For the calibration of an optical tweezer, the PSD of position values are plotted. If it follows a certain behavior having two regions - free diffusion and potential limited regions, then the trap is considered working fine.
I read that $\text{PSD} = \left\lvert \text{DFT}(X) \right \rvert^2/T_m$ where $X$ is the signal, $T_m$ is the time over which measurement is made, and $\text{DFT}$ means the discrete Fourier transform.,
In the above equation, why do we have time of measurement in the denominator? Does the value of $\left\lvert \text{DFT}(X) \right \rvert^2$ increase with $T_m$? If so, to make PSD independent of time variable are we doing the same?
What is the density in PSD? What information do we get from PSD given in $\text{V}^2/\text{Hz}$?
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