My recorded signal x = s + v, where s = A*sin(ωt) and v = noise. SNR < 1 or ~ 1. So the sine wave is buried under a lot of noise.
I need to compare the relative amplitudes of s for each recording window, so essentially track the ability of the system to receive the stimulus. The good news is that I know what I'm looking for (the stimulus and signal are causally linked, so I know ω) and my system is highly linear.
Question: is this a task for FFT or Cross correlation?
In more detail: Should I just perform a simple FFT and compare the amplitudes of the Fourier peak at frequency ω? Or could I do better by cross-correlating it with a reference signal sin(ωt)? If cross-correlation is the answer, should I apply a matched filter before cross-correlating? The SNR is a big problem which is why I'm exploring options outside of the FFT. As a non-expert to the field, a explanation of pros/cons to these two techniques would be greatly appreciated.
PS. as far as FFT goes, I know there are tricks such as band-pass filters and hamming windows. With these applied, I'm getting decent but not great results.