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I have the following problem. I have $M$ synchronized, noisy measurements of a MIMO system (2 inputs, 2 outputs) of all inputs and outputs. The inputs are synchronized (no phase shift, coherent measurements) and linear independent, the noise is not synchronized, normally distributed and zero mean. My goal is to estimate the FRF (frequency response function) with phase from my measurements. There are several estimators (H1, H2, Hiv, Hev) suitable for the task. Using the coherency of my measurements, I would expect that simple time averaging (Hev) would give the best result. So:

$Y(jw) = H(jw) U(jw)$

Which would lead to

$H(jw) = Y(jw)U(jw)^{-1}$

where $Y$,$U$ $\in$ $\mathbb{C^{2x2}}$, representing one measurement(or the average of all measurements) of both linear independent input signals and corresponding output signals.

Using this formula, I don't see any way I can reduce the variance of noise apart from said time averaging. I would love to use something like welch's method, but I need the phase information, which I would lose that way. Is there anything else I can do, given the circumstances?

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