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Signal processing - getting exact frequency from short ADC sample

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RoGeorge:
Without reading very carefully all the proposed solutions, the OP problem looks to me like an ideal application for a lock-in amplifier, simply because there is prior knowledge of the Tx signal.

There were some quadrature based solutions mentioned, not sure if those will eventually implement an ad-hoc lock-in amplifier or not (at a draft look I perceived them as an implementation of a heterodyne).

I'll go for the homodyne method first (in EE also known as a lock-in amplifier, in optics known as an interferometer) and see if it can get the required resolution.  Also very important, try to make use of all of the prior knowledge, including expected S/N, expected frequency shift ranges, rate of frequency change.

I never had to solve a similar problem, so my advice might be completely off.   ;D

Whatever method you'll choose, "One can not find what one is not looking for", here meaning if you want to squeeze out the best results out of those few samples, you must take advantage of any prior knowledge you have about them, here the most important is that you have the original Tx-ed signal, followed by the expectations about the Rx signal (expected S/N, deviation range, etc.).

Chances are you might be able to vary the Tx signal parameters, too (from the OP is not very clear if this is allowed).  If true, this ability might improve the end results even more, depending on the exact application (e.g. the chirp modulation in radar/sonar type of applications).

ogden:

--- Quote from: RoGeorge on March 01, 2020, 10:20:01 am ---Without reading very carefully all the proposed solutions, the OP problem looks to me like an ideal application for a lock-in amplifier, simply because there is prior knowledge of the Tx signal.

--- End quote ---
Apparently you did not read your lock-in amplifier homework as well. Homodyne detectors (lock-in amplifiers) are used to demodulate either phase or amplitude, not frequency modulation/shift.

RoGeorge:
You could have said that without commenting about my person.   :)

"Frequency modulation/shift" can always be seen as a phase modulation.

ogden:

--- Quote from: RoGeorge on March 01, 2020, 07:55:55 pm ---"Frequency modulation/shift" can always be seen as a phase modulation.

--- End quote ---
Shifted carrier frequency can't be considered as modulation. Anyway lock-in amplifier requires carrier and LO frequencies to be identical which is not the case in doppler application.

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