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Recently, I'm working on modeling a sensor's system model using system identification.

Subject to the experiment condition, I only have the sine input signal. In addition, the frequency can not continuous change. In other words, I only have some specific frequencies experiment data.

I'm new about system identification, but clearly this kind of signal can not let the system show all of the feature. So, is there any algorithm can get the system model only using sine input signal?

Thanks a lot.

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  • $\begingroup$ SE.DSP wishes you a happy new year 2017, with a kind reminding signal that your question or its answers may require some action (update, votes, acceptance, etc.) $\endgroup$ – Laurent Duval Jan 2 '17 at 22:54
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Knowing the amplitude (and phase) for several frequencies allows you to fit a model with as many parameters, hoping the system is linear.

With little information you cannot observe the whole system behavior accurately, but just a simplified model. This might be enough for your purpose.

Knowing the internal system structure should help you select an empirical model.

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If the sensor is linear and invariant in time (an LTI system for linear and time-invariant), the output to a sine should be a sine with the same frequency, and a different phase and amplitude.

Assuming that you will only probe the sensorin its linearity range (e.g. outside saturation), and that you only have access to the magnitude of the output sine, you can add a causality assumption, and reconstruct the complex spectrum from its magnitude only by Creating Minimum Phase Filters and Signals (Matlab code mps.m for instance). Since you only have assess to a limited amout of frequencies, you might need to interpolate the spectrum on a finer grid (splines could do the job if the spectrum is smooth), and to set the unknown spectrum to a low-value outise for frequency span.

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