How to calculate the frequency response of LTI system based on measured impedance 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.
this is more about electronics, but i think it can be asked here.

when you are looking for a frequency response of an impedance, i believe this means you have a two-terminal (a.k.a. one-port) device.  so, instead of an input voltage and output voltage to relate by a transfer function (and from the transfer function you get a frequency response), what you have is a voltage applied to the two terminals and a current measured, or a current shoved into (and out of) the terminals and the resulting voltage measured.

the complex impedance of the two-terminal device, as a function of frequency, is the frequency response the device assuming current is the input and voltage is the output.  you can plot it on a dB scale, but without a reference resistance, you don't have a reference for 0 dB on that frequency response plot.  but you have relative dB for the different impedances at different frequencies.

maybe ask the EE guys this question.  i dunno.