this question is in two parts. Firstly, can you please tell me what the structure and amplitude distribution is of harmonics generated by a differentiated square wave of 50% duty cycle, where the time constant is very short, producing alternating bipolar spikes of short duration? I know a square wave produces odd order harmonics that decay in amplitude by 1/n, but not sure if the above does - or has even order harmonics as well? Secondly, what change to the harmonic series and amplitudes occurs for duty cycles tending towards 0% or 100%, from 50%, as if the source was PWM'd by a lower freq signal. Thanks.
You can model this as a series of positive and negative Dirac delta functions. You'll find that this ideal case gives you the (similarly ideal) result mentioned by Dave Tweed in the comments: the Fourier transform of a square wave multiplied by that of a differentiator. The drop in amplitude of the square wave harmonics and the rise with frequency of the differentiator cancel out, leaving a series of spikes on the fundamental and odd harmonics, all of equal amplitude.