As was proven here: https://math.stackexchange.com/questions/228614/why-doesnt-repeating-a-signal-give-rise-to-a-finer-resolution-of-dft-fft repeating a certain sequence does not improve DFT frequency resolution. However, it is known that oberserving a signal for a longer time will in fact improve the ability to resolve two tones in a signal (because the 'beamwidth' of the window in the frequency domain will become narrower: it is 2/NT with NT the total observation time).
I do not understand this discrepancy: If we assume the signal has two tones f1 and f2, and has a period T. Let's say we observe it over a time N*T such that 1/(NT) becomes small enough to distinguish f1 and f2. We have improved the frequency resolution by observing the signal over a longer time. Why is this not equivalent to simply observing the signal for 1 period, and then paste it together N times? This will give the same signal in the time domain, but according to the proof in the link that I posted, it will not improve the frequency resolution.
The only explanation that I can think of myself is: observing for a longer time period does not improve the frequency resolution further once the observation time becomes larger than T. However, I have written some matlab code where I do an FFT on a pure sine over a certain time. I clearly see the 'beam width' in the frequency domain associated with the windowing start to narrow down as I increase the observation time. Given that a pure sine is also periodic and the observation times that I used are bigger than this period, I must thus conclude that my 'explanation' is incorrect.
Could someone try to show me the correct explanation?