The relation between a link speed and Fourier coefficients
I'll try to group all your questions together because they are related.

To find the spectrum of a signal (frequency content) one has to look at a finite period of time. Let's say one looks at the 1st 10 seconds of a signal. The fundamental frequency is the sinusoidal signal that can make 1 revolution in the measured time. The period is 10 seconds, the fundamental frequency is 0.1 Hz. If one is looking at the discrete Fourier transform of a signal they are looking to see how many multiples of this fundamental frequency there are. The 1st frequency is 0.1 Hz, the 2nd is 0.2 Hz, the 13 is 1.3 Hz, etc. The coefficients are the amount of each frequency present (the 0.5 Hz signal is the 5th harmonic of the fundamental frequency, which is 0.1 Hz). One could say they have 0.3 of the 1st harmonic, 0.2 of the 8th harmonic, etc. Different signals are made by having different amounts of each harmonic.

Certain signals might not have all harmonics. Ideal square waves are made of odd harmonics (0.1 Hz, 0.3 Hz, 0.5 Hz, etc, but no 0.2 Hz, 0.4 Hz, etc). Sawtooth waves are made of only even harmonics.

When using the DFT there is a midpoint where signals start aliasing. If you have 100 samples of your signal over 10 seconds then the highest frequency that should be present in your original signal is a 5 [Hz] signal. This is due to aliasing where 4.9 Hz looks like 5.1 Hz, 0.1 Hz looks like 9.9 Hz, etc.

Short answers to your questions:


Period is calculated based on the signal used to calculate the Fourier transform. You can rx/tx whatever you want.
Coefficients represent the quantity of each harmonic.
Bandwidth limits the frequencies that can be used. Cutoff = 10 Hz, only Dc through 10 Hz signals can be sent. 1st harmonic is calculated from the period of the signal used for Fourier transform.
Depends on the signal being sent, not all signals have all frequencies.