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Spectral slope

  1. Jun 10, 2016 #1
    1. The problem statement, all variables and given/known data
    I have some registration of sound gathered by hydrophone. Next I have created a power spectral density (dB re 1 Pa^2/Hz) vs frequency plot (semilog in matlab). And now I want to find spectral slope in dB/octave (one octave is log2(f2/f1).
    I suppose that I should calculate the difference between two PSD points (max and min) and then divide this value by amount of octaves estimated based on the mentioned formula?
    Could you if I'm right? Or mby there should use some different formula?

    2. Relevant equations


    3. The attempt at a solution
     
  2. jcsd
  3. Jun 10, 2016 #2

    NascentOxygen

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    Staff: Mentor

    Semilog....and your horizontal axis is f or log(f/fo)?

    One actave is a doubling in frequency. So if linear f can you draw a straight line approximation to any region of interest, then extend that line over an exact octave and read the change in dB.

    Drawing by hand has inherent noise-averaging, in comparison with a two points reliance which does not.
     
  4. Jun 10, 2016 #3
    Here is an example
    https://i.imgsafe.org/b3c770eb73.png [Broken]
     
    Last edited by a moderator: May 8, 2017
  5. Jun 10, 2016 #4

    NascentOxygen

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    Staff: Mentor

    Are you looking for a fixed dB/oct figure? If so, you will be looking for a straight line best fit to this.
     
  6. Jun 14, 2016 #5
    Ok, so for that I must count the difference value of dB i.e. from 1 Hz - 1.5 Hz and then calculate the amount of decades from taken frequencies?
     
  7. Jun 14, 2016 #6

    NascentOxygen

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    Staff: Mentor

    Why do you mention "decade" when you are interested in per "octave"? Note that 1.5 Hz is difficult to read, it's definitely not midway between grid lines on a log plot.

    There is a grid line at 1 Hz, the next grid line adjacent to that is 2 Hz, so why not use that for your double frequency? If you take a plastic ruler and measure this horizontal distance between these 2 grid lines, then everywhere and anywhere along the horizontal axis this same distance (in mm) represents a doubling in frequency. (Try it on the 2 Hz, 3 Hz, 4 Hz, and 5 Hz grid lines to demonstrate this is true.)

    Is this noise on the recording, and you want to smooth it before doing calculations? If there are spectral peaks that you want to preserve, then I guess you'll want to exclude them from your smoothing.
     
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