Hi all. I have been playing a bit with bispectra of stationary signals that contain one fundamental sinusoidal and lots of harmonics. The bispectra come out as expected, showing peaks in a reular grid pattern, and now I wonder if these types of analyses can be used to compare different signals, say, the two channels in a stereo recording. If the power spectrum can be said to be a "polyspectrum" of order 1, and the bispectrum is a polyspectrum of order 2, how is the order 2 quivalent of a cross spectrum defined? Any hints and references are appreciated. Rune
Higher order statistics
Started by ●September 5, 2005
Reply by ●September 5, 20052005-09-05
Hi!> If the power spectrum can be said to be a "polyspectrum" > of order 1, and the bispectrum is a polyspectrum of order 2, > how is the order 2 quivalent of a cross spectrum defined? > > Any hints and references are appreciated.1.) The point of the cross spectrum is to obtain a transfer function. And coherence gives information about linearity of the observed process. 2.) The point of the bicoherence is to obtain information about specific phase relations (quadratic phase coupling) between spectral components. I know that a lot of theory has been written, but I dont have one of my books here to comment on the cross bispectrum. (if it exists). Best Regards! Atmapuri
Reply by ●September 6, 20052005-09-06
Rune Allnor wrote:> Hi all. > > I have been playing a bit with bispectra of stationary > signals that contain one fundamental sinusoidal and > lots of harmonics. The bispectra come out as expected, > showing peaks in a reular grid pattern, and now I wonder > if these types of analyses can be used to compare different > signals, say, the two channels in a stereo recording. > > If the power spectrum can be said to be a "polyspectrum" > of order 1, and the bispectrum is a polyspectrum of order 2, > how is the order 2 quivalent of a cross spectrum defined? > > Any hints and references are appreciated. > > Rune >Rune, I believe there was a tutorial style article written in the IEEE Sig. Proc. Magazine (it was quite awhile ago though). There is also a brief introduction into HOS in Therrien's book "Discrete Random Signals and Statistical Signal Processing", which I believe you have. Hope that helps. Cheers, Dave
Reply by ●September 7, 20052005-09-07
David Kirkland wrote:> Rune Allnor wrote: > > Hi all. > > > > I have been playing a bit with bispectra of stationary > > signals that contain one fundamental sinusoidal and > > lots of harmonics. The bispectra come out as expected, > > showing peaks in a reular grid pattern, and now I wonder > > if these types of analyses can be used to compare different > > signals, say, the two channels in a stereo recording. > > > > If the power spectrum can be said to be a "polyspectrum" > > of order 1, and the bispectrum is a polyspectrum of order 2, > > how is the order 2 quivalent of a cross spectrum defined? > > > > Any hints and references are appreciated. > > > > Rune > > > > Rune, > > I believe there was a tutorial style article written in the IEEE Sig. > Proc. Magazine (it was quite awhile ago though). > > There is also a brief introduction into HOS in Therrien's book "Discrete > Random Signals and Statistical Signal Processing", which I believe you > have.Hi David. You are right, I have the Therrien book. The introduction is too brief to make much out of, though. I found the paper Ibrahim & al: "A Higher Order Statistics-Based Adaptive Algorithm for Line Enhancment" IEEE Trans. Sig. Proc., Vol 47, No 2, February 1999, p 527-532 which is a non-linear filter based on the 4th order cumulant, that is supposed to remove the Gaussian components of the noise. The algorithm *seems* straight-forward to implement (I got the formulas up an running in less than 10 min with matlab) but I am not able to reproduce the results as stated in the article. For once, there is an article where everything about the simulations is stated nice and clearly. And then I can't get the algorithm to work... oh well. It's probably some obscure detail I have missed. I get results similar to those in the article if I use the uniform pseudo-random number generator (RAND in matlab) and not the Gaussian pseudo-random generator (RANDN). I don't know what conclusions to draw from that... I'll look for the SP Mag article. Rune
Reply by ●September 7, 20052005-09-07
Rune Allnor wrote:> David Kirkland wrote: > >>Rune Allnor wrote: >> >>>Hi all. >>> >>>I have been playing a bit with bispectra of stationary >>>signals that contain one fundamental sinusoidal and >>>lots of harmonics. The bispectra come out as expected, >>>showing peaks in a reular grid pattern, and now I wonder >>>if these types of analyses can be used to compare different >>>signals, say, the two channels in a stereo recording. >>> >>>If the power spectrum can be said to be a "polyspectrum" >>>of order 1, and the bispectrum is a polyspectrum of order 2, >>>how is the order 2 quivalent of a cross spectrum defined? >>> >>>Any hints and references are appreciated. >>> >>>Rune >>> >> >>Rune, >> >>I believe there was a tutorial style article written in the IEEE Sig. >>Proc. Magazine (it was quite awhile ago though). >> >>There is also a brief introduction into HOS in Therrien's book "Discrete >> Random Signals and Statistical Signal Processing", which I believe you >>have. > > > Hi David. > > You are right, I have the Therrien book. The introduction is too > brief to make much out of, though. > > I found the paper > > Ibrahim & al: "A Higher Order Statistics-Based > Adaptive Algorithm for Line Enhancment" > IEEE Trans. Sig. Proc., Vol 47, No 2, > February 1999, p 527-532 > > which is a non-linear filter based on the 4th order cumulant, > that is supposed to remove the Gaussian components of the noise. > The algorithm *seems* straight-forward to implement (I got the > formulas up an running in less than 10 min with matlab) but I > am not able to reproduce the results as stated in the article. > > For once, there is an article where everything about the > simulations is stated nice and clearly. And then I can't get > the algorithm to work... oh well. It's probably some obscure > detail I have missed. I get results similar to those in the > article if I use the uniform pseudo-random number generator > (RAND in matlab) and not the Gaussian pseudo-random generator > (RANDN). I don't know what conclusions to draw from that... > > I'll look for the SP Mag article. > > Rune >My experience with cummulants are that they take a lot of data, at least 10 times the data required for a second order statistic.
Reply by ●September 7, 20052005-09-07
Stan Pawlukiewicz wrote:> Rune Allnor wrote: > > David Kirkland wrote: > > > >>Rune Allnor wrote: > >> > >>>Hi all. > >>> > >>>I have been playing a bit with bispectra of stationary > >>>signals that contain one fundamental sinusoidal and > >>>lots of harmonics. The bispectra come out as expected, > >>>showing peaks in a reular grid pattern, and now I wonder > >>>if these types of analyses can be used to compare different > >>>signals, say, the two channels in a stereo recording. > >>> > >>>If the power spectrum can be said to be a "polyspectrum" > >>>of order 1, and the bispectrum is a polyspectrum of order 2, > >>>how is the order 2 quivalent of a cross spectrum defined? > >>> > >>>Any hints and references are appreciated. > >>> > >>>Rune > >>> > >> > >>Rune, > >> > >>I believe there was a tutorial style article written in the IEEE Sig. > >>Proc. Magazine (it was quite awhile ago though). > >> > >>There is also a brief introduction into HOS in Therrien's book "Discrete > >> Random Signals and Statistical Signal Processing", which I believe you > >>have. > > > > > > Hi David. > > > > You are right, I have the Therrien book. The introduction is too > > brief to make much out of, though. > > > > I found the paper > > > > Ibrahim & al: "A Higher Order Statistics-Based > > Adaptive Algorithm for Line Enhancment" > > IEEE Trans. Sig. Proc., Vol 47, No 2, > > February 1999, p 527-532 > > > > which is a non-linear filter based on the 4th order cumulant, > > that is supposed to remove the Gaussian components of the noise. > > The algorithm *seems* straight-forward to implement (I got the > > formulas up an running in less than 10 min with matlab) but I > > am not able to reproduce the results as stated in the article. > > > > For once, there is an article where everything about the > > simulations is stated nice and clearly. And then I can't get > > the algorithm to work... oh well. It's probably some obscure > > detail I have missed. I get results similar to those in the > > article if I use the uniform pseudo-random number generator > > (RAND in matlab) and not the Gaussian pseudo-random generator > > (RANDN). I don't know what conclusions to draw from that... > > > > I'll look for the SP Mag article. > > > > Rune > > > > My experience with cummulants are that they take a lot of data, at > least 10 times the data required for a second order statistic.The application I have in mind generates lots of data. It's a 24/7 logging system where the sampling frequency is tens of kHz. Rune
Reply by ●September 7, 20052005-09-07
Rune Allnor wrote:> Stan Pawlukiewicz wrote: >(snip)> > > The application I have in mind generates lots of data. It's a 24/7 > logging system where the sampling frequency is tens of kHz. > > Rune >The only way to find out is to try it. I tend to be skeptical of higher order statistics. I've had trouble repeating results that have published and I know of others who have also. IMHO, One should never buy a used care from a higher order spectra guy.
Reply by ●September 7, 20052005-09-07
Stan Pawlukiewicz wrote:> ... IMHO, One should never buy > a used care from a higher order spectra guy.I have plenty of used cares of my own. I'll give some away to anyone who wants them. 8^) Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●September 8, 20052005-09-08
Stan Pawlukiewicz wrote:> Rune Allnor wrote: > > Stan Pawlukiewicz wrote: > > > (snip) > > > > > > The application I have in mind generates lots of data. It's a 24/7 > > logging system where the sampling frequency is tens of kHz. > > > > Rune > > > > > The only way to find out is to try it. I tend to be skeptical of higher > order statistics. I've had trouble repeating results that have > published and I know of others who have also. IMHO, One should never buy > a used care from a higher order spectra guy.Well, scepticism is good, particularly if one can not repeat published results. On the other hand, having tried hands-on yourself gives a better foundation for critique later on. And it instills the awareness of the difficult questions when others try to sell "groundbreaking" methods. Rune
Reply by ●September 8, 20052005-09-08
Rune Allnor wrote:> Stan Pawlukiewicz wrote: > >>Rune Allnor wrote: >> >>>Stan Pawlukiewicz wrote: >>> >> >>(snip) >> >>> >>>The application I have in mind generates lots of data. It's a 24/7 >>>logging system where the sampling frequency is tens of kHz. >>> >>>Rune >>> >> >> >>The only way to find out is to try it. I tend to be skeptical of higher >>order statistics. I've had trouble repeating results that have >>published and I know of others who have also. IMHO, One should never buy >>a used care from a higher order spectra guy. > > > Well, scepticism is good, particularly if one can not repeat > published results. On the other hand, having tried hands-on > yourself gives a better foundation for critique later on. > > And it instills the awareness of the difficult questions when > others try to sell "groundbreaking" methods. > > Rune >I recall that you don't have a lot of respect for matched field processing as posed by Hinich. Oddly enough the last time I was in the New Orleans area I attended a conference where he (Hinich) was eager to show his bispectrum results. IMHO, bullshit atracts bullshiters.
