FFT and estimating frequencies not on discrete points

On Sep 25, 2:57 pm, "mnentwig" <mnent...@elisanet.fi> wrote:
> >>Bad in what way? Maximum likelihood is hard to beat.
>
> Huh? What does FFT have to do with maximum likelyhood?
>
> From a practical point of view, I doubt think that a majority of carrier
> recovery schemes relies on FFT, and that may be what the OP really needs.
>
> >Why FM demod? Once the PLL is locked up, read it's frequency. If the
> >frequency is variable, the PLL *is* the FM demod.
>
> That's right and that's my point. But search for PLL alone, and I doubt
> something relevant will come up at the top. Search for FM demodulation
> -and- PLL... well, you said it already.
>
> -mn

The original post says nothing about carrier recovery.

 As far as Maxlikelihood, read the article I cited.

Ah, we are talking about different things.
Those discussions are usually the best. Well, the most entertaining for
the audience at least, not necessarily the most productive. 
I am actually not arguing with you.

My statement was and is that the original poster might need a standard
"Proakis-chapter-six" carrier recovery instead of a wild FFT scheme, as is
the subject of the thread. Yes, the original post says nothing about
carrier recovery. But that's still what might be the most useful.

I hope that clarifies.

-mn

All of you,

Thank you very much for the information. Sorry for the delay on this,
I didn't have time to do this in the past month, so I decided I will
wait until I can do it well. I tried some of the things mentioned
above (like quadratic interpolation found in the links mnentwig gave)
and I applied Hann window (which I didn't before), so it worked pretty
well. I am still not completely satisfied with the result and I will
look into this a little more.

Thanks again and good day to you all!

On Sep 23, 12:26 pm, wi...@yahoo.com wrote:
> Assume there is a real function f and its spectrum F. If f is discrete
> sampled, we have samples at some t = st * k, where st is sampling
> period and k = 0, 1, 2, ..., N - 1. Also assume every frequency in f
> is within [-fc..fc] range, fc = Nyqist frequency. If f is a simple
> sine function whose minimums, zeros and maximums are at the sampling
> points, F will be very "good", without leakage and just by looking at
> some point of F we can see what is the frequency m of f =
> sin(2*pi*m).
>
> However, if this is not the case, i.e. extremal points of f do not lay
> on the sampled points (k = 0, 1, 2, ..., N - 1), this will not be the
> case - there will be leakage. Assume that I calculated F from the
> known f and I have N/2 bins of F at my hand. Bin n - 1 is for
> frequency m - j, bin n is for frequency m and bin n + 1 for frequency
> m + j. How can I calculate the power for frequency e.g. m - j / 2 or m
> + j / 3 or such? That is, calculate the power at some frequency for
> which I don't have F defined, which I presume would allow me to see
> which frequency is the "main" one (let away special cases).


dunno if you're interested, but i did a paper in 2001 (Mohonk, geez, i
wonder if it's going on now?) where, in the case of using a Gaussian
window on the data, i had an reasonably elegant solution for
estimating the instantaneous frequency (at the midddle of the window),
the sweep-rate, and ramp-rate in log amplitude (and amplitude).  it
requires FFT, discrete-derivative, complex log, least-squares fit to a
linear function, and a closed form expression for extracting the
parameters we want out of the complex slope and offset parameters from
the linear function.

it *does* assume it's not interfered with significantly by ohter swept
sinusoids.  that's a deficiency in the algorithm.

r b-j