# Finding the best principle component

The title might be unclear, but the problem is this. I have a signal sampled 1500 times with a rate of 60/s, and a sensor array 512 units large. There is a lot of noise, echo and other frequencies being picked up, but I am interested in only one. First I do a spike removal, then a bandpassfilter (butterworth) around the frequency range I suspect the signal is hidden. I then do a PCA to find wich of the 512 sensors picks up any systematic variation. Then I search for the best fit sinuswave in each of the top sensors (say 5 out of 512).

So main question, how to determine which of the PCA's is the one picking up the true signal without me knowing excactly what the frequency of the signal is? Second question, does the above steps seem reasonable? I am no expert in this, but experiments seems to indicate that with high STN objects of measurements (say a pendulum) it is clearly visible which PCA fits best (amplitude, hz, residuals of fit), but with low STN (say heartbeat), it is not so clear.

Sorry for lengthy text. Thanks alot for any answers!

edit: Running spectral analysis (using different Methods) gives different results depending on wich PC i am analysing. Might there be a spectral Method that does multivariate samples?

edit 2: So while waiting for answers I have chosen to filter out principle components based on the correlation coefficient from a sinus wave fit (r>0.5) and % of data explained (p>0.15). So in other words, the signal i am looking for has to be present in at least 15 out of the 512 sensors (if I understand PCA correctly), and the best fit sinewave has to explain at least 25% of the variation. This works well with test setups in a noisy environment. Question: Is my approach sensible? Should or shouldnt I forego FFT and spectral estimation? Besides visualization, does frequency estimation based on the FFT gain anything over a iterative sinewave fitting, given that I know the signal is sinusoidal?

Thanks alot