Can anyone explain what spectral entropy is?

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

  • $\begingroup$ this isn't quite what i meant but alas i cannot delete $\endgroup$ May 27, 2015 at 3:03
  • 2
    $\begingroup$ But you can edit it. $\endgroup$
    – sugab
    May 28, 2015 at 1:04
  • $\begingroup$ Have the same spectral entropy as what? $\endgroup$
    – jojek
    May 28, 2015 at 7:12
  • $\begingroup$ as white noise i mean $\endgroup$ May 28, 2015 at 20:05
  • $\begingroup$ 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 $\endgroup$ May 28, 2015 at 20:54

2 Answers 2


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.

  • $\begingroup$ 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 ? $\endgroup$ May 27, 2015 at 9:42
  • 1
    $\begingroup$ Indeed, pink/red/brown, etc. noise has lower spectral entropy than a white noise. $\endgroup$
    – jojek
    May 27, 2015 at 12:41
  • $\begingroup$ does amplifying past clip change the spectral entropy? could sinc filtering white noise leave the spectral entropy unchanged ? $\endgroup$ May 27, 2015 at 14:03

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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  • $\begingroup$ i thought spectral flatness was noise? i was gonna edit the question, anyway but thanks ! $\endgroup$ May 27, 2015 at 3:51
  • $\begingroup$ 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! $\endgroup$ May 27, 2015 at 18:16

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