What do different Cepstral or MFCC coefficients represent intuitively?

Question

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.

Answer 1

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.