Fourier Transform minimum sample requirement Assuming a signal is sampled adequately, what is the minimum size of an FFT window that would allow detecting a specific frequency?  Is it necessary to have samples for at least one complete period at that frequency?
Please define "specific frequency".

Any signal with no frequency components above the Nyquist limit can be exactly recorded and re-constructed.

However, the number of samples determines the frequency resolution.

if you mean "i want to be able to tell the difference between silence and a 1000hz signal, then you would need 4 samples taken less 1/2000th of a second apart - using that you can solve for the 0 frequency signal (dc offset), and the strength of the other frequency.

if you mean "i want to be able to separate a 900hz signal from a 1000hz", then you need to resolve 11 frequency windows, ie, you'll need 22 samples taken at at least 2000 samples per second; then you'll have measured "frequencies around 0, 100,200,300...900,1000 hz", and you can answer "do i have a 900hz signal".

if you want to measure to the nearest hz the frequency of a N hz signal, then you would need to take at least 2N samples, taken at atleast 2N samples/second.