Converting PSD into equivalent sound pressure for an underwater hydrophone

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Discussion Overview

The discussion revolves around converting Power Spectral Density (PSD) measurements from an underwater hydrophone into equivalent underwater sound pressure levels. The focus includes the implications of measurement techniques, the appropriateness of using PSD for single frequency measurements, and the necessary considerations for bandwidth in the conversion process.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant states the hydrophone has a known receive sensitivity and provides a PSD measurement, seeking assistance in conversion to underwater sound pressure level.
  • Another participant argues that PSD is not appropriate for single frequency measurements and suggests that only voltage should be measured instead.
  • A different participant notes that if the signal is noise-like, the total bandwidth of the electronics must be considered for accurate conversion.
  • One participant proposes that with a narrow resolution bandwidth, the PSD can be converted to voltage by multiplying by the square root of the bandwidth, although they acknowledge the complexity of the situation and the need for phase information for a complete analysis.
  • The same participant corrects themselves regarding the mathematical expression used in the conversion process, indicating a potential misunderstanding in their initial explanation.

Areas of Agreement / Disagreement

Participants express differing views on the appropriateness of using PSD for the measurements in question, with some advocating for its use under specific conditions while others contest its relevance for single frequency signals. The discussion remains unresolved regarding the best approach for conversion.

Contextual Notes

There are limitations regarding the assumptions made about the nature of the signal (noise-like vs. single frequency) and the dependence on the bandwidth of the measurement, which may affect the conversion process.

nauman
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Hi all

I have a underwater hydrophone with known receive sensitivity e.g. -190dB ref 1v/upa with a preamplifier having gain of 40dB at frequency e.g. 200Hz. I measure preamplifier output using spectrum analyzer and it gives PSD of around -80dBvrms/sqrtHz. I need to convert this PSD value into equivalent underwater sound pressure level with unit of dB ref 1upa.
Any help is much appreciated.
 
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The measurement is of a single frequency, so that Power Spectral Density is not the appropriate measurement. All you need to measure is voltage. PSD is used for measuring noise like signals.
 
If you are actually measuring a noise-like signal, then the electronics must respond to the full sound spectrum and you need to know what the total bandwidth is.
 
If you have a narrow resolution bandwidth you can use that to convert the spectral density into a voltage. You can assume the psd is flat and just multiply by the measurement BW squared sqrt(BW). Of course the BW measured may only be part of the time domain signal.

For a more complex situation, it's like doing an inverse Fourier transform. It can't really be done without the phase information the spectrum analyzer threw out, but you could do the integral to get an estimate.

https://www.ti.com/content/dam/videos/external-videos/en-us/1/3816841626001/4078827152001.mp4/subassets/opamps-noise-calculating-root-mean-squared-noise-presentation-quiz.pdf#:~:text=To convert voltage spectral density to RMS,,to convert back to voltage or current.

edit: Oops! it's ##\sqrt{BW}## not ##BW^2##. Duh!, sorry
 
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