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Can anyone explain what spectral entropy is?

Does noise with a restricted bandwidth have the same spectral entropy as white noise?

  • this isn't quite what i meant but alas i cannot delete –  May 27 '15 at 03:03
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    But you can edit it. – sugab May 28 '15 at 01:04
  • Have the same spectral entropy as what? – jojeck May 28 '15 at 07:12
  • as white noise i mean –  May 28 '15 at 20:05
  • it's not clear why this question "Does noise with a restricted bandwidth have the same spectral entropy as white noise?" is being downvoted, it would save me a hell a lot of time if someone just came out and said –  May 28 '15 at 20:54
  • For me at least, the question is unclear because I understand white noise to be just a random signal with a flat power spectrum over a specified bandwidth, thus white noise can be in any restricted bandwidth you want to define. Because of this, Its also unclear to me what you are trying to compare white noise to (do you mean comparing white noise over a wide bandwidth to white noise in a narrower bandwidth?). – RTbecard Oct 01 '16 at 15:47

2 Answers2

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Spectral Entropy describes the complexity of a system. It is defined as follows:

  1. Calculate the spectrum $X(\omega_i)$ of your signal.
  2. Calculate the Power Spectral Density of your signal via squaring its amplitude and normalizing by the number of bins.

$$P(\omega_i)=\dfrac{1}{N}\left|X(\omega_i) \right|^2 $$

  1. Normalize the calculated PSD so that it can be viewed as a Probability Density Function (integral is equal to 1).

$$p_i=\dfrac{P(\omega_i)}{\sum_iP(\omega_i)} $$

  1. The Power Spectral entropy can be now calculated using a standard formula for an entropy calculation.

$$PSE = -\sum_{i=1}^np_i\ln p_i $$

In case of boosting of your noise signal, without performing any other processing, the Entropy will change. I guess there is no other way around that.

jojeck
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  • thanks for the reply, though i don't really understand it alas... is there any further processing i could perform after boosting the bass frequencies so that i didn't lose spectral entropy ? does coloured noise have a lower spectral entropy than white noise ? –  May 27 '15 at 09:42
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    Indeed, pink/red/brown, etc. noise has lower spectral entropy than a white noise. – jojeck May 27 '15 at 12:41
  • does amplifying past clip change the spectral entropy? could sinc filtering white noise leave the spectral entropy unchanged ? –  May 27 '15 at 14:03
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Maximal variance in spectral flatness can be observed in white noise (versus minimal variance in flatness from a pure sine tone). So white noise is your answer and yes, you can generate that in Audacity.

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ruoho ruotsi
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  • i thought spectral flatness was noise? i was gonna edit the question, anyway but thanks ! –  May 27 '15 at 03:51
  • No, spectral flatness is a measure of how tonal (pointy) or noisy (flat, uniform distribution) a spectrum is. If the question is answered, please mark it as so. Cheers! – ruoho ruotsi May 27 '15 at 18:16