Whats the easy way to obtain inductor impedance fed with square wave? It cannot simply be ωFL since afaik thats only applicable for sine waves.
I understand from your question that you want to get the transfer function of a pure inductor when it is excited by a square wave. So, we should define the transfer function first: Is it the ratio between the voltage and current (the impedance) in the frequency domain?
If the answer is true, then we cannot access this question using omega domain (or Fourier Transform). We use Laplace transform instead.
I mean that, as long as the excitation is not sinusoidal, we cannot use the formula Z = jwL, as we will not be dealing with omega domain in the circuit. We will not solve such circuit using omega domain. Then, we use Laplace domain and say simply that Z = SL, where S is the complex frequency used in Laplace domain.
If your purpose is to know the waveform of the inductor output due to square wave input, it is rather simpler to use time domain in this case. The inductor voltage and current are simply related by v = L di/dt. If the voltage is square wave, then the current is the integral of the square waveform and so is triangular waveform.
If the current is itself square wave, then the voltage will be a series of shots (impulses) at the instant of current step transitions.
Hope this helps.