I have an analog circuit containing unknown resistance, capacitance, and inductance. I have measured its complex impedance across the frequency range of interest. Is there an equation that will allow me to compute the frequency response (complex voltage gain as a function of frequency) of the circuit given the impedance? Clearly lower impedance magnitude would result in greater voltage gain magnitude, but what is the exact mathematical relationship?
As an aside, I am aware that I could directly measure the frequency response e.g. by taking the Fourier transform of its impulse response. This question is not about how to measure the frequency response, it is about the mathematical relationship between the impedance and frequency response.