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- 6th December 2016, 14:04 #1

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## When to use Laplace or Fourier Transform for Circuit Analysis

Hey Guys,

so I have an electronic system, whose exact structure is unknown. I can however measure what it does to a specific input. This means I have two vectors, which represent current/voltage signals for the input/output. Theoretically I could represent the transfer function of the system in the Laplace-Domain if I knew all the components. Since I do not have an analytic functions for the output, I can only solve this problem numerically. Matlab however does not provide a method for a numerical Laplace transform. That's why I have been using the FFT in order to get the transfer function (Dividing FFT of the output by FFT of input). Is this even legit? Can a transfer function of such a system be represented in the Fourier domain? Or do I lose some information by doing so? Does someone have an alternative solution to this problem? Basically I would like to get an analytical representation of the system's transfer function. Thanks!

- 6th December 2016, 14:04

- 6th December 2016, 14:39 #2

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## Re: When to use Laplace or Fourier Transform for Circuit Analysis

You must have 3 columns: Input/Output and time.

Having those 3 columns, MATLAB is able to find a transfer function that models your circuit with its toolbox called System Identification Toolbox.

https://es.mathworks.com/products/sysid.html

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- 6th December 2016, 14:39

- 7th December 2016, 08:44 #3

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## Re: When to use Laplace or Fourier Transform for Circuit Analysis

Thanks for your reply. The System Identification Toolbox is indeed very interesting. For my task I want - after acquiring the transfer function - to obtain the input of my system for an arbitrary output vector.

I.e., I have the transfer function in the laplace domain as an analytic function and my output which is a vector of finite length.

What is the best way to do so?

- 7th December 2016, 08:44

- 7th December 2016, 21:06 #4

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## Re: When to use Laplace or Fourier Transform for Circuit Analysis

I think you are looking for the "inv" function then.Take a look here: https://es.mathworks.com/help/control/ref/inv.html

- 9th December 2016, 13:58 #5

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## Re: When to use Laplace or Fourier Transform for Circuit Analysis

How do I know if I obtained the real transfer function of my system? It seems the results are decent for various numbers of zeros and poles (>99% for e.g. 2 zeros 4poles AND 2 zeros 3 poles).

- 9th December 2016, 13:58

- 9th December 2016, 16:00 #6

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## Re: When to use Laplace or Fourier Transform for Circuit Analysis

In control systems, sometimes in order to get things more easily calculable, every high order system can be reduced to an equivalent 2nd order sistem and still get a fairly good respones i.e. as the original system. So it is expected to work as your sistem for more than one combination. Of course, choose the one that best matches your system but is more easier, in this case the one with 3 poles.

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