MTF Concept

Speech is carried by amplitude modulations at rates between about 0.5 and 16 Hz. The syllable rate of typical speech produces modulation peaks around 3-5 Hz. The MTF quantifies how faithfully these modulations pass through the room or PA system.

For each octave band k and modulation frequency Fm, the MTF m(Fm,k) ranges from 0 to 1. A value of 1 means the modulation depth at the receiver equals the modulation depth at the source. A value of 0 means the amplitude envelope is completely flat — no modulation survives.

MTF from Room Acoustics

For a reverberant room with exponential decay, the MTF due to reverberation alone is:

m_reverb(Fm,k) = 1 / √(1 + (2π·Fm·T/13.8)²)

Where T is the reverberation time in the octave band. Longer RT means lower MTF at all modulation frequencies. This formula shows why rooms with T > 2s have poor speech intelligibility — the high modulation frequencies (which carry consonant information) are severely attenuated.

MTF Including Noise

Background noise further reduces the MTF by partially filling modulation troughs:

m(Fm,k) = m_reverb(Fm,k) / (1 + 10^(-SNR(k)/10))

Where SNR(k) is the signal-to-noise ratio in octave band k. Even moderate noise (SNR = 10 dB) reduces MTF significantly. The masking section covers the complete noise interaction model.

Full STI vs STIPA MTF Grid

The full STI computation evaluates 14 modulation frequencies (0.63, 0.80, 1.00, 1.25, 1.60, 2.00, 2.50, 3.15, 4.00, 5.00, 6.30, 8.00, 10.0, 12.5 Hz) in 7 octave bands (125 Hz to 8 kHz), producing a 7×14 matrix of 98 MTF values. STIPA uses only 2 modulation frequencies per band (14 total), selected to be maximally representative.

MTF from Impulse Response

IEC 60268-16 Clause A.4 provides a direct method for computing MTF from the measured impulse response:

m(Fm,k) = |∫₀^∞ h²(t) · e^(-j2πFm·t) dt| / ∫₀^∞ h²(t) dt

This is the magnitude of the Fourier transform of the squared impulse response, normalized by total energy. This method captures the actual room response without assuming exponential decay.

SonaVyx MTF Display

The STI tool displays the per-band MTF values as a bar chart, with color coding indicating contribution to overall STI. In Pro mode, the full 7×14 matrix is shown. The MTF feeds into the STI calculation pipeline including masking corrections and band weighting.