Transfer Function
Definition
Transfer Function
A transfer function H(f) describes the frequency-dependent gain and phase relationship between the input and output of an audio system. Computed using dual-channel FFT analysis with the H1 estimator, transfer functions reveal magnitude response, phase response, and coherence simultaneously. SonaVyx measures transfer functions in real time in your browser.
H1(f) = Gxy(f) / Gxx(f), where Gxy = cross-spectrum, Gxx = input auto-spectrum
How Transfer Functions Are Measured
Transfer function measurement requires two simultaneous signals: a reference signal (the electrical output sent to the system under test) and a measurement signal (the acoustic response captured by a microphone). SonaVyx uses dual-channel FFT to compute the cross-spectral density Gxy and auto-spectral density Gxx, then divides them to obtain the H1 estimator. Welch's method with overlapping windows provides spectral averaging for stable results.
Practical Example
A sound engineer measures the transfer function of a PA speaker in a venue and discovers a 12 dB dip at 250 Hz with low coherence (0.3). Low coherence at that frequency indicates the dip is caused by destructive interference from a room reflection rather than a speaker defect. Moving the speaker 0.5 meters forward shifts the null frequency, and coherence rises above 0.8, confirming the fix.
Magnitude Response
The magnitude of the transfer function, expressed in decibels, shows how much the system amplifies or attenuates each frequency. A flat magnitude response (within ±3 dB from 80 Hz to 16 kHz) indicates accurate frequency reproduction. Deviations reveal speaker limitations, room resonances, or comb filtering effects. SonaVyx displays magnitude with adjustable octave smoothing from 1/1 to 1/24 octave resolution.
Phase Response
Phase describes the time delay applied to each frequency component. A linear phase response (constant group delay) means all frequencies arrive at the listener simultaneously. Non-linear phase introduces frequency-dependent time smearing, degrading transient accuracy. Wrapped phase displays values between -180 and +180 degrees, while unwrapped phase reveals the total accumulated delay across the frequency range.
Coherence Function
Coherence (gamma-squared) ranges from 0 to 1 and indicates how much of the measured output is linearly related to the input. High coherence (above 0.8) means the measurement is reliable at that frequency. Low coherence indicates contamination by noise, reflections, or nonlinear distortion. Coherence is the quality indicator for transfer function data — always check it before trusting magnitude or phase readings.
H1 vs H2 Estimators
The H1 estimator minimizes noise at the output (measurement microphone) and is appropriate when the primary noise source is ambient sound at the measurement location. The H2 estimator minimizes noise at the input and is used when the reference signal itself is noisy. For most live sound applications, H1 is the correct choice because microphone-side ambient noise dominates the error budget.
Applications in System Alignment
Transfer function measurement is the foundation of professional sound system alignment. Engineers use it to set EQ corrections, verify crossover alignment between drivers, time-align delay speakers, and confirm polarity. By storing a baseline transfer function and comparing it to post-adjustment measurements, SonaVyx quantifies the improvement and validates that changes achieve the intended result.
Try It Now
Measure transfer function — free dual-channel analysis in your browser