What is the general feature of a time domain signal that gives a step like spectrum? I'm trying to study a nonlinear system by sending a pulsed signal into the system and look at the response spectrum. The signal I send to the system is something like



and the response spectrum from I get from the system is something like (note the spectrum is plotted log scale, ie, (frequency, log of absolute value of Fourier transform at that frequency))



where we can see that there is a stair like structure in the spectrum. So what is the general feature the time domain response signal should have in order to give a stair like spectrum like this? And have you ever encountered a spectrum like this, and is there something in general we can say about the system just from the stair like spectrum?

Could you give a model of this behavior that generate stair like spectrum?
If there is a time invariant linear response region in your non-linear system, then a time domain input resembling a Sinc function $\frac{\sin(x)}{x}$ in that linear region, will produce an approximation to rectangular frequency response in the frequency domain.