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I've seen two sort of audio signals, one where the y-axis takes values between -1 and +1. I'd think this means 1 means loudest? Not really sure

And the second one I saw goes between $-10 000$ and $+10 000$. What do these values actually mean? Are they arbitrary?

I'm doing work on audio features using MFCC but it seems that when I take a file with values between $[-10k,+10k]$, I get normal cepstral coeffecients of which we take the first $12$. But when I take audio with values in $[-1, 1]$, the cepstral coeffecients are in a negative range.

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What do these values actually mean? Are they arbitrary?

Yes, pretty much: they will just be the scale of numbers your system works with. In floating point systems, we often see that samples get normalized to [-1,+1], whereas in fixed-point system, it's often things like [-2⁻¹⁵,+2¹⁵-1], depending on the bit width of the samples to begin with.

So, this is purely conventional. Most algorithms don't care about the absolute scale of things.

So, if your algorithm does depend on amplitudes, well, normalize your signal before you process it.

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For a sampled audio waveform (at least destined for human ears), any DC will typically be removed acoustically, electrically and digitally, and what you are left with is a nominally symmetric waveform (speech can have some asymmetry) fluctuating between +A and -A. For «loudness» you want to take the absolute value or square for a power estimate and do some temporal smoothing (envelope).

If you are working with floating point numbers, it is good practice to: 1. Establish some «nominal» range and stick to it 2. Ensure that your algorithms behaves ~the same irrespective of absolute scaling.

With fixed point integers your algorithm, numerical representation and code is interlinked much more strongly, so you do what you have to do.

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