Greetings, I'm currently working on a problem and would like some suggestions to 'open my eyes' on alternative ways to estimate the parameters of a sinusoid, possibly in the presence of noise. The sinusoid I want to estimate has been sampled, although currently not at a particularly high rate, but is sufficient. I have experimented with correlation, which seems to have issues with producing reliable results in the presence of noise, and Kalman filtering, which while accurate, is very computationally demanding. I was wondering if there any other methods that I should take into consideration for this problem? I would be implementing this algorithm in a fixed point DSP, and would like to keep computational complexity to a minimum, although accuracy is also of importance.
sinusoidal parameter estimation
Started by ●August 13, 2009
Reply by ●August 13, 20092009-08-13
You wrote many words but you didn't tell any numbers. Dan wrote:> Greetings, > > I'm currently working on a problem and would like some suggestions to > 'open my eyes' on alternative ways to estimate the parameters of a > sinusoid, possibly in the presence of noise. The sinusoid I want to > estimate has been sampled, although currently not at a particularly > high rate, but is sufficient. I have experimented with correlation, > which seems to have issues with producing reliable results in the > presence of noise, and Kalman filtering, which while accurate, is very > computationally demanding. I was wondering if there any other methods > that I should take into consideration for this problem? > > I would be implementing this algorithm in a fixed point DSP, and would > like to keep computational complexity to a minimum, although accuracy > is also of importance.
Reply by ●August 14, 20092009-08-14
On 14 Aug, 01:36, Dan <danluong...@gmail.com> wrote:> Greetings, > > I'm currently working on a problem and would like some suggestions to > 'open my eyes' on alternative ways to estimate the parameters of a > sinusoid, possibly in the presence of noise. The sinusoid I want to > estimate has been sampled, although currently not at a particularly > high rate, but is sufficient. I have experimented with correlation, > which seems to have issues with producing reliable results in the > presence of noise, and Kalman filtering, which while accurate, is very > computationally demanding. I was wondering if there any other methods > that I should take into consideration for this problem?Frequency estimation is a well established field. There are plenty of methods around, MUSIC and ESPRIT are some of the more popular acronyms. There are also quite a few more or less quick'n dirty methods around. One of the former regulars here used to host a web page where a lot of methods were lised. Don't know where it is, though.> I would be implementing this algorithm in a fixed point DSP, and would > like to keep computational complexity to a minimum, although accuracy > is also of importance.Sure. Everybody wants to make do with no tools, have to do no work, and still get perfect results. You wouldn't happen to have a degree in economy? Rune
Reply by ●August 14, 20092009-08-14
On Aug 14, 2:32�am, Rune Allnor <all...@tele.ntnu.no> wrote:> On 14 Aug, 01:36, Dan <danluong...@gmail.com> wrote: > > > Greetings, > > > I'm currently working on a problem and would like some suggestions to > > 'open my eyes' on alternative ways to estimate the parameters of a > > sinusoid, possibly in the presence of noise. The sinusoid I want to > > estimate has been sampled, although currently not at a particularly > > high rate, but is sufficient. I have experimented with correlation, > > which seems to have issues with producing reliable results in the > > presence of noise, and Kalman filtering, which while accurate, is very > > computationally demanding. I was wondering if there any other methods > > that I should take into consideration for this problem? > > Frequency estimation is a well established field. > There are plenty of methods around, MUSIC and ESPRIT > are some of the more popular acronyms. There are also > quite a few more or less quick'n dirty methods around. > > One of the former regulars here used to host a web > page where a lot of methods were lised. Don't know > where it is, though. > > > I would be implementing this algorithm in a fixed point DSP, and would > > like to keep computational complexity to a minimum, although accuracy > > is also of importance. > > Sure. Everybody wants to make do with no tools, > have to do no work, and still get perfect results. > You wouldn't happen to have a degree in economy? > > RuneHere perhaps: http://home.comcast.net/~kootsoop/freqalgs.htm and http://home.comcast.net/~kootsoop/EricJ2/index.htm Clay
Reply by ●August 14, 20092009-08-14
On Aug 13, 11:32 pm, Rune Allnor <all...@tele.ntnu.no> wrote:> On 14 Aug, 01:36, Dan <danluong...@gmail.com> wrote: > > > Greetings, > > > I'm currently working on a problem and would like some suggestions to > > 'open my eyes' on alternative ways to estimate the parameters of a > > sinusoid, possibly in the presence of noise. The sinusoid I want to > > estimate has been sampled, although currently not at a particularly > > high rate, but is sufficient. I have experimented with correlation, > > which seems to have issues with producing reliable results in the > > presence of noise, and Kalman filtering, which while accurate, is very > > computationally demanding. I was wondering if there any other methods > > that I should take into consideration for this problem? > > Frequency estimation is a well established field. > There are plenty of methods around, MUSIC and ESPRIT > are some of the more popular acronyms. There are also > quite a few more or less quick'n dirty methods around. > > One of the former regulars here used to host a web > page where a lot of methods were lised. Don't know > where it is, though.Looks like I've hit upon a bit of a sore topic, but thanks for the info/links. I'll look into those soon, but beforehand I'll try to clarify the problem. I'm trying to estimate the frequency, amplitude, phase and offset of a single (real, undamped) sinusoid of the form (A*cos(2*pi*f*t+phi)+K), where initially A = 1, f = 5e3, phi = 0, K = 0, that passes through an system that can have bursts of noise, and other factors that will change each of the parameters. Each of the parameters will need to be estimated at the receiver (change in freq, amplitude, phase, offset). For the sake of example, the noise is AWGN and the SNR is in the 30dB range during those periods. The waveform is sampled at 6.25us (16x Nyquist).> > > I would be implementing this algorithm in a fixed point DSP, and would > > like to keep computational complexity to a minimum, although accuracy > > is also of importance. > > Sure. Everybody wants to make do with no tools, > have to do no work, and still get perfect results. > You wouldn't happen to have a degree in economy? > > RuneFair enough, to state it more clearly, a faster method is preferable.
Reply by ●August 14, 20092009-08-14
Dan wrote:> On Aug 13, 11:32 pm, Rune Allnor <all...@tele.ntnu.no> wrote: >> On 14 Aug, 01:36, Dan <danluong...@gmail.com> wrote: >> >>> Greetings, >>> I'm currently working on a problem and would like some suggestions to >>> 'open my eyes' on alternative ways to estimate the parameters of a >>> sinusoid, possibly in the presence of noise. The sinusoid I want to >>> estimate has been sampled, although currently not at a particularly >>> high rate, but is sufficient. I have experimented with correlation, >>> which seems to have issues with producing reliable results in the >>> presence of noise, and Kalman filtering, which while accurate, is very >>> computationally demanding. I was wondering if there any other methods >>> that I should take into consideration for this problem? >> Frequency estimation is a well established field. >> There are plenty of methods around, MUSIC and ESPRIT >> are some of the more popular acronyms. There are also >> quite a few more or less quick'n dirty methods around. >> >> One of the former regulars here used to host a web >> page where a lot of methods were lised. Don't know >> where it is, though. > > > Looks like I've hit upon a bit of a sore topic, but thanks for the > info/links. I'll look into those soon, but beforehand I'll try to > clarify the problem. > > I'm trying to estimate the frequency, amplitude, phase and offset of a > single (real, undamped) sinusoid of the form (A*cos(2*pi*f*t+phi)+K), > where initially A = 1, f = 5e3, phi = 0, K = 0, that passes through an > system that can have bursts of noise, and other factors that will > change each of the parameters. Each of the parameters will need to be > estimated at the receiver (change in freq, amplitude, phase, offset). > For the sake of example, the noise is AWGN and the SNR is in the 30dB > range during those periods. The waveform is sampled at 6.25us (16x > Nyquist).How might noise affect the frequency? Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●August 14, 20092009-08-14
On Aug 14, 11:32�am, Jerry Avins <j...@ieee.org> wrote:> Dan wrote: > > On Aug 13, 11:32 pm, Rune Allnor <all...@tele.ntnu.no> wrote: > >> On 14 Aug, 01:36, Dan <danluong...@gmail.com> wrote: > > >>> Greetings, > >>> I'm currently working on a problem and would like some suggestions to > >>> 'open my eyes' on alternative ways to estimate the parameters of a > >>> sinusoid, possibly in the presence of noise. The sinusoid I want to > >>> estimate has been sampled, although currently not at a particularly > >>> high rate, but is sufficient. I have experimented with correlation, > >>> which seems to have issues with producing reliable results in the > >>> presence of noise, and Kalman filtering, which while accurate, is very > >>> computationally demanding. I was wondering if there any other methods > >>> that I should take into consideration for this problem? > >> Frequency estimation is a well established field. > >> There are plenty of methods around, MUSIC and ESPRIT > >> are some of the more popular acronyms. There are also > >> quite a few more or less quick'n dirty methods around. > > >> One of the former regulars here used to host a web > >> page where a lot of methods were lised. Don't know > >> where it is, though. > > > Looks like I've hit upon a bit of a sore topic, but thanks for the > > info/links. I'll look into those soon, but beforehand I'll try to > > clarify the problem. > > > I'm trying to estimate the frequency, amplitude, phase and offset of a > > single (real, undamped) sinusoid of the form (A*cos(2*pi*f*t+phi)+K), > > where initially A = 1, f = 5e3, phi = 0, K = 0, that passes through an > > system that can have bursts of noise, and other factors that will > > change each of the parameters. Each of the parameters will need to be > > estimated at the receiver (change in freq, amplitude, phase, offset). > > For the sake of example, the noise is AWGN and the SNR is in the 30dB > > range during those periods. The waveform is sampled at 6.25us (16x > > Nyquist). > > How might noise affect the frequency? > > Jerry > -- > Engineering is the art of making what you want from things you can get. > �����������������������������������������������������������������������The sinusoid passes through a system which changes the parameters, and incidentally noise may also be introduced. Think of it like ultrasound where the sinusoid passes through tissue, which changes its amplitude, freq, phase, etc., but where some outside interference could cause noise. So I'm saying the system itself and not the noise would affect the frequency and phase. However, the noise could affect the amplitude and offset.
Reply by ●August 14, 20092009-08-14
Dan wrote:> On Aug 14, 11:32 am, Jerry Avins <j...@ieee.org> wrote: >> Dan wrote: >>> On Aug 13, 11:32 pm, Rune Allnor <all...@tele.ntnu.no> wrote: >>>> On 14 Aug, 01:36, Dan <danluong...@gmail.com> wrote: >>>>> Greetings, >>>>> I'm currently working on a problem and would like some suggestions to >>>>> 'open my eyes' on alternative ways to estimate the parameters of a >>>>> sinusoid, possibly in the presence of noise. The sinusoid I want to >>>>> estimate has been sampled, although currently not at a particularly >>>>> high rate, but is sufficient. I have experimented with correlation, >>>>> which seems to have issues with producing reliable results in the >>>>> presence of noise, and Kalman filtering, which while accurate, is very >>>>> computationally demanding. I was wondering if there any other methods >>>>> that I should take into consideration for this problem? >>>> Frequency estimation is a well established field. >>>> There are plenty of methods around, MUSIC and ESPRIT >>>> are some of the more popular acronyms. There are also >>>> quite a few more or less quick'n dirty methods around. >>>> One of the former regulars here used to host a web >>>> page where a lot of methods were lised. Don't know >>>> where it is, though. >>> Looks like I've hit upon a bit of a sore topic, but thanks for the >>> info/links. I'll look into those soon, but beforehand I'll try to >>> clarify the problem. >>> I'm trying to estimate the frequency, amplitude, phase and offset of a >>> single (real, undamped) sinusoid of the form (A*cos(2*pi*f*t+phi)+K), >>> where initially A = 1, f = 5e3, phi = 0, K = 0, that passes through an >>> system that can have bursts of noise, and other factors that will >>> change each of the parameters. Each of the parameters will need to be >>> estimated at the receiver (change in freq, amplitude, phase, offset). >>> For the sake of example, the noise is AWGN and the SNR is in the 30dB >>> range during those periods. The waveform is sampled at 6.25us (16x >>> Nyquist). >> How might noise affect the frequency? >> >> Jerry >> -- >> Engineering is the art of making what you want from things you can get. >> ����������������������������������������������������������������������� > > The sinusoid passes through a system which changes the parameters, and > incidentally noise may also be introduced. Think of it like ultrasound > where the sinusoid passes through tissue, which changes its amplitude, > freq, phase, etc., but where some outside interference could cause > noise. So I'm saying the system itself and not the noise would affect > the frequency and phase. However, the noise could affect the amplitude > and offset.As far as I know, Doppler changes frequency, not noise as it's usually defined. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●August 14, 20092009-08-14
On Aug 14, 11:59 am, Jerry Avins <j...@ieee.org> wrote:> Dan wrote: > > On Aug 14, 11:32 am, Jerry Avins <j...@ieee.org> wrote: > >> Dan wrote: > >>> On Aug 13, 11:32 pm, Rune Allnor <all...@tele.ntnu.no> wrote: > >>>> On 14 Aug, 01:36, Dan <danluong...@gmail.com> wrote: > >>>>> Greetings, > >>>>> I'm currently working on a problem and would like some suggestions to > >>>>> 'open my eyes' on alternative ways to estimate the parameters of a > >>>>> sinusoid, possibly in the presence of noise. The sinusoid I want to > >>>>> estimate has been sampled, although currently not at a particularly > >>>>> high rate, but is sufficient. I have experimented with correlation, > >>>>> which seems to have issues with producing reliable results in the > >>>>> presence of noise, and Kalman filtering, which while accurate, is very > >>>>> computationally demanding. I was wondering if there any other methods > >>>>> that I should take into consideration for this problem? > >>>> Frequency estimation is a well established field. > >>>> There are plenty of methods around, MUSIC and ESPRIT > >>>> are some of the more popular acronyms. There are also > >>>> quite a few more or less quick'n dirty methods around. > >>>> One of the former regulars here used to host a web > >>>> page where a lot of methods were lised. Don't know > >>>> where it is, though. > >>> Looks like I've hit upon a bit of a sore topic, but thanks for the > >>> info/links. I'll look into those soon, but beforehand I'll try to > >>> clarify the problem. > >>> I'm trying to estimate the frequency, amplitude, phase and offset of a > >>> single (real, undamped) sinusoid of the form (A*cos(2*pi*f*t+phi)+K), > >>> where initially A = 1, f = 5e3, phi = 0, K = 0, that passes through an > >>> system that can have bursts of noise, and other factors that will > >>> change each of the parameters. Each of the parameters will need to be > >>> estimated at the receiver (change in freq, amplitude, phase, offset). > >>> For the sake of example, the noise is AWGN and the SNR is in the 30dB > >>> range during those periods. The waveform is sampled at 6.25us (16x > >>> Nyquist). > >> How might noise affect the frequency? > > >> Jerry > >> -- > >> Engineering is the art of making what you want from things you can get. > >> ����������������������������������������������������������������������� > > > The sinusoid passes through a system which changes the parameters, and > > incidentally noise may also be introduced. Think of it like ultrasound > > where the sinusoid passes through tissue, which changes its amplitude, > > freq, phase, etc., but where some outside interference could cause > > noise. So I'm saying the system itself and not the noise would affect > > the frequency and phase. However, the noise could affect the amplitude > > and offset. > > As far as I know, Doppler changes frequency, not noise as it's usually > defined. > > Jerry > -- > Engineering is the art of making what you want from things you can get. > �����������������������������������������������������������������������I see what you are getting at, and yes frequency shift is not likely in the system I am talking about. The input sinusoid frequency could be taken as given, and the the problem just becomes one about calculating the other parameters (amplitude, phase, and offset). Knowing that, what are the best ways to estimate those values? Like I mentioned earlier, correlation can give me the accurate values for high SNR, but is there something better out there for when parts of the signal are lower SNR?
Reply by ●August 14, 20092009-08-14
On 14 Aug, 23:20, Dan <danluong...@gmail.com> wrote:> On Aug 14, 11:59 am, Jerry Avins <j...@ieee.org> wrote: > > > > > > > Dan wrote: > > > On Aug 14, 11:32 am, Jerry Avins <j...@ieee.org> wrote: > > >> Dan wrote: > > >>> On Aug 13, 11:32 pm, Rune Allnor <all...@tele.ntnu.no> wrote: > > >>>> On 14 Aug, 01:36, Dan <danluong...@gmail.com> wrote: > > >>>>> Greetings, > > >>>>> I'm currently working on a problem and would like some suggestions to > > >>>>> 'open my eyes' on alternative ways to estimate the parameters of a > > >>>>> sinusoid, possibly in the presence of noise. The sinusoid I want to > > >>>>> estimate has been sampled, although currently not at a particularly > > >>>>> high rate, but is sufficient. I have experimented with correlation, > > >>>>> which seems to have issues with producing reliable results in the > > >>>>> presence of noise, and Kalman filtering, which while accurate, is very > > >>>>> computationally demanding. I was wondering if there any other methods > > >>>>> that I should take into consideration for this problem? > > >>>> Frequency estimation is a well established field. > > >>>> There are plenty of methods around, MUSIC and ESPRIT > > >>>> are some of the more popular acronyms. There are also > > >>>> quite a few more or less quick'n dirty methods around. > > >>>> One of the former regulars here used to host a web > > >>>> page where a lot of methods were lised. Don't know > > >>>> where it is, though. > > >>> Looks like I've hit upon a bit of a sore topic, but thanks for the > > >>> info/links. I'll look into those soon, but beforehand I'll try to > > >>> clarify the problem. > > >>> I'm trying to estimate the frequency, amplitude, phase and offset of a > > >>> single (real, undamped) sinusoid of the form (A*cos(2*pi*f*t+phi)+K), > > >>> where initially A = 1, f = 5e3, phi = 0, K = 0, that passes through an > > >>> system that can have bursts of noise, and other factors that will > > >>> change each of the parameters. Each of the parameters will need to be > > >>> estimated at the receiver (change in freq, amplitude, phase, offset). > > >>> For the sake of example, the noise is AWGN and the SNR is in the 30dB > > >>> range during those periods. The waveform is sampled at 6.25us (16x > > >>> Nyquist). > > >> How might noise affect the frequency? > > > >> Jerry > > >> -- > > >> Engineering is the art of making what you want from things you can get. > > >> ����������������������������������������������������������������������� > > > > The sinusoid passes through a system which changes the parameters, and > > > incidentally noise may also be introduced. Think of it like ultrasound > > > where the sinusoid passes through tissue, which changes its amplitude, > > > freq, phase, etc., but where some outside interference could cause > > > noise. So I'm saying the system itself and not the noise would affect > > > the frequency and phase. However, the noise could affect the amplitude > > > and offset. > > > As far as I know, Doppler changes frequency, not noise as it's usually > > defined. > > > Jerry > > -- > > Engineering is the art of making what you want from things you can get. > > ����������������������������������������������������������������������� > > I see what you are getting at, and yes frequency shift is not likely > in the system I am talking about. The input sinusoid frequency could > be taken as given, and the the problem just becomes one about > calculating the other parameters (amplitude, phase, and offset). > > Knowing that, what are the best ways to estimate those values? Like I > mentioned earlier, correlation can give me the accurate values for > high SNR, but is there something better out there for when parts of > the signal are lower SNR?Some of the parametric frequency estimators work at quite low SNRs. However, they are based on the assumption that the signal can be described by a sum-of-sines model. If the signal does not comply to those assumptions, the estimator still produces a result, but without giving any indications that it has broken. I commented on that in a post a few weeks ago, but google's search engine seems to have broken, so I can't find it for you. Rune
