The dB correction that level-matches a LOW-tier band to the HIGH tier's reference (issue #97).
The tiers are amplitude-calibrated PER BIN — a full-scale sine reads ~unity in either — but a
band's value is the RMS ACROSS the bins it spans, which divides by the bin count, and the LOW
tier packs 8× more bins into the same Hz range (same fftSize, an eighth of the sample rate). A
signal's band ENERGY is tier-invariant: a tone's mainlobe occupies the same few bins at the same
per-bin amplitude, and a noise floor's per-bin power scales with bin width, cancelling the count.
So the RMS reads √8 (~9 dB) LOWER from the LOW tier — a visible step at the crossover, and the
low-end lump operators kept reporting. Correct by the bin-density ratio.
A degenerate tier (a zero or negative rate or size) makes the ratio non-finite; decline to
correct rather than emit a NaN into the trace.
The dB correction that level-matches a LOW-tier band to the HIGH tier's reference (issue #97).
The tiers are amplitude-calibrated PER BIN — a full-scale sine reads ~unity in either — but a band's value is the RMS ACROSS the bins it spans, which divides by the bin count, and the LOW tier packs 8× more bins into the same Hz range (same fftSize, an eighth of the sample rate). A signal's band ENERGY is tier-invariant: a tone's mainlobe occupies the same few bins at the same per-bin amplitude, and a noise floor's per-bin power scales with bin width, cancelling the count. So the RMS reads √8 (~9 dB) LOWER from the LOW tier — a visible step at the crossover, and the low-end lump operators kept reporting. Correct by the bin-density ratio.
A degenerate tier (a zero or negative rate or size) makes the ratio non-finite; decline to correct rather than emit a NaN into the trace.