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I am trying to figure out how one goes about to try and find the transfer function (impulse response) of a real life system. Assuming the system is LTI.

This "system" I speak of is a channel that is comprised of components such as linear amps, a mixer (can we even assume a mixer is linear? If i'm not mistaken a mixer exists due to the nonlinearities of nature) and a DAC.

I know to find the transfer function (or impulse response) of a system (theoretically speaking) one should findV(or input a delta function and find the output in the case of the impulse response. I know this is not possible since the delta function is only an ideal construct)._{o}(ω) / V_{i}(ω)

One question I have is, for finding V_{o}(ω) / V_{i}(ω), do we just input a function (say a sin wave, sin(ω_{1}) ) with a certain frequency and read the output, say f_{o}? Is the transfer function then = f_{o}/ sin(ω_{1})?

The only way I can think of that seems to make sense to me is to sweep through the frequencies that seem important to me (or the system) through the input and study the output. This will give me a plot (or a set of data points) that represents the transfer function would it not?

I apologize if my post seems all over the place, but I thought I would let you know my process of thought.

Basically, my question is:

"How do you find the transfer function of a real world system, assuming the system is LTI?"

Thank you : )

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# How to find transfer function of real world system?

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