The Sinc Estimator - now with graphs

On May 22, 7:20 am, "Michael P." <m...@home.com> wrote:
> "steve" <bungalow_st...@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
yes for mulitple signals you would have to figure out what is the
worse case interaction, and perhaps increase the FFT resolution by
increasing the total sampling period, if you can't then 2 samples may
be the best you can hope for.