# System Identification with large Input/Output Data

I have some questions about system identification. I made some measurement of current step (input) and voltage response(output) and I want to fine the parameters of my impedance. The sample rate is 1000 samples/s so that I have a very large list of current and voltage samples include noise (40000 Samples). My voltage is U(kT) and current is I(kT) where k=1,2,3,.....40000.

1. to filter the noise I used ExponentialMovingaverage; is there any other possibility to filter the noise from the list?
2. in Mathematica there is a function with the name NonlinearModelfit to find system parameters. Is there any other possibility to find the system parameters like nonlinear Least Square?
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## 1 Answer

1. Apart from ExponentialMovingaverage there are several other functions that you can use to filter the noise. MovingAverage and MovingMedian come to mind. ListConvolve, GaussianFilter, MeanFilter, LowpassFilter (v9) would probably work too.
2. GeneralizedLinearModelFit, FindFit. For a few specific situations ProbitModelFit and LogitModelFit
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Thank you, How can i determine the Cutoff Frequency of the LowpassFilter. i know that Fc<Fs/2 also Fc<500Hz. but what is the optimal cutoff Frequency to make the LowpassFilter better than ExponentialMovingAverage. – Nimo Bradly Jan 11 '13 at 10:09
@NimoBradly First, you should provide LowpassFilter with information about the sample rate, otherwise the cutoff frequency doesn't mean what you want it to. You can use the SampleRate option for that. What would be the best cutoff frequency depends on the typical frequency range of your signals and noise. Perhaps Manipulate would be useful here. – Sjoerd C. de Vries Jan 11 '13 at 12:12