Hi, all!
I measure transient response with an ADC. I receive a column of values. How to apply Laplace transform to these values to obtain amplitude response (transfer function)? Is there a tool freeware or commercial to solve it? Could a kind person give a concrete example, detailed answer? I have attached a file - example of the measured data. Thanks.
The Laplace transform is related to the Fourier transform by,
L{f(x)}(-is) = F{f(x)}(s)
Where (i) is the imaginary number. So, if you take the discrete Fourier transform and multiply by negative i, then recover the real set of numbers, Re, then you have your discrete Laplace transform.
Proof: consider f(x)=H(x),
F{f(x)}(s) = 1/(is) + pi × delta(s) /.s -> -is => Re{1/(s)},
Where last transform is the direct Laplace transform of Heaviside's step function, i.e.
L{H(x)}(s) = 1/s
Reference:
1] https://en.m.wikipedia.org/wiki/Laplace_transform, then read section "Fourier transform."
2] http://fourier.eng.hmc.edu/e102/lectures/Laplace_Transform/node1.html
Dear Luis-Felipe Velázquez-León !
Thank you very much for your time and the steps written! You are very kind!
I understand all the things you have written above. And I think you are absolutely right. I wanted to know if there are any other ways to obtain a transfer function for amplitude response using the data measured (processed) without analytical transformations.
Dear Luis-Felipe Velázquez-León
Yes you are right. It is the transient response after mathematical processing obtained from a pyroelectric detector. I would like to know how to receive the transfer function.
Dear Luisiana Cundin !
Thank you very much for your time and attention addressed to my problem!
I bookmarked your references. I wanted to know if there is a way/tool that allowed me to receive the frequency domain Laplace transform for the data measured in the time domain. I want to continue Mathematical Processing of a Pyroelectric Detector.
Alexander Bondarenko
An experimental transfer function is just that--experimental. You can model the transfer function with any mathematical formula desired, e.g. polynomials.
Reference:
1] https://www.mathworks.com/help/control/ref/tf.html
2] https://www.mathworks.com/help/control/ug/transfer-functions.html
Now, you can also go from a theoretical angle and design a transfer function from some mechanical, electrical, etc, model.
Reference:
1] https://x-engineer.org/graduate-engineering/signals-systems/control-systems/find-transfer-function-system/
In the first case, you don't care what physics are at play, per se, but are simply deriving a heuristic formula to enable you to model input to output, where the blackbox has been trained by your experimental results.
In the second case, you are using physics to describe what you think is occurring fundamentally, then testing that model against your experimental results; modifying as needed.
In either case, the convolution of your input or transient with the impulse response function (transfer function) of your system gives the expected output.
You are free to choose which path you wish to take.
Also, see this:
https://www.researchgate.net/post/How_to_estimate_transfer_function_from_the_input_and_output_data
- Badges
- Science topic
- Similar topics
- Control Systems Engineering
- Filtering