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(Just as clarification on what I am doing, I am attempting to use MATLAB to create PSD plots of time series from pressure and accelerometer sensors. Wave gauge sensors might still be helpful for me. I did not discuss accelerometer sensors in the post but maybe I could figure it out if I get the basic idea).

At the very least, I would like to make sure I am correct that the Fourier Transform of a time series with some units ##U## (##U## referring to any arbitrary unit), would be ##U/Hz## (so ##Us##). If this is wrong, then I think I have a fundamental misunderstanding.

I'm trying to understand Power Spectral Distributions; I think my confusion can largely be reduced to a question of units. I am particularly concerned with the PSD created from time series of wave height and pressure, but I think a general understanding of a PSD would be useful. From what I understand, the units for the y axis of a PSD depends on the time series from which the PSD was created. On this Stack Overflow thread, someone states that a PSD of ##V^2/Hz## can be used when the time series is voltage. I think this make sense because ##P=V^2/R##.

I don't understand how I would extend this to other cases. I understand that there should be some way of relating the amplitude of the time series to the power. I don't quite understand how much freedom I have when doing this. Could I for example, just declare the following: $$E=\rho g H^2$$ where ##H## is the wave height? In that case ##E## would be some quantity which in some is sense associated with energy. As energy is dimensionally equivalent to power divided by frequency, and ##\rho## and ##g## are constants, could I simply square the Fast Fourier Transform and just let the y axis be ##H^2## with the understanding that there's a clear relation to power?

In the case of pressure sensors, I am a bit more confused. I do understand that sound waves are pressure waves and the PSDs for sound waves use dB as the y axis. This is computed by ##\log_{10} (P/P_0)## (multiplied by 10 but I believe this is a detail in this context). Could I do something similar in my case?

At the very least, I would like to make sure I am correct that the Fourier Transform of a time series with some units ##U## (##U## referring to any arbitrary unit), would be ##U/Hz## (so ##Us##). If this is wrong, then I think I have a fundamental misunderstanding.

I'm trying to understand Power Spectral Distributions; I think my confusion can largely be reduced to a question of units. I am particularly concerned with the PSD created from time series of wave height and pressure, but I think a general understanding of a PSD would be useful. From what I understand, the units for the y axis of a PSD depends on the time series from which the PSD was created. On this Stack Overflow thread, someone states that a PSD of ##V^2/Hz## can be used when the time series is voltage. I think this make sense because ##P=V^2/R##.

I don't understand how I would extend this to other cases. I understand that there should be some way of relating the amplitude of the time series to the power. I don't quite understand how much freedom I have when doing this. Could I for example, just declare the following: $$E=\rho g H^2$$ where ##H## is the wave height? In that case ##E## would be some quantity which in some is sense associated with energy. As energy is dimensionally equivalent to power divided by frequency, and ##\rho## and ##g## are constants, could I simply square the Fast Fourier Transform and just let the y axis be ##H^2## with the understanding that there's a clear relation to power?

In the case of pressure sensors, I am a bit more confused. I do understand that sound waves are pressure waves and the PSDs for sound waves use dB as the y axis. This is computed by ##\log_{10} (P/P_0)## (multiplied by 10 but I believe this is a detail in this context). Could I do something similar in my case?

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