Amplitude estimation of frequencies in the same bin

Hello,

I am transmitting a number of known sine frequencies with known
transmition amplitude.
The recieved frequencies are in the same bin (this can not be changed).
My Q is:
Is there a method to estimate the recieved amplitude of every
frequency???

Thank you
Benny

Have you tried using super resolution methods such as MUSIC ?

bennylif33@hotmail.com wrote:

  ...

> The recieved frequencies are in the same bin (this can not be changed).

Who laid that restriction on you?  If you have the data to do an FFT,
you could instead do whatever you want with them. If all the other bins
are empty, the task becomes rather easy.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
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bennylif33@hotmail.com wrote:

>
> I am transmitting a number of known sine frequencies with known
> transmition amplitude.
> The recieved frequencies are in the same bin (this can not be changed).
> My Q is:
> Is there a method to estimate the recieved amplitude of every
> frequency???
>

If you were, say, using FFT for some "raw localization" (and had a
constraint of FFT size, CPU resources, whatever), or you already had
this information from another subsystem anyway, and needed better
localization/resolution within the initially found bin, you could try
using a "not so fast" DFT (convolution with sin/cos) to localize the
frequency(ies) with better precision. Probably some kind of search
would be appropriate too, with several iterations.

Everything of course depends on the task details (how many frequencies,
how close to each other, required localization precision, SNR, etc.),
and probably it's better to review the constraints, especially if "a
number of known freqs" is big.

Regards,
Dmitry.

bennylif33@hotmail.com wrote:
> I am transmitting a number of known sine frequencies with known
> transmition amplitude.
> The recieved frequencies are in the same bin (this can not be changed).
> My Q is:
> Is there a method to estimate the recieved amplitude of every
> frequency???

Each frequency sharing a bin will add a Sinc shaped function
to the total FFT/DFT magnitude vector.  If the number of known
frequencies is sufficiently less than the number of data
points, then you could try to do a regression fit of a sum
of N Sinc functions to your FFT/DFT result vector.  Of course,
this regression might be very sensitive to noise.


IMHO. YMMV.
-- 
Ron
rhn A.T nicholson d.0.t C-o-M
http://www.nicholson.com/rhn

hi benny,
             just look at some ICA methods. may be that can help you..

particlereddy

Hello Ikaro,

I didnt try the MUSIC method, because to my anderstanding the coplexity
is much higher then DFT and simple estimation methods.
However, I will look at it and will check it out.
thanks
Benny

Hello Jerry,

The restrictions cant be changed because of a fixed sampling frequency
and analog amplifires with fixed working frequencies.
the problem is that I need to estimate more frequencies amplitude then
free bins, because of my constraines.

Benny

Hello Dmitry,

You wrote: "you could try using a "not so fast" DFT (convolution with
sin/cos) to localize the frequency(ies) with better precision. Probably
some kind of search would be appropriate too, with several iterations".

What do you mean by, "not so fast DFT". And by, "Probably some kind of
search would be appropriate too, with several iterations" ?
BTW
the constrains are fixed and cant be changed.

Thanks
Benny

Hello Dmitry,

You wrote: "you could try using a "not so fast" DFT (convolution with
sin/cos) to localize the frequency(ies) with better precision. Probably
some kind of search would be appropriate too, with several iterations".

What do you mean by, "not so fast DFT". And by, "Probably some kind of
search would be appropriate too, with several iterations" ?
BTW
the constrains are fixed and cant be changed.

Thanks
Benny