Depending on the size of the main synchronous generator (alternator), there can be a number of excitation elements.
For "separately excited" systems, the main synchronous field circuit is fed by DC which is passed to the winding through a mechanical (brush-and-collector) interface. The source feeding the interface can be an old-school DC generator or a dedicated power electronics supply.
For "self-excited" systems, there are typically one (or more) rotating elements involved. In the most complete case, we have:
Permanent Magnet Generator - Rare earth magnets mounted on rotor; AC winding on stator. Supplies 3-phase AC to downstream component(s).
Automatic Voltage Regulator - could be analog, but most modern versions feature power electronics. Receives 3-phase AC and outputs DC.
Rotating Exciter - this is essentially a very small synchronous machine (for fixed speed applications). Requires DC input for stator winding; outputs 3-phase AC via rotor winding.
Rotating Rectifier Bridge/Control - Requires 3-phase AC input to power electronics. Output is DC.
Main synchronous machine rotor winding - requires DC input.
The output voltage of the main synchronous machine (generator) is related to the CURRENT applied to the rotor winding. This means it is the current ripple (within the rotor circuit) that affects the possible voltage ripple on the output.
We need to look at the relevant windings in terms of their damping effects on the current ripple. The PMG has virtually none, since it is a very small machine with relatively low impedance (inductance typically measured in tens of microHenries) windings. The AVR has none as it is essentially more power electronics. The rotating exciter - if there is one - has somewhat more impedance (inductance typically measured in milliHenries) compared to the PMG, thus acting as a "damper" for the PMG and/or AVR output. The rotating rectifier assembly has none as it is essentially power electronics. The main synchronous rotor field has a relatively huge impedance (inductance measured in Henries), acting as a pretty good damper for all the prior waveform distortion.
Some of the potential for distortion is sorted out by the fact that both the PMG and the rotating exciter will have different pole counts from the main synchronous machine. For high-speed (> 900 rpm) designs, the exciters will tend to have more poles than the actual generator, resulting in high-frequency distortion that can be damped effectively. For low-speed (< 450 rpm) designs, the exciters tend to have lower pole counts with respect to the main rotor, resulting in a low frequency distortion which can also be effectively damped.
At the end of the day, the largest source of distortion in the generator voltage output waveform in a salient pole machine is caused not by the field strength of individual rotor pole windings (assuming they are all balanced), but rather by the physical interpolar gap (quadrature axis).