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?

• Since you have a nonlinear system, lots of things that people will tell you to do will not be quite relevant or might need re-thinking. One thing that people do is to linearize the system by building a small-signal model for very small-amplitude inputs. So try your system with an input smaller in amplitude by 6 dB, say, and see if the Fourier spectrum of the output changes very much from what you already have found. Jun 8 '14 at 3:00
• For non-linear system, you must try a single tone and try to understand its response w.r.t different amplitudes and phases. This will be the initial model. Now change the frequency incrementally and see if the initial model holds. You'd then modify your model to include frequency dependence. Once all effort is done, then you should apply a banded signal, in order to check your model. Jun 8 '14 at 8:52

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.