Formant Synthesis: Building Vowels From a Buzz and a Filter

Source-filter: a buzz shaped into a vowel

The classical model of voiced human speech splits the vocal system into two independent stages. The source is the glottis — the vocal folds vibrating open and shut, producing a buzzy, harmonically rich pulse train at the fundamental frequency F0 (perceived as pitch). The filter is the vocal tract above the larynx — throat, mouth, tongue, lips — a tube of varying cross-section that resonates at frequencies determined by its shape, boosting some harmonics of the source and damping others. What comes out is the source spectrum multiplied by the filter's frequency response; change the source and pitch changes without changing the vowel, change the filter shape and the vowel changes without changing the pitch. This separation is why the source-filter model, formalised by Gunnar Fant in the 1960s, remains the basis of almost all formant speech synthesis.

Formants: the vocal tract's resonances

The vocal tract behaves acoustically like a tube closed at one end (the glottis) and open at the other (the lips), and such a tube has a series of resonant frequencies called formants, labelled F1, F2, F3... in ascending order. For an adult vocal tract roughly 17 cm long, the formants sit near odd multiples of c/4L (~500 Hz, 1500 Hz, 2500 Hz for a neutral schwa), but tongue position and lip rounding shift them substantially: raising and fronting the tongue (as in "ee") raises F2 sharply while lowering F1; opening the jaw (as in "ah") raises F1. The vowel space of a language is essentially the F1-F2 plane, and vowels that sound distinct occupy different corners of it.

vowel   F1 (Hz)   F2 (Hz)      description
/i/ ee    270       2290     tongue high & front
/a/ ah    730       1090     tongue low & back-ish
/u/ oo    300        870     tongue high & back, lips rounded

Building a formant synthesiser

A formant synthesiser generates the glottal source directly — commonly a Liljencrants-Fant or a simpler impulse-train model, shaped to have the right spectral tilt — and then passes it through a filter bank of resonators, one per formant, each a second-order bandpass tuned to a centre frequency and bandwidth. Cascading three to five such resonators and summing (or cascading) their outputs reproduces the spectral envelope of a target vowel closely enough to be intelligible and, with careful tuning, natural-sounding. Consonants are handled with separate source models: unvoiced fricatives ("s", "f") replace the periodic glottal buzz with filtered turbulent noise generated at a constriction, and plosives ("p", "t", "k") are modelled as a brief silence (the closure) followed by a noise burst.

Voiced versus whispered speech

Normal voiced speech uses a quasi-periodic glottal source, and it is that periodicity that gives speech its pitch. Whispering replaces the periodic vibration with the vocal folds held close together but not vibrating, so airflow through the narrow gap becomes turbulent and the source is broadband noise instead of a harmonic buzz — no F0, no pitch, but the vocal tract filtering above it still shapes that noise into recognisably the same vowels, because formants depend on tract shape, not on the source. This is exactly why a whisper is intelligible but toneless: the filter survives, the source's periodicity does not.

Why this still beats naive playback for many uses

Modern commercial systems mostly use concatenative or neural (WaveNet-style, diffusion, or autoregressive) synthesis, trained on large recorded corpora, because they sound far more natural. But the formant, source-filter model remains valuable because it is fully parametric and physically interpretable: every control (F0, F1-F3, tract length, voicing) has a direct articulatory meaning, it needs no training data or corpus, runs in real time on trivial hardware, and lets you smoothly morph between vowels or exaggerate a parameter — which is precisely why it survives in accessibility tools, telecommunication-bandwidth speech coding (vocoders) and interactive teaching demonstrations like this one.

Frequently asked questions

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