Answers.Body: <p><a href="https://www.pamguard.org" rel="nofollow noreferrer">PAMGuard</a> has a &quot;Filtered Noise Measurement&quot; module which can apply an arbitrary FIR filter to sound data prior to measuring the RMS and SEL outputs of that filter at selected time intervals. If you design a filter which matches the audiogram of the species you're interested in, this module may provide a solution.</p>
  
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Answers.Text: Wow - I didn't know this was a thing. Thanks Doug!
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Answers.Body: <p>To apply the frequency-specific audiogram weighting, you must calculate SEL in the spectral domain.
  <a href="https://en.wikipedia.org/wiki/Parseval%27s_theorem" rel="nofollow noreferrer">Parseval's theorem</a> tells us that the sum of a square of a function is equal to the sum of the square of it's transform. That means that the integrated spectrum will be equal to the integrated time series. You can test this by comparing the integral from your time series to the integral of a spectrum; they should be the same.</p>
  <p>So you will need to</p>
  <ol>
  <li>Define appropriate time and frequency bounds for your signal</li>
  <li>Calculate the power spectral density  (Note - applying a window
  function here may not be appropriate for impulsive signals!)</li>
  <li>Apply the frequency specific weighting function</li>
  <li>Integrate the power spectral density. Usually my PSDs are in dB values, but I convert the PSD into linear values, then integrate, then convert back to dB. Make sure you account for FFT size in integral!</li>
  </ol>
  <p><strong>Example code for high-frequency weighted Sound Exposure Level (SELwHF):</strong>
  SELwHF&lt;-10*log10(sum(10^(PSDhf/10))/(Nfft * sr))</p>
  <p>where:
  Nfft = number of samples in your signal, sr = sample rate, PSDhf = power spectral density in dB units after weighting function is applied</p>
  
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Body: <p>Not all marine mammals have the same hearing abilities, therefore National Marine Fisheries <a href="https://www.fisheries.noaa.gov/resource/document/technical-guidance-assessing-effects-anthropogenic-sound-marine-mammal-hearing" rel="noreferrer">(2020)</a> recommends using audiogram-weighting for sound exposure levels (SELs) based on different marine mammal hearing groups. They also provide weighting functions for different hearing groups. Normally I calculate SEL as an integral in the time domain, so how do I incorporate the weighting function if I want to calculate a weighted SEL?</p>
  
Tags: <noise><anthropogenic-noise><hearing>
Title: How to incorporate audiogram functions into weighted sound exposure levels based on different hearing groups?
ThreadText: # How to incorporate audiogram functions into weighted sound exposure levels based on different hearing groups?
  
  (Asked by: username_0 on 2022-07-05)
  
  Not all marine mammals have the same hearing abilities, therefore National Marine Fisheries [(2020)](https://www.fisheries.noaa.gov/resource/document/technical-guidance-assessing-effects-anthropogenic-sound-marine-mammal-hearing) recommends using audiogram-weighting for sound exposure levels (SELs) based on different marine mammal hearing groups. They also provide weighting functions for different hearing groups. Normally I calculate SEL as an integral in the time domain, so how do I incorporate the weighting function if I want to calculate a weighted SEL?
  
  **Tags:** noise, anthropogenic-noise, hearing
  
  
  ---
  
  ## 2 answers
  
  ### Answer by username_1 on 2022-07-06. Score: 4
  
  [PAMGuard](https://www.pamguard.org) has a "Filtered Noise Measurement" module which can apply an arbitrary FIR filter to sound data prior to measuring the RMS and SEL outputs of that filter at selected time intervals. If you design a filter which matches the audiogram of the species you're interested in, this module may provide a solution.
  
  > **Comments:**
  > **username_0**: Wow - I didn't know this was a thing. Thanks Doug!  
  
  ---
  
  ### Answer by username_0 on 2022-07-05. Score: 3
  
  To apply the frequency-specific audiogram weighting, you must calculate SEL in the spectral domain.
  [Parseval's theorem](https://en.wikipedia.org/wiki/Parseval%27s_theorem) tells us that the sum of a square of a function is equal to the sum of the square of it's transform. That means that the integrated spectrum will be equal to the integrated time series. You can test this by comparing the integral from your time series to the integral of a spectrum; they should be the same.
  
  So you will need to
  
  1. Define appropriate time and frequency bounds for your signal
  2. Calculate the power spectral density (Note - applying a window
     function here may not be appropriate for impulsive signals!)
  3. Apply the frequency specific weighting function
  4. Integrate the power spectral density. Usually my PSDs are in dB values, but I convert the PSD into linear values, then integrate, then convert back to dB. Make sure you account for FFT size in integral!
  
  **Example code for high-frequency weighted Sound Exposure Level (SELwHF):**
  SELwHF<-10\*log10(sum(10^(PSDhf/10))/(Nfft \* sr))
  
  where:
  Nfft = number of samples in your signal, sr = sample rate, PSDhf = power spectral density in dB units after weighting function is applied
  
  
  ---
  
  