Given a signal, $s(t)$, sampled at frequency $f_s$, how does one calculate the power of the signal at one specific frequency $f_q$? Since I am only interested in the power at $f_q$, computing the FFT seems like over kill.
I can identify the following pre-existing content on stackexchange:
This post suggest band-pass filtering the signal then taking the sum of the squared signal. This seems to make sense to me but I wonder how selective the band-pass filter can actually be given the sync-like frequency content of the windowing function.
This post deals with power in a specific signal band with suggestions of using MUSIC, goertzel, etc.
My interest is not in a frequency band but the power at one specific frequency. My thought is to convolve a sinusoid whose frequency is fq with the signal and then summing the power in the resultant signal (a matched filter).
I would have thought there would be a more straightforward solution but I struggle to find the words to start an effective literature review.