Jerry Avins wrote:> Well, if you know in advance that there is only a single frequency in > the signal, what about the spectrum do you want to measure? The OP is > interested in a spectrum measurement, not a frequency identification.Often, the physics (or biology) of the problem will constrain the probable interpretation of the data (how many resonators are in the system, how closely they can possibly be spaced, the long term distribution of background noise, etc.). A single sine wave in zero noise is obviously a limiting case, but one can often use less limiting constraints to help interpret the data. This a priori knowledge is commonly used. For instance when you see a well separated and symmetric sinc shaped distribution in an FFT spectrum, do you assume you can interpolate halfway between the center two bins, or that multiple adjacent exactly on-bin frequencies are present with a distribution of amplitudes that just happen to look sinc shaped? If you a tuning a flute, you might just assume the former. But if you are hunting for a hidden jamming transmitter installed by an alien intelligence, you might make different assumptions. IMHO. YMMV. -- Ron rhn A.T. nicholson d.O.t C-o-M
minimum cycles for fft, and limits of filling short sample out with zeros
Started by ●September 4, 2005
Reply by ●September 7, 20052005-09-07
Reply by ●September 7, 20052005-09-07
glen herrmannsfeldt wrote:> Stan Pawlukiewicz wrote: > > (snip) > >> The problem with this, is that in quantum mechanics the location of >> the particle is governed by a probability density which is related to >> the observation. In signal processing, the transform broadens but >> the location of peak governs the frequency measurement. The frequency >> content of a truncated signal increases but its not a probability >> density, i.e. the true frequency isn't a random parameter governed by >> chance, like a quantum particle. > > > Say I have a signal that in frequency space has a broad peak, > maybe not so peak shaped at all. What do I call the frequency > of that signal? Somewhere within the peak, but where?Let's make one of those. Posit a narrow bandpass filter with a nearly flat top acting on white noise. Consider the output spectrum. Once you specify what you want "peak" to mean, you'll know where it is. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●September 7, 20052005-09-07
rhnlogic@yahoo.com wrote: ...> Often, the physics (or biology) of the problem will constrain the > probable interpretation of the data (how many resonators are > in the system, how closely they can possibly be spaced, the long > term distribution of background noise, etc.). A single sine wave > in zero noise is obviously a limiting case, but one can often use > less limiting constraints to help interpret the data. > > This a priori knowledge is commonly used. For instance when you > see a well separated and symmetric sinc shaped distribution in > an FFT spectrum, do you assume you can interpolate halfway between > the center two bins, or that multiple adjacent exactly on-bin > frequencies are present with a distribution of amplitudes that > just happen to look sinc shaped? If you a tuning a flute, you > might just assume the former. But if you are hunting for a hidden > jamming transmitter installed by an alien intelligence, you > might make different assumptions.The description of a method based even partly on a-priori knowledge should be clear about what assumptions are being made. With that caveat, I agree. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●September 7, 20052005-09-07
glen herrmannsfeldt <gah@ugcs.caltech.edu> writes:> Stan Pawlukiewicz wrote: > > (snip) > >> The problem with this, is that in quantum mechanics the location of >> the particle is governed by a probability density which is related >> to the observation. In signal processing, the transform broadens >> but the location of peak governs the frequency measurement. The >> frequency content of a truncated signal increases but its not a >> probability density, i.e. the true frequency isn't a random >> parameter governed by chance, like a quantum particle. > > Say I have a signal that in frequency space has a broad peak, > maybe not so peak shaped at all. What do I call the frequency > of that signal? Somewhere within the peak, but where?That is an excellent question, Glen. At least it sure got me thinking. I think I see the "time-frequency" uncertainty thing now and understand at least partially why it doesn't necessarily apply to some types of frequency measurements. This may seem really obvious, but if you look at the frequency domain from the purely mathematical POV, you can only have a *perfect* sinusoid if that sinusoid extends infinitely in time. If you have only an "observation" of that sinusoid, which can be modeled by multiplying the infinite sinusoid by a rectangular window with a width corresponding to the observation period, then that infinite-thin peak in the frequency domain spreads out. Why? Cause you don't know what that sinusoid is "doing" outside the window. Now, those facts are perfectly correct WHEN ANALYZING A SIGNAL OF INFINITE EXTENT. However, we are free to perform an *instantaneous* frequency measurement by, e.g., measuring the change in phase of the analytic signal from one sample to the next and dividing by the sample interval. Thus even thought that "sine" wave may be doing some really funky things outside the observation interval, we can still measure the INSTANTANEOUS frequency and that frequency can be measured PERFECT ACCURATELY if there is NO NOISE. Now if there IS noise, you can't measure even the INSTANTANEOUS frequency accurately and must do some averaging or whatever to get the accuracy up, so introducing noise requires that we measure the signal longer to get an accurate estimate. Does that make sense? -- % Randy Yates % "Ticket to the moon, flight leaves here today %% Fuquay-Varina, NC % from Satellite 2" %%% 919-577-9882 % 'Ticket To The Moon' %%%% <yates@ieee.org> % *Time*, Electric Light Orchestra http://home.earthlink.net/~yatescr
Reply by ●September 7, 20052005-09-07
Randy Yates wrote:> ... we are free to perform an *instantaneous* frequency > measurement by, e.g., measuring the change in phase of the analytic signal > from one sample to the next and dividing by the sample interval.It takes "mono" samples to get two analytic samples, and more to generate Is from Qs with an HT. What procedure can measure two instantaneous phases accurately from two (or four) samples taken with the kind of ADC I can buy? Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●September 7, 20052005-09-07
Randy Yates wrote: > ... we are free to perform an *instantaneous* frequency measurement by, e.g., measuring the change in phase of the analytic signal from one sample to the next and dividing by the sample interval. It takes four "mono" samples to get two analytic samples, and more to generate Is from Qs with an HT. What procedure can measure two instantaneous phases accurately from two (or four) samples taken with the kind of ADC I can buy? Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●September 8, 20052005-09-08
"Jerry Avins" <jya@ieee.org> wrote in message news:Ubidnfh9AeElPoLeRVn-hg@rcn.net...> Randy Yates wrote: > > > ... we are free to perform an *instantaneous* frequency measurement > by, e.g., measuring the change in phase of the analytic signal from one > sample to the next and dividing by the sample interval. > > > It takes four "mono" samples to get two analytic samples, and more to > generate Is from Qs with an HT. What procedure can measure two > instantaneous phases accurately from two (or four) samples taken with the > kind of ADC I can buy? > > Jerry > -- > Engineering is the art of making what you want from things you can get. > �����������������������������������������������������������������������Hello Jerry and others, In the case of evenly temporally spaced real values, the 3 pt formula for frequency is: f = (fs/2pi) *acos( (y0+y2)/(2*y1) ) where fs is the sampling rate and y0, y1, y2 are three consecutive samples all assumed to be within 360 degrees of each other. Clay
Reply by ●September 8, 20052005-09-08
Clay S. Turner wrote:> "Jerry Avins" <jya@ieee.org> wrote in message > news:Ubidnfh9AeElPoLeRVn-hg@rcn.net... > >>Randy Yates wrote: >> >> >>>... we are free to perform an *instantaneous* frequency measurement >> >>by, e.g., measuring the change in phase of the analytic signal from one >>sample to the next and dividing by the sample interval. >> >> >>It takes four "mono" samples to get two analytic samples, and more to >>generate Is from Qs with an HT. What procedure can measure two >>instantaneous phases accurately from two (or four) samples taken with the >>kind of ADC I can buy? >> >>Jerry >>-- >>Engineering is the art of making what you want from things you can get. >>����������������������������������������������������������������������� > > > Hello Jerry and others, > > In the case of evenly temporally spaced real values, the 3 pt formula for > frequency is: > > f = (fs/2pi) *acos( (y0+y2)/(2*y1) ) > > where fs is the sampling rate and y0, y1, y2 are three consecutive samples > all assumed to be within > 360 degrees of each other.And when y1 happens to be zero? Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●September 8, 20052005-09-08
Firstly, did I say these notions had a direct connection to a real-world system? Secondly, did I say you could do this with a single ADC? --RY
Reply by ●September 8, 20052005-09-08
