Let's say I am generating pure sine oscillations with a laboratory instrument on which vibration frequency and amplitude are tunable (there are uncertainties +/- 1 % with my inputs), and I get my output data from accelerometers (also with white noise).

The question is how can I estimate the transfer function of the aforementioned instrument from measured data ? Doing FFT and amplitude estimation from the output will provide information, but how can I take into account noises and uncertainties ?

PS: My data acquisition frequency is always 10 times higher than input frequency.


  • 2
    $\begingroup$ Please read this answer (and this similar one) and let me know if that answers your question. It gives details on transfer function estimation when there is noise in the input and the output. This reference also has some useful stuff. $\endgroup$
    – Jdip
    Nov 6, 2023 at 21:32
  • $\begingroup$ Thanks for your answer and links ! DSP is new to me so mostly the linked reference helps me the most to understand what is going on. May be a final question : since I assume there is uncertainties (not noise) with my input and noise with my output, can I assume as input (time series of) a pure sine function ? and then calculate directly the H_1 estimate ? Thank you again for your help $\endgroup$
    – aRedDish
    Nov 8, 2023 at 22:10


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