I wonder if the following basic property I thought up is a real property of FFT (or more specifically the discrete version of Fourier series), and if so what is it officially called?
The property works like this, take a signal that is the length of N, and perform the discrete Fourier transform.
Next, zero pad the original time domain signal so that the length will be 2N (or any multiple that contains all of the original frequency bins, ie 2,4,8...). Again, perform discrete Fourier transform.
Now, the frequency domains signal will be the same for the padded and non-padded versions, for the bins representing the same frequencies, when both of the frequency domains are defined. Additionally, the padded version of the signal contains twice as many defined frequencies as the original.
Does this property also work in the case that the padded signal contains only some of the original frequency bins (IE, pad so that the resulting signal is the length of 6N, for example). If this is the case, then by sweeping all the different padded lengths from N to 2N and combining the DFTs, the result will be the same as DTFT, with the low frequencies (lower than possible in 2N) undefined. Interesting...