Hello, I have the sinusoidal signal (f=1050Hz) with some frequency offset (in range of -5; +5 Hz). Length of signal is 1024 samples. I need to measure the frequency offset with accuracy ~0.01 Hz. What method can i use for doing this? Thanks.
Frequency offset estimation.
Started by ●May 12, 2004
Reply by ●May 12, 20042004-05-12
Andrey wrote:> Hello, > > I have the sinusoidal signal (f=1050Hz) with some frequency offset > (in range of -5; +5 Hz). Length of signal is 1024 samples. I need to > measure the frequency offset with accuracy ~0.01 Hz. What method can i > use for doing this? > > Thanks.Try the Goertzel Algorithm. OUP
Reply by ●May 12, 20042004-05-12
Andrey wrote:> Hello, > > I have the sinusoidal signal (f=1050Hz) with some frequency offset > (in range of -5; +5 Hz). Length of signal is 1024 samples. I need to > measure the frequency offset with accuracy ~0.01 Hz. What method can i > use for doing this? > > Thanks.The straight-forward way to measure frequency to .01 Hz requires samples for 1/.01 = 100 seconds. You don't indicate your sampling frequency, but the theoretical minimum frequency (assuming that the description of your signal covers no hidden gotchas) is 40 Hz. and you will want to sample at at least 60 Hz for practical reasons. But even 40/second times 100 seconds exceeds 1024 by about 4x. There may be tricks you can play to reduce the count, but it won't be easy to go as far as you need. What is your sample rate? What is the signal-to-noise ratio? How much timing jitter is there? These all affect what tricks you can use. Jerry -- Here's a great marketing idea: a beer bottle with a square screw cap. �����������������������������������������������������������������������
Reply by ●May 12, 20042004-05-12
Jerry Avins <jya@ieee.org> writes:> Andrey wrote: > > > Hello, > > I have the sinusoidal signal (f=1050Hz) with some frequency offset > > > (in range of -5; +5 Hz). Length of signal is 1024 samples. I need to > > measure the frequency offset with accuracy ~0.01 Hz. What method can i > > use for doing this? > > Thanks. > > > The straight-forward way to measure frequency to .01 Hz requires samples > for 1/.01 = 100 seconds.This is not correct, Jerry. The time required to obtain a specific accuracy depends on the accuracy and the noise. Without noise, one may obtain a perfect estimate in two complex samples (assuming complex sampling). -- Randy Yates Sony Ericsson Mobile Communications Research Triangle Park, NC, USA randy.yates@sonyericsson.com, 919-472-1124
Reply by ●May 12, 20042004-05-12
The Goertzel Algorithm can give you the magnitude of single frequency component. I suppose you could apply Goertzel at every required frequency step in the interval and look for the largest value--is that what you were thinking? "One Usenet Poster" <me@my.computer.org> wrote in message news:10a4hjng2iotte7@corp.supernews.com...> Andrey wrote: > > Hello, > > > > I have the sinusoidal signal (f=1050Hz) with some frequency offset > > (in range of -5; +5 Hz). Length of signal is 1024 samples. I need to > > measure the frequency offset with accuracy ~0.01 Hz. What method can i > > use for doing this? > > > > Thanks. > > Try the Goertzel Algorithm. > > OUP
Reply by ●May 12, 20042004-05-12
Jon Harris wrote:> The Goertzel Algorithm can give you the magnitude of single frequency component. > I suppose you could apply Goertzel at every required frequency step in the > interval and look for the largest value--is that what you were thinking?Yes. OUP
Reply by ●May 12, 20042004-05-12
Randy Yates wrote:> Jerry Avins <jya@ieee.org> writes: > > >>Andrey wrote: >> >> >>>Hello, >>> I have the sinusoidal signal (f=1050Hz) with some frequency offset >> >>>(in range of -5; +5 Hz). Length of signal is 1024 samples. I need to >>>measure the frequency offset with accuracy ~0.01 Hz. What method can i >>>use for doing this? >>>Thanks. >> >> >>The straight-forward way to measure frequency to .01 Hz requires samples >>for 1/.01 = 100 seconds. > > > This is not correct, Jerry. The time required to obtain a specific accuracy > depends on the accuracy and the noise. Without noise, one may obtain a > perfect estimate in two complex samples (assuming complex sampling).I did write "straight-forward". The part you snipped included, "There may be tricks you can play to reduce the count, but it won't be easy to go as far as you need" and "What is the signal-to-noise ratio? How much timing jitter is there? These all affect what tricks you can use." Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●May 13, 20042004-05-13
Jerry Avins <jya@ieee.org> writes:> Randy Yates wrote: > >> Jerry Avins <jya@ieee.org> writes: >> >>>Andrey wrote: >>> >>> >>>>Hello, >>>> I have the sinusoidal signal (f=1050Hz) with some frequency offset >>> >>>>(in range of -5; +5 Hz). Length of signal is 1024 samples. I need to >>>>measure the frequency offset with accuracy ~0.01 Hz. What method can i >>>>use for doing this? >>>>Thanks. >>> >>> >>>The straight-forward way to measure frequency to .01 Hz requires samples >>> for 1/.01 = 100 seconds. >> This is not correct, Jerry. The time required to obtain a specific >> accuracy depends on the accuracy and the noise. Without noise, one >> may obtain a perfect estimate in two complex samples (assuming >> complex sampling). > > I did write "straight-forward". The part you snipped included, "There > may be tricks you can play to reduce the count, but it won't be easy to > go as far as you need" and "What is the signal-to-noise ratio? How much > timing jitter is there? These all affect what tricks you can use."Jerry, I'm going to be anal about this. Regardless of what you said after the sentence I quoted, the sentence is, at a minimum, extremely misleading. The implication is that the amount of time to make a measurement to a certain frequency accuracy is the inverse of that frequency accuracy. That is untrue, whether or not there is noise present. The time required is a function of the technique used, the noise, and the required accuracy, but it is not at all "approximately" the inverse of the required frequency accuracy. That's like saying the inverse of a number between 0 and 1 is approximately 2. -- % Randy Yates % "Though you ride on the wheels of tomorrow, %% Fuquay-Varina, NC % you still wander the fields of your %%% 919-577-9882 % sorrow." %%%% <yates@ieee.org> % '21st Century Man', *Time*, ELO http://home.earthlink.net/~yatescr
Reply by ●May 13, 20042004-05-13
Randy Yates wrote:> Jerry Avins <jya@ieee.org> writes: > > >>Randy Yates wrote: >> >> >>>Jerry Avins <jya@ieee.org> writes: >>> >>> >>>>Andrey wrote: >>>> >>>> >>>> >>>>>Hello, >>>>> I have the sinusoidal signal (f=1050Hz) with some frequency offset >>>> >>>>>(in range of -5; +5 Hz). Length of signal is 1024 samples. I need to >>>>>measure the frequency offset with accuracy ~0.01 Hz. What method can i >>>>>use for doing this? >>>>>Thanks. >>>> >>>> >>>>The straight-forward way to measure frequency to .01 Hz requires samples >>>>for 1/.01 = 100 seconds. >>> >>>This is not correct, Jerry. The time required to obtain a specific >>>accuracy depends on the accuracy and the noise. Without noise, one >>>may obtain a perfect estimate in two complex samples (assuming >>>complex sampling). >> >>I did write "straight-forward". The part you snipped included, "There >>may be tricks you can play to reduce the count, but it won't be easy to >>go as far as you need" and "What is the signal-to-noise ratio? How much >>timing jitter is there? These all affect what tricks you can use." > > > Jerry, > > I'm going to be anal about this.You and R.B-J. seem to enjoy constipation. That's good company! :-)> Regardless of what you said after the > sentence I quoted, the sentence is, at a minimum, extremely misleading. > The implication is that the amount of time to make a measurement to a > certain frequency accuracy is the inverse of that frequency accuracy.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.> The time required > is a function of the technique used, the noise, and the required accuracy, > but it is not at all "approximately" the inverse of the required frequency > accuracy. That's like saying the inverse of a number between 0 and 1 is > approximately 2.I claimed no useful approximation. I took it as an upper bound sufficiently far above the requirement to suggest that solving the problem isn't trivially easy. If I'm wrong and there is an easy way, share it with Andrey instead of (or in addition to) arguing with me. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●May 13, 20042004-05-13
Jerry Avins wrote: ...> That with more information, the actual time can't be estimated?without ^ ... Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
