Transfer Function & Coherence
Understand how AudioMap measures system response using dual-channel FFT analysis, H1 estimation, and coherence-weighted processing
What is a Transfer Function?
A transfer function H(f) describes how a system modifies a signal at each frequency. It captures both magnitude changes (how much louder or quieter) and phase shifts (how much the signal is delayed) across the entire audible spectrum.
AudioMap measures the transfer function by comparing what was sent to the speakers (the source signal) with what was received by the microphones (the measured signal), using dual-channel FFT analysis.
The Formula
H(f) = Y(f) × conj(X(f)) / |X(f)|²
Where Y = receiver (microphone), X = source (reference signal)
What You Get
Magnitude Response
How much each frequency is amplified or attenuated by the system. Displayed in dB — the frequency response curve you see in AudioMap's main display.
Phase Response
How much each frequency is delayed (in degrees). Critical for crossover alignment, subwoofer integration, and multi-way speaker systems.
Coherence
How reliably the output relates to the input at each frequency. Values near 1.0 mean the measurement is trustworthy; low values indicate noise, reflections, or nonlinearity.
Measurement Signal Flow
Signal Generator
Pink noise output to speakers
Reference Capture
Source signal recorded (physical or virtual)
Microphone Capture
Room response recorded at mic position
Dual-Channel FFT
Both signals transformed to frequency domain
H1 Estimation
Transfer function computed with coherence
Technical Specifications
SIMD-optimized (4x parallel)
Below threshold defaults to unity
Power-domain magnitude averaging
Wrapped at ±180°
Raw → temporal averaged → smoothed
uint64 generation counter
H1 Estimator Details
AudioMap uses the H1 estimator, which minimizes noise on the output (microphone) signal. This is the correct choice for acoustic measurements where the noise is predominantly at the receiver.
H1(f) = Gxy(f) / Gxx(f)
Gxy = cross-spectral density, Gxx = source auto-spectral density