Per-channel energy normalization (PCEN)

Description

PCEN (Wang et al.) seems to be a good alternative to log-amplitude scaling for speech recognition systems; see also: (Battenberg, et al.). Since it’s fairly easy to implement in the static (non-trainable) form, do folks thing it’s worth including in librosa?

Here’s a quick reference implementation of eq.1 in the paper, using the default parameters listed in section 2:

def pcen(E, alpha=0.98, delta=2, r=0.5, s=0.025, eps=1e-6):   
    M = scipy.signal.lfilter([s], [1, s - 1], E)
    smooth = (eps + M)**(-alpha)
    return (E * smooth + delta)**r - delta**r

It could probably be made more numerically stable. It could also be vectorized to support channel-dependent parameters, which might make it more useful for things like CQT.

[f0k]

Since it’s fairly easy to implement in the static (non-trainable) form, do folks thing it’s worth including in librosa?

As this is the first search result when looking for an implementation, it might be interesting to note that the trainable form is also fairly easy to implement, here’s a version of PCEN for Lasagne: https://gist.github.com/f0k/c837bcf0bfde189ca16eab63637839cb I’ve used Vincent’s formulation in there as well, thanks for the discussion here!

[bmcfee]

I think I’m inclined to leave it parameterized by s so that it more closely resembles the paper. I’d actually like to rename the parameters to something interpretable, but provide the equation and reference to the paper in docs.