Hi Group Please look at the graphs in the document I have uploaded at http://users.cybercity.dk/~dsl70261/The%20Sinc%20Estimator.pdf A picture says more than a 1000 words :-) Let me just add that my viewpoint is purely theoretical and mathematical. So I am just considering a pure sine signal with no noise. I don't know if my method would be useful in practise. Best wishes, Michael
The Sinc Estimator - now with graphs
Started by ●May 20, 2011
Reply by ●May 20, 20112011-05-20
On May 20, 7:47�am, "Michael P." <m...@home.com> wrote:> Hi Group > > Please look at the graphs in the document I have uploaded at > > http://users.cybercity.dk/~dsl70261/The%20Sinc%20Estimator.pdf > > A picture says more than a 1000 words :-) > > Let me just add that my viewpoint is purely theoretical and mathematical. > So I am just considering a pure sine signal with no noise. > I don't know if my method would be useful in practise. > > Best wishes, > Michael �Hello Michael, This is good, try putting your frequency between the DC term and the 1st bin and see what happens with your estimator. Clay
Reply by ●May 20, 20112011-05-20
On May 20, 7:47�am, "Michael P." <m...@home.com> wrote:> Hi Group > > Please look at the graphs in the document I have uploaded at > > http://users.cybercity.dk/~dsl70261/The%20Sinc%20Estimator.pdf > > A picture says more than a 1000 words :-) > > Let me just add that my viewpoint is purely theoretical and mathematical. > So I am just considering a pure sine signal with no noise. > I don't know if my method would be useful in practise. > > Best wishes, > Michael �In practice you would use more then two bins, more bin info contains more information, especially with the high side lobes of rectangular windows. This can be applied, in theory, to windowed FFT's, with the appropriate modifed "sinc like" expected response, although it won't be a nice closed form solution.
Reply by ●May 20, 20112011-05-20
On May 20, 7:34�am, steve <bungalow_st...@yahoo.com> wrote:> ... > > In practice you would use more then two bins, more bin info contains > more information, especially with the high side lobes of rectangular > windows.In practice there is a trade-off between more information and more noise or probability of interference.> > This can be applied, in theory, to windowed FFT's, with the > appropriate modifed "sinc like" expected response, although it won't > be a nice closed form solution.There are closed form solutions for some windows.The maximum sidelobe rolloff windows have exact solutions. Parabolic interpolation is exact for the log of the Gaussian windowed power spectrum. There have been windows designed to have triangular frequency domain response to allow closed form calculation. Other intentional window designs may allow other direct calculations. Dale B. Dalrymple
Reply by ●May 21, 20112011-05-21
"Clay" <clay@claysturner.com> wrote in message news:eb7fad2f-4a32-43fa-81e1-2968a812848a@v10g2000yqn.googlegroups.com...> On May 20, 7:47 am, "Michael P." <m...@home.com> wrote: >> Hi Group >> >> Please look at the graphs in the document I have uploaded at >> >> http://users.cybercity.dk/~dsl70261/The%20Sinc%20Estimator.pdf >> >> A picture says more than a 1000 words :-) >> >> Let me just add that my viewpoint is purely theoretical and mathematical. >> So I am just considering a pure sine signal with no noise. >> I don't know if my method would be useful in practise. >> >> Best wishes, >> Michael > > Hello Michael, > > This is good, try putting your frequency between the DC term and the > 1st bin and see what happens with your estimator. > > Clay >Hi Clay Do you mean when b0=0 and b1=1? I don't see a problem with that because m0 and m1 will not both be zero. My text version showed that m0 and m1 are interchangeable in "The Sinc Magnitude Estimator". Also remember that Sinc(0)=1. Best wishes, Michael
Reply by ●May 21, 20112011-05-21
"steve" <bungalow_steve@yahoo.com> wrote in message news:71b4891d-b718-46ee-8ffc-59a700a119c6@x10g2000yqj.googlegroups.com...> On May 20, 7:47 am, "Michael P." <m...@home.com> wrote: >> Hi Group >> >> Please look at the graphs in the document I have uploaded at >> >> http://users.cybercity.dk/~dsl70261/The%20Sinc%20Estimator.pdf >> >> A picture says more than a 1000 words :-) >> >> Let me just add that my viewpoint is purely theoretical and mathematical. >> So I am just considering a pure sine signal with no noise. >> I don't know if my method would be useful in practise. >> >> Best wishes, >> Michael > > > In practice you would use more then two bins, more bin info contains > more information, especially with the high side lobes of rectangular > windows. > > This can be applied, in theory, to windowed FFT's, with the > appropriate modifed "sinc like" expected response, although it won't > be a nice closed form solution.Actually two bins define the Sinc function completely. But maybe you can take account for rounding errors if you use more bins. I would think that calculating on only the two largest magnitudes would be less prone to rounding errors. Michael
Reply by ●May 21, 20112011-05-21
On May 21, 4:36 am, "Michael P." <m...@home.com> wrote:> "steve" <bungalow_st...@yahoo.com> wrote in message > > news:71b4891d-b718-46ee-8ffc-59a700a119c6@x10g2000yqj.googlegroups.com... > > > > > On May 20, 7:47 am, "Michael P." <m...@home.com> wrote: > >> Hi Group > > >> Please look at the graphs in the document I have uploaded at > > >>http://users.cybercity.dk/~dsl70261/The%20Sinc%20Estimator.pdf > > >> A picture says more than a 1000 words :-) > > >> Let me just add that my viewpoint is purely theoretical and mathematical. > >> So I am just considering a pure sine signal with no noise. > >> I don't know if my method would be useful in practise. > > >> Best wishes, > >> Michael > > > In practice you would use more then two bins, more bin info contains > > more information, especially with the high side lobes of rectangular > > windows. > > > This can be applied, in theory, to windowed FFT's, with the > > appropriate modifed "sinc like" expected response, although it won't > > be a nice closed form solution. > > Actually two bins define the Sinc function completely. > But maybe you can take account for rounding errors if you use more bins. > I would think that calculating on only the two largest magnitudes > would be less prone to rounding errors. > > Michaelthe lobe magnitudes are pretty significant, so I wouldn't be concerned with rounding error, when I said in practice I was referring to noise. think of it this way, 2 samples is the effective nyquist rate, but more samples gets you a better estimate.
Reply by ●May 21, 20112011-05-21
On May 21, 7:32�am, "Michael P." <m...@home.com> wrote:> "Clay" <c...@claysturner.com> wrote in message > > news:eb7fad2f-4a32-43fa-81e1-2968a812848a@v10g2000yqn.googlegroups.com... > > > > > > > On May 20, 7:47 am, "Michael P." <m...@home.com> wrote: > >> Hi Group > > >> Please look at the graphs in the document I have uploaded at > > >>http://users.cybercity.dk/~dsl70261/The%20Sinc%20Estimator.pdf > > >> A picture says more than a 1000 words :-) > > >> Let me just add that my viewpoint is purely theoretical and mathematical. > >> So I am just considering a pure sine signal with no noise. > >> I don't know if my method would be useful in practise. > > >> Best wishes, > >> Michael > > > Hello Michael, > > > This is good, try putting your frequency between the DC term and the > > 1st bin and see what happens with your estimator. > > > Clay > > Hi Clay > > Do you mean when b0=0 and b1=1? > I don't see a problem with that because m0 and m1 will not both be zero. > My text version showed that m0 and m1 are interchangeable > in "The Sinc Magnitude Estimator". > Also remember that Sinc(0)=1. > > Best wishes, Michael- Hide quoted text - > > - Show quoted text -The issue is not with their being zero. It has to do with the FFT's output being special at DC and f_s/2 compared to the other bins. Try it. Clay
Reply by ●May 22, 20112011-05-22
"steve" <bungalow_steve@yahoo.com> wrote in message news:2138abae-4dc8-442f-ba9e-cea6eb1a1e88@f31g2000pri.googlegroups.com...> On May 21, 4:36 am, "Michael P." <m...@home.com> wrote: >> "steve" <bungalow_st...@yahoo.com> wrote in message >> >> news:71b4891d-b718-46ee-8ffc-59a700a119c6@x10g2000yqj.googlegroups.com... >> >> >> >> > On May 20, 7:47 am, "Michael P." <m...@home.com> wrote: >> >> Hi Group >> >> >> Please look at the graphs in the document I have uploaded at >> >> >>http://users.cybercity.dk/~dsl70261/The%20Sinc%20Estimator.pdf >> >> >> A picture says more than a 1000 words :-) >> >> >> Let me just add that my viewpoint is purely theoretical and >> >> mathematical. >> >> So I am just considering a pure sine signal with no noise. >> >> I don't know if my method would be useful in practise. >> >> >> Best wishes, >> >> Michael >> >> > In practice you would use more then two bins, more bin info contains >> > more information, especially with the high side lobes of rectangular >> > windows. >> >> > This can be applied, in theory, to windowed FFT's, with the >> > appropriate modifed "sinc like" expected response, although it won't >> > be a nice closed form solution. >> >> Actually two bins define the Sinc function completely. >> But maybe you can take account for rounding errors if you use more bins. >> I would think that calculating on only the two largest magnitudes >> would be less prone to rounding errors. >> >> Michael > > the lobe magnitudes are pretty significant, so I wouldn't be concerned > with rounding error, when I said in practice I was referring to noise. > think of it this way, 2 samples is the effective nyquist rate, but > more samples gets you a better estimate.I see what you mean. So in order to eliminate the influence of noise maybe use 2 more bins - 1 on each side. Of course if more than one frequency is in the signal there is a greater risk of overlapping the more bins you use. Michael
Reply by ●May 22, 20112011-05-22
"Clay" <clay@claysturner.com> wrote in message news:a0da2a8a-0697-46bd-b7a7-a0242467e4fe@g3g2000vbl.googlegroups.com...> On May 21, 7:32 am, "Michael P." <m...@home.com> wrote: >> "Clay" <c...@claysturner.com> wrote in message >> >> news:eb7fad2f-4a32-43fa-81e1-2968a812848a@v10g2000yqn.googlegroups.com... >> >> >> >> >> >> > On May 20, 7:47 am, "Michael P." <m...@home.com> wrote: >> >> Hi Group >> >> >> Please look at the graphs in the document I have uploaded at >> >> >>http://users.cybercity.dk/~dsl70261/The%20Sinc%20Estimator.pdf >> >> >> A picture says more than a 1000 words :-) >> >> >> Let me just add that my viewpoint is purely theoretical and >> >> mathematical. >> >> So I am just considering a pure sine signal with no noise. >> >> I don't know if my method would be useful in practise. >> >> >> Best wishes, >> >> Michael >> >> > Hello Michael, >> >> > This is good, try putting your frequency between the DC term and the >> > 1st bin and see what happens with your estimator. >> >> > Clay >> >> Hi Clay >> >> Do you mean when b0=0 and b1=1? >> I don't see a problem with that because m0 and m1 will not both be zero. >> My text version showed that m0 and m1 are interchangeable >> in "The Sinc Magnitude Estimator". >> Also remember that Sinc(0)=1. >> >> Best wishes, Michael- Hide quoted text - >> >> - Show quoted text - > > The issue is not with their being zero. It has to do with the FFT's > output being special at DC and f_s/2 compared to the other bins. Try > it. > > ClayI didn't know that about the FFT. I have only used FFT for analysing music, so I have never paid much attention to the end bins. But I have never seen any estimators taking this fact into account. I wrote the document a couple of years ago, but I will dig out the program that I used and test as you say. Michael
