i'm currently working on a circuit transient simulation, and I'm wondering how the type of input excitation can affect the final result. In particular the focus is on impulse input vs step input, to understand the advantage/disadvantage of the input based on the application. Some ideas which came across my mind are:

  • Step response has a finite bandwidth which depends on its rise time, thus can give limited information regarding temporal resolution. Nevertheless, it provides more complete (longer) information in the time domain.
  • Impulse response would behave opposite, since its fourier transform is a unitary across all the frequency domain. It has ideally perfect temporal solution, but doesn't provide information in the time domain.

Are those considerations correct? Are other effect based on the choice of the excitation to be considered?

Thanks in advance

  • $\begingroup$ Are your circuits all linear and time invariant (LTI)? That will probably impact the answer to your question. $\endgroup$ Apr 30, 2022 at 12:22
  • $\begingroup$ Yes, they are LTI $\endgroup$
    – Spaetzle22
    Apr 30, 2022 at 12:34

1 Answer 1


This depends a bit on how you actually want to model this. Time discrete or time continuous ? Differential equations or difference equations?

Impulse excitation gives you directly the impulse response and by Fourier Transform the transfer function as well.

The main downside is that in a time continuous application, the signal to noise ratio will be very poor. An ideal impulse requires a very very large amplitude for very very short time. The ratio of peak to energy is enormous.

If your system is time discrete and you have decent numerical precision, than a unit impulse is can actually be a very useful test signal. The discrete version is much better behaved than the continuous one and easy to implement.

The step response at least easier to realize but the spectrum is not flat and it has a singularity at DC. You can recover the impulse response by differentiation by that's the equivalent of multiplying with $j\omega$ which can result in a lot of noise amplification at high frequencies.


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