⚙️ ENGINEER LEVEL: Psychoacoustic Basis and Binaural Processing
Interaural Time Difference (ITD) and Level Difference (ILD)
Spatial perception uses two complementary cues:
ITD (Interaural Time Difference):
ITD_max = d / c = 0.215m / 343 m/s ≈ 0.63 ms
Where d = head diameter (approx. 0.215m). Maximum ITD for sound directly to one side.
Just-noticeable difference for ITD: 10–20 μs (microseconds).
This means time alignment must be accurate to better than 0.01ms (10 μs) for the finest spatial discrimination. DSPs with 0.01ms resolution (common in quality units) provide adequate precision.
ILD (Interaural Level Difference):
At high frequencies (> 1.5 kHz), the head creates an acoustic shadow — the ear facing away from the source receives less energy. Level difference provides directional cue above 1.5 kHz.
Below 1.5 kHz: ITD dominant. Above 1.5 kHz: ILD dominant. Crossover: Both contribute.
Implication: The critical frequency region for imaging precision is above 1.5 kHz — the tweeter range. Subwoofer time alignment affects integration with mid-bass but not phantom imaging. Tweeter and midrange time alignment is what produces the phantom center image.
Head-Related Transfer Function (HRTF):
The ear's pinna (outer ear shape) causes frequency-dependent filtering that varies with sound source angle and elevation. This HRTF provides elevation cues and front/rear discrimination.
In-car audio, HRTFs are modified by the interior reflective environment. Seat backs, headrests, and glass create reflections that partially simulate HRTF elevation cues — which is why careful positioning of tweeters (angled, elevated) can create convincing elevated soundstage without explicit elevation EQ.