Jerry Avins <jya@ieee.org> writes:> [...] > By "straight-forward", I mean the time needed to determine the frequency > with a frequency counter or an FFT. Other more indirect methods exist. > > > That is untrue, whether or not there is noise present. > > Is it untrue that the methods I call straight forward need that much > time? That that time represents an upper bound? That other, more > sophisticated methods exist? That with more information, the actual time > can't be estimated? It seems to me that you jumped to an erroneous > conclusion. then argued with it.OK, maybe you have something of a point here, Jerry. I see the FFT argument as true. But I see the "delta theta / delta t" computation being "straightforward" too, though, and knowing that can be way way less than 1/Accuracy is what threw me. -- Randy Yates Sony Ericsson Mobile Communications Research Triangle Park, NC, USA randy.yates@sonyericsson.com, 919-472-1124
Frequency offset estimation.
Started by ●May 12, 2004
Reply by ●May 13, 20042004-05-13
Reply by ●May 14, 20042004-05-14
Jerry Avins <jya@ieee.org> writes:> [...] > By "straight-forward", I mean the time needed to determine the frequency > with a frequency counter or an FFT.Do you know what technique a (analog) frequency counter uses to perform its measurement? -- % Randy Yates % "Maybe one day I'll feel her cold embrace, %% Fuquay-Varina, NC % and kiss her interface, %%% 919-577-9882 % til then, I'll leave her alone." %%%% <yates@ieee.org> % 'Yours Truly, 2095', *Time*, ELO http://home.earthlink.net/~yatescr
Reply by ●May 14, 20042004-05-14
"Randy Yates" <randy.yates@sonyericsson.com> wrote in message news:xxpoeos3s3d.fsf@usrts005.corpusers.net...> Jerry Avins <jya@ieee.org> writes: > > [...] > > By "straight-forward", I mean the time needed to determine thefrequency> > with a frequency counter or an FFT. Other more indirect methodsexist.> > > > > That is untrue, whether or not there is noise present. > > > > Is it untrue that the methods I call straight forward need thatmuch> > time? That that time represents an upper bound? That other, more > > sophisticated methods exist? That with more information, theactual time> > can't be estimated? It seems to me that you jumped to an erroneous > > conclusion. then argued with it. > > OK, maybe you have something of a point here, Jerry. I see the FFT > argument as true. But I see the "delta theta / delta t" computation > being "straightforward" too, though, and knowing that can be way way > less than 1/Accuracy is what threw me. > -- > Randy Yates > Sony Ericsson Mobile Communications > Research Triangle Park, NC, USA > randy.yates@sonyericsson.com, 919-472-1124I'm not sure if this "counts" (sorry! ;-) as a straightforward method, but there are frequency counters like the Agilent 53132A which offer 12 digits of resolution per second of measurement time: http://we.home.agilent.com/USeng/nav/-11154.536880944/pd.html There are app notes off there. Regards Ian
Reply by ●May 14, 20042004-05-14
Randy Yates <randy.yates@sonyericsson.com> writes:> Jerry Avins <jya@ieee.org> writes: > > [...] > > By "straight-forward", I mean the time needed to determine the frequency > > with a frequency counter or an FFT. Other more indirect methods exist. > > > > > That is untrue, whether or not there is noise present. > > > > Is it untrue that the methods I call straight forward need that much > > time? That that time represents an upper bound? That other, more > > sophisticated methods exist? That with more information, the actual time > > can't be estimated? It seems to me that you jumped to an erroneous > > conclusion. then argued with it. > > OK, maybe you have something of a point here, Jerry. I see the FFT > argument as true. But I see the "delta theta / delta t" computation > being "straightforward" too, though, and knowing that can be way way > less than 1/Accuracy is what threw me.Jerry, I think your statement bears more scrutiny, and I may have conceded the point too soon. Your original statement was The straight-forward way to measure frequency to .01 Hz requires samples for 1/.01 = 100 seconds. By using the phrase "The straight-forward way," it appears that you are saying "there is one and only one straight-forward way to measure frequency," or that if there is more than one, they all take 1/F seconds to measure, F being the required frequency accuracy. Well, neither of these interpretations are true, thus your statement is not true. Now I can ease up a bit and acknowledge that perhaps what you meant to say was "The FFT way to measure frequency to .01 Hz requires samples for 1/.01 = 100 seconds." That would be true. I still think it's a little misleading though because there are other "straight-forward" methods that don't relate to the duration you cite, and people don't usually think carefully enough to understand that some algorithms (the FFT) do require this time duration while other straight-forward algorithms have no relationship to it. The FFT *can* be used to estimate the frequency of a sinusoid, but it is really giving you much, much more. It is giving you an entire frequency-domain view of the corresponding time-domain signal. Because of this, the uncertainty relationship holds, and it is precisely this fact that causes the duration of measurement with an FFT to be on the order of the required accuracy. -- Randy Yates Sony Ericsson Mobile Communications Research Triangle Park, NC, USA randy.yates@sonyericsson.com, 919-472-1124
Reply by ●May 14, 20042004-05-14
Ian Buckner wrote: ...> I'm not sure if this "counts" (sorry! ;-) as a straightforward method, > but there are frequency counters like the Agilent 53132A which > offer 12 digits of resolution per second of measurement time: > > http://we.home.agilent.com/USeng/nav/-11154.536880944/pd.html > > There are app notes off there. > > Regards > IanI don't have time to read it now, but I'll bet that they're measuring the time interval between recognizable points on the waveform, rather than working from samples taken at an unrelated rate. If so, that's a whole different kettle of fish, If not, I hope to learn a lot when I do get to read it. Thanks for the link. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●May 14, 20042004-05-14
Randy Yates wrote: ...> By using the phrase "The straight-forward way," it appears that you > are saying "there is one and only one straight-forward way to measure > frequency,"No.> or that if there is more than one, they all take 1/F > seconds to measure, F being the required frequency accuracy.That's what I meant, considering that the problem constrains us to deal with samples taken at fixed intervals.> Well, > neither of these interpretations are true, thus your statement is not > true.That's as may be. I can't think of a way to compute to the required accuracy in the presence of some noise and aperture jitter that I would call straight forward and that produces a result in a few seconds. If you can enlighten me, I'd be [delighted? lighted?] very pleased.> Now I can ease up a bit and acknowledge that perhaps what you meant > to say was "The FFT way to measure frequency to .01 Hz requires samples > for 1/.01 = 100 seconds." That would be true.What I meant to say is that the simple ways I know how to do it with an ADC and a processor take nearly that long, and it will be a struggle using sophisticated techniques to do in in an order of magnitude less time. Mind, I don't claim that that's correct, but its the meaning I intended to convey. ... Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●May 14, 20042004-05-14
"If the only tool you have is a hammer, everything looks like a nail." In article <40a25cec$0$3063$61fed72c@news.rcn.com>, Jerry Avins <jya@ieee.org> wrote:>The straight-forward way to measure frequency to .01 Hz requires samples >for 1/.01 = 100 seconds.The above is true if the only tool you have is an FFT (or equivalent). If you have some straight-forward tools which do not include an FFT (correlation, least squares curve fitting, etc.), you might be able to get by with a far shorter sample window, depending on what you know about the signal. Exactly one well placed sample might work if you already know the exact amplitude and phase, the frequency is bounded, and the noise floor is low enough. Far more than 100 seconds might be required if the noise floor is high enough. IMHO. YMMV. -- Ron Nicholson rhn AT nicholson DOT com http://www.nicholson.com/rhn/ #include <canonical.disclaimer> // only my own opinions, etc.
Reply by ●May 14, 20042004-05-14
Randy Yates wrote:> Jerry Avins <jya@ieee.org> writes: > >>[...] >>By "straight-forward", I mean the time needed to determine the frequency >>with a frequency counter or an FFT. > > > Do you know what technique a (analog) frequency counter uses to > perform its measurement?The ones I built to run at high speed -- short measurement intervals -- opened a gate on one zero crossing of the waveform to be measured and closed it N zero crossings later. The count from a high-speed clock accumulates while the gate is open. For example, with a 500 MHz ECL clock and a 20 cycles of the measured waveform, its period is measured with a precision of 100 picoseconds and an accuracy that depends on its cycle-to-cycle uniformity. When measuring stable frequencies in the low MHz range, the measured accuracy is compromised by the uncertainty of the reference crystal's frequency. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●May 14, 20042004-05-14
Ronald H. Nicholson Jr. wrote:> "If the only tool you have is a hammer, everything looks like a nail." > > In article <40a25cec$0$3063$61fed72c@news.rcn.com>, > Jerry Avins <jya@ieee.org> wrote: > >>The straight-forward way to measure frequency to .01 Hz requires samples >>for 1/.01 = 100 seconds. > > > The above is true if the only tool you have is an FFT (or equivalent). > > If you have some straight-forward tools which do not include an FFT > (correlation, least squares curve fitting, etc.), you might be able > to get by with a far shorter sample window, depending on what you know > about the signal.I don't think of those ways as straight forward. (My shortcoming, perhaps.)> > Exactly one well placed sample might work if you already know the exact > amplitude and phase, the frequency is bounded, and the noise floor is > low enough. Far more than 100 seconds might be required if the noise > floor is high enough.That is why I asked about noise, timing jitter, and sample rate. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●May 15, 20042004-05-15
Jerry Avins <jya@ieee.org> writes:> Randy Yates wrote: > >> Jerry Avins <jya@ieee.org> writes: >> >>>[...] >>>By "straight-forward", I mean the time needed to determine the frequency >>> with a frequency counter or an FFT. >> Do you know what technique a (analog) frequency counter uses to >> perform its measurement? > > The ones I built to run at high speed -- short measurement intervals -- > opened a gate on one zero crossing of the waveform to be measured and > closed it N zero crossings later. The count from a high-speed clock > accumulates while the gate is open. For example, with a 500 MHz ECL > clock and a 20 cycles of the measured waveform, its period is measured > with a precision of 100 picosecondsWhere did 100 picoseconds come from? I would think the precision is 1/2 of 1/500 MHz = 1 nanosecond.> and an accuracy that depends on its > cycle-to-cycle uniformity. When measuring stable frequencies in the low > MHz range, the measured accuracy is compromised by the uncertainty of > the reference crystal's frequency.If you knew the cycle-to-cycle uniformity was perfect (and the input was relatively noise-free) and the reference was perfect, could you not measure to precision in very few cycles? This does not seem to be a "duration-(1/accuracy)" process. -- % Randy Yates % "And all that I can do %% Fuquay-Varina, NC % is say I'm sorry, %%% 919-577-9882 % that's the way it goes..." %%%% <yates@ieee.org> % Getting To The Point', *Balance of Power*, ELO http://home.earthlink.net/~yatescr
