Function extract_spectral_amplitudes 

pub fn extract_spectral_amplitudes(
    fft_out: &[Complex<f32>],
    f0_bin: f32,
) -> SpectralAmplitudes

Extract harmonic amplitudes from the FFT half-spectrum.

For each harmonic k from 1 to L, integrate the magnitude across the three bins nearest to k · f0_bin (centre bin ± 1). Using a 3-bin window rather than a single round-to-nearest bin recovers energy for harmonics that fall between bin centres (fractional f0_bin from pitch periods that aren’t integer factors of the FFT size). Without this, harmonics at bin offset ±0.5 drop ~3 dB below their true amplitude — measurable on real voice captures against the DVSI chip’s own extraction, where the missing energy produced flat Gm vectors that the PRBA codebook search always resolved to near-origin entries (flat envelope → no formants).

We use sum-of-squares then sqrt so the window accumulates power rather than raw magnitudes; this is the canonical way to pool nearby bins without the magnitude-vs-phase ambiguity.

L is limited by both the FFT size and the AMBE codec: L = min(floor((N − 1) / f0_bin), MAX_HARMONICS).