Fourier Transform minimum sample requirement
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.