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As is shown in the picture, a template signal is delayed and overlapped in time domain, the shape of template signal is already known The positions of each template are already known.

Each template has its own carrier frequency, and amplitude. Or the carrier has a Gaussian distribution $\mathcal{N}$($\mu$,$\sigma^2$).

How to estimate them? Please provide some recommendations, thank you.


If the auto correlation of the signal is sharp enough, you can do Matched Filter and search for local extreme points.

Yet it seems the figure you'e displaying is in the frequency domain.
But we can treat the frequency domain as it was time domain and work with the same "Trick".

Namely searching for the frequency in the frequency is like searching for the delay in the time domain.
Since the signal is known, its multiplication by a carrier is known whihc will be used as the Matched Filter.
Applying it will yield 3 peaks each with its own "Delay" which corresponds to its frequency.
Going back to that frequency bin (Or calculating the DTFT at that point) will yield the amplitude.


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