Loudness is computed in a wrong way

[nielsrolf]

Hello,
Some time ago, I noticed a bug in compute_loudness in magenta/ddsp, and I think this repo has a similar issue. Below is the loudness curve extracted for a sine wave with pitch interpolating linearly between 100Hz to 4000Hz

Here is a notebook that compared the magenta/ddsp loudness, the proposed fix and the loudness as computed by this repo. I would be happy to create a pull request if you agree that this should be fixed.
Here is a colab notebook that generated the graph above

[caillonantoine]

Hi! Thanks for the issue ! About the PR, sure! Most of the preprocessing stuff is heavily inspired from the original repo so I guess it could use a fix !

[nielsrolf]

Do you prefer to keep the loudness computation in librosa/numpy over doing it in torch as well? I imagine there could be cases where you'd like to backpropagate through this, for example when you do self-supervised training like in the inv-DDSP paper (although that particular model does not use compute_loudness at all).