <stanp@nospam_mitre.org> wrote in message news:<bi30ll$ldt$1@newslocal.mitre.org>... > >>Eric Jacobsen wrote: >> >>>On Wed, 20 Aug 2003 22:06:40 -0400, Jerry Avins <jya@ieee.org> wrote: >>> >>> >>> >>>>Raymond Toy wrote: >>>> >>>>... >>>> >>>> >>>>>So, if I were blindfolded, I could tell if I were in a train moving >>>>>towards a whistle instead of the whistle moving towards me? >>>>> >>>> >>>>Only if you knew the original pitch and the speed very accurately. Let's >>>>say that the train is moving at Mach .2 (fast, but possible) and its >>>>whistle has a frequency of f. when the train is approaching, its >>>>whistle's frequency sounds like f/(1 - .2), or 1.25f. If the train is in >>>>the station and you are on another approaching it at Mach .2, the pitch >>>>you would hear would be f(1 + .2) or 1.2f. The nonlinearity that Clay >>>>wrote of -- I hadn't thought of it explicitly before, but its tickling >>>>was the reason I started this thread -- is that the magnitude of the >>>>pitch shift from a moving source is different for the same speeds to and >>>>away. >>>> >>>>Jerry >>> >>> >>>I'm not sure if that's really a nonlinearity, since the cases are >>>different. Writing the expression as you did with the terms for the >>>emitter and receiver separated clarifies the issue, I think. >>> >>>There's actually a lot of information about the situation that can be >>>obtained merely by observing the Doppler history of things moving >>>around you (this was the topic of my MS thesis). Back in the day I >>>set out to show that one could even determine how far away the emitter >>>was by the Doppler history observed at a single sensor (i.e., >>>microphone). After some initial failed attempts I told my advisor >>>that I was going to drop that parameter from my analysis, and he >>>emphatically replied in his Korean accent, "No! Must do range!" I >>>then set out to prove that range could not be determined in this >>>manner and after a weekend hunched over a pad of engineering paper I >>>had an algorithm for determining range from the Doppler observation. >>>It worked pretty well. >>> >>>So my effort to prove that it couldn't be done failed, too. >>> >>> >>>Eric Jacobsen >>>Minister of Algorithms, Intel Corp. >>>My opinions may not be Intel's opinions. >>>http://www.ericjacobsen.org >> >>There's a derivation in Quinn and Hannan's "The Estimation and Tracking >> of Frequency" > > > Eh... what's the trick? Assuming a stationary reciever, the Doppler > history would show some atan type of behaviour. If you observe for long > enough (and conditions otherwise allow), you will get the asymptotic > boundaries of the frequency, which means you can determine the time of > the Closest Point of Approach and thus the emitted frequency. So far so > good. > > If you want to estimate CPA range, you need to know the target velocity > as well. You don't know that, do you? Or maybe the velocity is given by > the asymptotics of the atan? > > RuneHi Rune, I recall you said you had a bunch of Jasa on CD. Look at Quinn, B.G. "Doppler speed and range estimation using frequency and amplitude estimates", JASA 98:5 part 1, pp 2560-2566 (1995).
Reply by ●August 22, 20032003-08-22
"robert bristow-johnson" <rbj@surfglobal.net> wrote in message news:BB6AE62D.31A6%rbj@surfglobal.net...> In article 3F453609.571AA6E5@ieee.org, Jerry Avins at jya@ieee.org wroteon> > There are a lot of LTV systems that change the frequency of an input > (imagine DC going into an amp and someone wiggling the volume control at 1 > Hz, lot'sa multiples on 1 Hz coming out and DC going in). it may not be > time-invariant, but it's linear.Robert, Well .... as we discussed a few months ago, the wiggles have to be *perfectly* periodic for it to be linear and time-varying with respect to the dc input. My hand is steady enough but not that steady! But since you said "dc", that makes a linear time-invariant system with respect to the input called "wiggles". Fred
Reply by ●August 22, 20032003-08-22
robert bristow-johnson wrote:> In article 3F453609.571AA6E5@ieee.org, Jerry Avins at jya@ieee.org wrote on > 08/21/2003 17:13: > > >>robert bristow-johnson wrote: >> >>>In article 3F45198E.351FEA2C@ieee.org, Jerry Avins at jya@ieee.org wrote on >>>08/21/2003 15:12: >>> >>> >>>>Eric Jacobsen wrote: >>>> >>>>>On Wed, 20 Aug 2003 22:06:40 -0400, Jerry Avins <jya@ieee.org> wrote: >>>>> >>>> >>>>>>... The nonlinearity that Clay wrote of >>>>>>-- I hadn't thought of it explicitly before, but its tickling >>>>>>was the reason I started this thread -- is that the magnitude of the >>>>>>pitch shift from a moving source is different for the same speeds to and >>>>>>away. >>>>>> >>>>>>Jerry >>>>> >>>>>I'm not sure if that's really a nonlinearity, since the cases are >>>>>different. Writing the expression as you did with the terms for the >>>>>emitter and receiver separated clarifies the issue, I think. >>>>> >>>> >>>>I think it is nonlinearity because the Doppler shift isn't proportional >>>>to speed. Had you thought of that? (I hadn't either until now.) >>> >>>Jerry, perhaps this is just semantic, but why do you say that the Doppler >>>shift "operator" ain't linear? doesn't superposition apply? it ain't >>>time-invariant, that's for sure, but ain't it linear? >> >>For a stationary observer, f' = f/(1 - s/c). Delta(f) = f - f' isn't >>proportional to s. Do you call it linear anyway? (f'/f isn't >>proportional either.) > > > okay, the frequency shift is not linear with speed. fine. what i was > thinking about when i would say that some box or "effect" or whatever is not > linear is that there are cases when the superposition does not hold. that > is does > > Doppler{x(t) + y(t)} = Doppler{x(t)} + Doppler{y(t)} > > ? > > There are a lot of LTV systems that change the frequency of an input > (imagine DC going into an amp and someone wiggling the volume control at 1 > Hz, lot'sa multiples on 1 Hz coming out and DC going in). it may not be > time-invariant, but it's linear. > > i think i understand what you were saying, but we have a different semantic. > > r b-j >If you use only f as a state variable, the system is linear. If you use f and v as state variables, the state equations are nonlinear. This article might be overkill, but look at the state equations in: Sonar tracking of multiple targets using joint probabilistic data association Fortmann, T.; Bar-Shalom, Y.; Scheffe, M.; Oceanic Engineering, IEEE Journal of , Volume: 8 Issue: 3 , Jul 1983 Page(s): 173 -184
Reply by ●August 22, 20032003-08-22
robert bristow-johnson wrote:>...> > Doppler{x(t) + y(t)} = Doppler{x(t)} + Doppler{y(t)} > > ? > > There are a lot of LTV systems that change the frequency of an input > (imagine DC going into an amp and someone wiggling the volume control at 1 > Hz, lot'sa multiples on 1 Hz coming out and DC going in). it may not be > time-invariant, but it's linear. > > i think i understand what you were saying, but we have a different semantic. > > r b-jRobert, I'll simplify by expressing velocities as ratios of the speed of sound. Numerically, the speed of sound becomes 1 (one, not ell) and the speed of motion becomes m, the Mach number. Also, I define D_s to be the Doppler shift due to moving source and D_o the shift due to moving observer. (D_x = f' - f for the appropriate case.) For an approaching observer, f' = f(1 + m), D_o = fm; clearly linear. For a approaching source, f' = f/(1-m), D_s = fm/(1 - m) = D_o/(1 - m). That's linear in f, but not in m. How does semantics enter into this? Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
