# What is spectral entropy?

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, 2015 at 3:03
• But you can edit it. May 28, 2015 at 1:04
• Have the same spectral entropy as what?
– jojek
May 28, 2015 at 7:12
• as white noise i mean May 28, 2015 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, 2015 at 20:54

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.

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

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