Métricas de calidad del habla PESQ y STOI

PESQ (Perceptual Evaluation of Speech Quality) and STOI (Short-Time Objective Intelligibility) are algorithms that estimate how humans would judge a speech recording, without running a listening test. Both are intrusive, also called full-reference, metrics: they need the original clean recording and the processed or degraded version, and they score the second against the first. They answer different questions. PESQ estimates quality, roughly how pleasant and natural the speech sounds. STOI estimates intelligibility, how many words a listener would understand. A noise suppressor can raise one while lowering the other, which is why papers usually report both.

PESQ was standardized by the International Telecommunication Union as Recommendation ITU-T P.862, approved on 23 February 2001 for narrow-band telephone networks and speech codecs. Companion documents followed: P.862.1 in November 2003 defines a mapping from PESQ's raw output to MOS-LQO, a listening-quality score on the same 1 to 5 mean opinion score (MOS) scale used in human tests, and P.862.2 in 2007 extends PESQ to wideband speech sampled at 16 kHz, covering 50 to 7,000 Hz according to Torcoli and colleagues. The ITU's catalog now lists P.862 and its parts as deleted on 5 January 2024 and points users to P.863, titled Perceptual objective listening quality prediction, whose current version dates from March 2018. Despite that, a 2025 paper by Torcoli, Halimeh and Habets notes that PESQ is still widely used.

PESQ works by modeling a listener. The standard pipeline aligns the overall level of both signals, applies a filter that imitates a telephone handset, estimates the time delay between them so the right moments are compared, and splits both into short frames. Kim, El-Khamy and Lee describe the next stages in their 2019 analysis: each frame's spectrum is warped onto the Bark scale, a frequency scale that matches how the ear groups pitches, using 49 bands; the clean and degraded spectra are equalized; and power is converted to perceived loudness with Zwicker's law. The difference in loudness between clean and degraded frames becomes a disturbance. PESQ keeps two versions, a symmetric disturbance and an asymmetric one that penalizes added sounds such as noise more than missing ones. These are averaged over frames and combined into a single score.

STOI was introduced by Taal, Hendriks, Heusdens and Jensen in IEEE Transactions on Audio, Speech, and Language Processing in 2011. It was built for speech that has been processed by time-frequency weighting, the family of methods, such as spectral masks, that turn individual frequency bands up or down over time. As summarized by Kolbaek, Tan and Jensen, STOI resamples both signals to 10 kHz, cuts them into 256-sample frames (25.6 ms) with 50% overlap, and groups the spectrum into 15 one-third octave bands from 150 Hz to about 3.8 kHz. For each band it takes the amplitude envelope over windows of 30 frames, about 384 ms, and computes the correlation between clean and processed envelopes. The final score is the average of these correlations across bands and windows. Because it is an average of correlations, the score can range from -1 to 1, and higher means more intelligible.

The two metrics complement older and newer alternatives. Simple signal measures such as signal-to-noise ratio contain no model of hearing at all. Human listening tests remain the reference but are slow and costly. POLQA, defined in P.863, is the ITU's named successor to PESQ, while PESQ keeps the advantage of several free, open implementations. For intelligibility, Jensen and Taal published extended STOI (ESTOI) in 2016 to handle modulated noise maskers, and the pystoi package offers both. Non-intrusive metrics such as DNSMOS, proposed by Microsoft researchers in 2020, estimate quality without a clean reference, which matters for real recordings where none exists.

The metrics have well-documented weaknesses. Because they are intrusive, they cannot score live calls or field recordings. PESQ was designed for telephone-band speech and handset listening, so its use on modern full-band audio, music or very low bit-rate neural codecs goes beyond what it was validated for. Version confusion is a practical hazard: Torcoli and colleagues found that on one test set, scores from the original P.862 and the wideband P.862.2 differed by a root-mean-square error of 0.62 and by as much as 1.82 points on a single item, and that a 2018 correction to the wideband filter changed scores by an RMSE of 0.56. Their advice is to always state the exact PESQ version and implementation. STOI, for its part, measures envelope correlation rather than understanding, so a higher score is a prediction of better intelligibility, not proof of it.

Optimizing directly for these numbers creates its own risk. Kim and colleagues showed that a differentiable PESQ-style loss improved PESQ and SDR together, but any metric becomes less trustworthy once it is a training target. Good practice pairs PESQ and STOI with at least one other measure, ideally a small human listening test.

The practical requirements are light. Both metrics need time-aligned clean and processed files at a supported sample rate: the pesq package accepts 8 kHz for narrowband mode and 16 kHz for wideband mode, and pystoi takes any rate and resamples internally to 10 kHz. The pesq Python package is MIT-licensed, and pystoi's tests match the original MATLAB implementation within a tolerance of 0.001.