FFT for Transfer Function of Electronic Circuit

[twig27]

Hi,

I have an eletronic circuit, whose exact components are basically unknown. I do know however the input and output signals as vectors. My goal is to obtain the input signal for an arbitrary output signal. My approach so for has been to apply a certain input, measure the output and then determining the transfer function by calculating the ratio FFT(Output)/FFT(Input).
For the following measurements I recorded the output, applied the FFT, divided it by the transfer function and then used the inverse FFT to obtain my input signal.

Is this approach valid? I know for transfer functions you usually use the Laplace transform, which is in my case however difficult to realize.
Are there any other ideas to solve this problem?

Regards

 

[elecrom]

This is not correct. FFT gives the frequency spectrum of the given signal.

What you need to do is as follows:
1) Get a signal generator
2) Apply a sine wave of 100 Hz with some fixed amplitude
3) Measure the output amplitude (or check the output amplitude using FFT, in FFT you will see only one line since input is sine wave)
4) Repeat this with all the frequencies you desire
5) What you have at the output is the frequency response of the circuit.

Feed this data to the transfer function estimator function (tfest()) in Matlab and you will get the coefficeints of the transfer function of the circuit.
Refer: https://in.mathworks.com/help/ident/ref/tfest.html

 

[twig27]

Thanks for your reply! Could you comment on the difference between frequency response and transfer function? As far as I understand the one is based on Fourier Transform while the other one goes back to the Laplace Transform.
Why is it not possible to describe the transfer characteristics of a system in the frequency domain?

 

[KlausST]

Hi,

first: I´m not a specialist in this.

But I think your approach is correct, at least from the idea. I don´t have the time now to check if all your mathematics is correct. Maybe another user is more familiar with this.
I recommend to use a dirac input or a step input. (At least it should contain all frequencies).


***
electrom´s solution is a single frequency solution. It needs n runs for n frequencies.
...whereas your solution is an "all in one" solution. One shot... all frequencies.

Klaus

 

[elecrom]

To get accurate estimate, you will need phase information as well. This can be obtained by manually computing the FFT from the RAW signal waveform capture.

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I am no expert behind the exact math part of your problem, however I found following discussion on stackexchange very informative :

https://dsp.stackexchange.com/quest...tion-from-a-magnitude-only-frequency-response