Modulation Transfer Function (MTF)

Speech intelligibility depends not just on frequency content but on temporal modulation — the rapid amplitude fluctuations at rates between 0.63 Hz and 12.5 Hz that carry consonant and vowel information. The MTF quantifies how faithfully these modulations are transmitted from source to listener. An MTF of 1.0 means perfect preservation; 0.0 means the modulation is completely lost. The full STI measurement requires 98 MTF values: 7 octave bands (125 Hz to 8 kHz) × 14 modulation frequencies (0.63 to 12.5 Hz in 1/3-octave steps). Each value represents the ratio of output modulation depth to input modulation depth at that specific combination. Reverberation smears the temporal pattern, reducing MTF at all modulation rates. Background noise fills in the gaps between speech peaks, also reducing apparent modulation. The MTF can be measured directly using modulated test signals (as in STIPA) or computed indirectly from the impulse response. The IR-based method uses the relationship: m(F,f) = |∫h²(t)e^(-j2πFt)dt|² / [∫h²(t)dt]², where h(t) is the impulse response, F is the modulation frequency, and f is the octave band center frequency. This approach gives the reverberation-only MTF, to which noise effects must be added separately. The Schroeder-Kuttruff approximation relates MTF to reverberation time: m(F) = 1/√(1 + (2πFT)²), where T is the reverberation time. This simplified model shows that longer reverberation reduces MTF at all modulation rates, with higher modulation frequencies affected more severely. It also reveals that modulation rates below about 0.5/T are relatively unaffected by reverberation. Understanding individual MTF values helps diagnose specific problems: low MTF at high modulation rates suggests excessive reverberation, while uniformly low MTF across all rates suggests noise dominance.