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STOI Implementation Notes

Goal

Implement STOI/ESTOI (Short-Time Objective Intelligibility) measure in Qlatt as a quality metric for synthesized speech.

Research Complete

Papers Processed

Taal et al. 2011 — papers/Taal_2011_STOI/ — Full STOI algorithm, all 8 equations, constants, logistic mapping. 12 pages read.
Jensen & Taal 2016 — papers/Jensen_2016_ESTOI/ — ESTOI extension, row-column normalization, spectral correlation. 14 pages read.

Reference Implementation Scouted

pystoi at ~/src/pystoi — full report at reports/stoi-scout-pystoi.md
~200 lines Python total
Key insight: OBM matrix is static (15x257 binary), can be hardcoded
Key insight: resampling can be avoided by using WebAudio OfflineAudioContext
Key insight: FFT is the only DSP primitive needed beyond basic linear algebra

Algorithm Summary

Shared Steps (STOI and ESTOI)

Resample both signals to 10 kHz
Remove silent frames (40 dB dynamic range threshold, based on clean signal only)
STFT: 256-sample Hann window, 50% overlap, 512-point FFT
Apply 15-band 1/3 octave matrix (150 Hz to ~4.3 kHz) → (15, T) envelopes
Extract N=30 frame segments (384 ms) → (S, 15, 30)

STOI-Specific

Energy-normalize y segments to match x (per-band, per-segment)
Clip to SDR floor: β = -15 dB
Compute Pearson correlation per band per segment
Average → scalar d

ESTOI-Specific

Row normalize (per-band: zero-mean, unit-variance) both x and y
Column normalize (per-frame: zero-mean, unit-variance) both x and y
Inner product of normalized columns, average → scalar d

Constants

Constant	Value
FS	10000 Hz
N_FRAME	256 samples
NFFT	512
NUMBAND	15
MINFREQ	150 Hz
N	30 frames (~384 ms)
BETA	-15 dB
DYN_RANGE	40 dB

JS Dependencies Needed

FFT library (fft.js or similar) for rfft
Hanning window (trivial to implement)
Matrix multiply, norms, means (manual on Float64Array)
Resampling: either port Octave-compatible Kaiser filter OR use OfflineAudioContext

Status