Delayed Auditory Feedback Fluency Simulator

DAF Parameters

Feedback delay τ 180 ms

Feedback gain K 0.70

Masking noise level 0%

Target speech rate 4.0 syll/s

Live Readouts

Produced rate

4.0 syll/s

Phase error

0°

Disfluency index (period CV)

0.0%

How it works

Speech timing is modelled as a self-sustained phase oscillator θ(t): every 2π of phase is one syllable, produced at the target angular rate ω₀ = 2π·rate. Normally the only feedback a speaker uses to hold that rate steady is their own voice, heard with essentially zero delay.

Delayed Auditory Feedback (DAF) reroutes the speaker's voice through headphones after a delay τ. This simulator keeps a ring buffer of the last ~300 ms of produced phase and reads it back τ seconds late — exactly what a DAF device does electronically. The mismatch between what was just said and what is heard perturbs the timing generator:

dθ/dt = ω₀ · [ 1 + K·(1 − mask)·sin(θ(t−τ) − θ(t)) ]
CV(period) = std(inter-syllable interval) / mean(interval)   ← disfluency index

Because sin(θ(t−τ)−θ(t)) depends on how far out of phase the delayed copy is, the disruption is not monotonic in τ — it is worst when the delay is close to a large fraction of the natural syllable period, and near-zero when τ is very short or a near-integer number of periods, reproducing the classic non-monotonic delay curve reported by Fairbanks (1955) and used ever since to tune DAF/FAF fluency-shaping devices (e.g. SpeechEasy) for stuttering therapy. Raising the gain K strengthens the coupling (worse disruption); raising masking noise attenuates how much of the delayed feedback the model can even use (informational masking), which is also why noise-masking headsets reduce DAF-induced stuttering in the clinic.

Delay τ — feedback-loop latency in milliseconds.
Gain K — how strongly the mismatched feedback perturbs the timing generator.
Masking noise — fraction of the feedback signal masked before it can act (0 = fully audible echo, 100% = fully masked, feedback ignored).
Target speech rate — the natural, undisturbed syllable rate ω₀/2π.

Production phase (ring) Delayed feedback pulse Syllable emission

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