fbe transform: is 10*log10(RMS) the intended dB convention (vs 20*log10)?

[d-chambers]

Summary

While reviewing the new fbe (Frequency Band Energy) transform on dev, the decibel conversion looks like it may be off by a factor of two (or, equivalently, mixing the amplitude and power dB conventions). Opening this for discussion before changing anything, since it may be an intentional choice tied to a reference implementation.

Current behavior

dascore/transform/fbe.py:

fbe = ((patch**2).rolling(**{dim: window, "step": step}).mean() ** 0.5)  # linear
if db:
    fbe = 10 * fbe.log10()

So the linear output is the windowed RMS amplitude of the band-passed signal:

fbe_linear = sqrt(mean(x^2))

and the dB output is:

fbe_dB = 10 * log10( sqrt(mean(x^2)) )
       = 5  * log10( mean(x^2) )

Why this looks inconsistent

There are two standard ways to express this in dB, and they agree with each other:

• Amplitude / field convention (the linear value is an amplitude): 20 * log10(RMS)
• Power / energy convention (FBE = "energy" ∝ amplitude²): 10 * log10(mean(x^2))

Both reduce to 20 * log10(RMS). The current code uses 10 * log10(RMS), which is exactly half of both — it applies the power factor (10) to an amplitude (RMS). A 10× change in RMS should read as 20 dB; today it reads as 10 dB.

Options

1. Treat FBE as energy (recommended): drop the ** 0.5 in the dB path (or apply 10*log10 to the pre-sqrt energy). Matches the "Energy" in the name.
2. Treat FBE as amplitude: keep RMS and use 20 * log10(RMS). Numerically identical to option 1 in dB, but the linear output stays RMS amplitude.
3. Leave as-is if this matches a specific reference/convention we want to reproduce — in which case we should document it explicitly so users know it isn't the textbook 20·log10.

A secondary point: the dB is currently referenced to 1 (raw data units), i.e. it's a relative "dBFS-like" measure. Worth documenting, and possibly exposing a reference level, but that's separable from the factor question.

Question

Was 10 * log10(RMS) intentional (matching an external tool), or should it be 20 * log10(RMS) / 10 * log10(energy)? Happy to open a PR for whichever convention we settle on, plus a docstring note and a test that pins the chosen definition.

Context: found during a review of the dev branch; unrelated fixes for file:// handling, remote HTTP headers, config thread-safety, and NetCDF remote scan are being handled separately.

[andreas-wuestefeld]

@d-chambers Thanks for pointing this out.

This is probably a leftover bug from an earlier version that simply used the amplitude.
The correct approach should indeed be to treat FBE as "Energy" and calculate dB as 20*log10( sqrt(mean(x^2)))

I will make a pull request