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I understand the explanation for separating slow and rapid changing log spectral components but i need to understand:

  1. Why lower coefficients have higher and mostly positive magnitudes?
  2. Why Higher coefficients have negative values more often?

I understand the mathematical computation i.e. taking log of spectrum to make the components with different change rates, linearly seperable and then taking IFFT of logspectrum to separate these components.

However, I analyzed the MFCC stats from a speech dataset and can't see why slowly changing components (lower coefficients) have more magnitude while higher ones have more negative values and what do negative valued coefficients indicate.

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  • $\begingroup$ Hi! Welcome here. These are four questions. Every one of them is broad, and I don't think all the things you say are inherently true. That makes this question (which is actually 4 questions) too broad to be answered concisely. Could you limit yourself to one question, for now, and explain what you've researched about it so far? It's very hard to help someone when you don't know what they already understand. (Please edit your question to do that!) $\endgroup$ – Marcus Müller Sep 17 '20 at 21:43
  • $\begingroup$ Hi thanx for your response. I removed the two relatively wague questions. I understand the mathematical computation i.e. taking log of spectrum to linearly seperate components with different change rates and taking ifft of logspectrum to seperate these components. However i analyzed the mfcc stats from speech dataset and cant get why slow changing components (lower coefficients) have more magnitude while higher ones have more negative values and what do negative valued coefficients indicate? Thanx $\endgroup$ – mohammad ali Humayun Sep 18 '20 at 6:36
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When you take the log of some measurement value, you are simply changing the nature of the scale of what you are measuring. Where the dividing line between positive and negative values on the new scale is depends only where the "1" was defined on the original scale. There is no qualitative distinction between positive and negative per se, so what you are really asking is why are slowly changing components (lower coefficients) larger than other ones.

If a sinusoidal is enlarged proportionally, then the amplitude is inversely proportional to the frequency. If your signal indicates this (regardless of context) it means similarity is being preserved across levels.

So this doesn't answer the title question, but hopefully helps with the enclosed ones.

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