âš™ï¸ ENGINEER LEVEL: Coherence, Gating, and Transfer Functions
Transfer Function Measurement
The complete system response is captured as a transfer function:
H(ω) = Y(ω) / X(ω)
Where X(ω) is the input (electrical signal) and Y(ω) is the output (acoustic pressure at microphone).
Coherence function:
γ²(ω) = |G_xy(ω)|² / [G_xx(ω) × G_yy(ω)]
γ² ranges from 0 to 1. Values below 0.8 indicate: - Background noise contamination (engine, traffic) - System nonlinearity (distortion) - Strong reflections creating multiple uncorrelated paths - Signal too low
Practical rule: Only trust frequency response where coherence > 0.85. Regions with low coherence should be measured again after reducing noise sources.
Gated (Quasi-Anechoic) Measurements
Car acoustics differ fundamentally from anechoic chambers. Sound bouncing from glass, seats, and panels reaches the microphone fractions of a millisecond after the direct sound. At low frequencies these reflections blend imperceptibly; at mid/high frequencies they cause comb filtering visible in the response.
Time windowing:
Apply a time-domain window to the impulse response that cuts off before the first significant reflection arrives. The resulting frequency response represents only direct sound.
This page is meant to include a finished diagram or annotated reference visual. The final asset is not published yet.
Planned visual: Two graphs side by side — ungated response showing comb filtering above 1 kHz vs gated response showing smooth tweeter roll-in above crossover
Frequency resolution limit:
Gating creates a fundamental trade-off:
Δf_min = 1 / T_window
A 10 ms gate allows resolution down to 100 Hz. A 5 ms gate down to 200 Hz. You cannot accurately measure lower frequencies with short gates.
Practical technique:
- Use full (ungated) measurement below 200 Hz — cabin is small, reflections are less damaging
- Use gated measurement above 300 Hz — remove reflections, see driver response cleanly
- Merge at 200–300 Hz transition in REW's Overlays tab
This gives you a clean picture across the full range.
Impedance Swept Measurement
Speaker impedance is not constant — it varies dramatically with frequency due to resonance and voice coil inductance.
Measurement circuit:
This page is meant to include a finished diagram or annotated reference visual. The final asset is not published yet.
Planned visual: Schematic showing audio interface output, known series resistor (10Ω), speaker under test, two voltage measurement points V1 (before resistor) and V2 (across speaker)
Z_speaker(ω) = R_series × [V2(ω) / (V1(ω) - V2(ω))]
REW can do this automatically with a known reference resistor. Connect: - Interface output → 10Ω resistor → Speaker → Ground - Interface input Ch 1: Before resistor (reference voltage) - Interface input Ch 2: Across speaker (measurement voltage)
Results reveal:
- Fs: Peak of impedance curve — free-air resonance
- Re: DC resistance — Y-intercept at very low frequency
- Le: Voice coil inductance — slope of impedance rise at high frequency
- Qes / Qms: Width and shape of resonance peak
All Thiele-Small parameters can be extracted from a careful impedance measurement — valuable for enclosure modeling when manufacturer specs are unavailable or suspect.