Coherence (Signal Analysis)
Definition
Coherence
Magnitude-squared coherence is a frequency-domain metric ranging from 0 to 1 that measures the degree of linear relationship between two signals at each frequency. Computed from cross-spectral and auto-spectral densities using Welch's method, coherence indicates measurement reliability in transfer function analysis. SonaVyx displays coherence alongside magnitude and phase.
γ²(f) = |Gxy(f)|² / (Gxx(f) × Gyy(f)), where G = spectral density
How Coherence Is Measured
Coherence requires simultaneous capture of reference (input) and measurement (output) signals over multiple averaging windows. SonaVyx computes the cross-spectral density Gxy and auto-spectral densities Gxx and Gyy using Welch's method with 50% or 75% overlapping Blackman-Harris windows. The squared magnitude of the cross-spectrum divided by the product of auto-spectra yields the coherence function at each frequency bin.
Practical Example
While tuning a PA system, a sound engineer observes the transfer function showing a -10 dB dip at 400 Hz. Before applying EQ correction, the engineer checks coherence at 400 Hz and finds it is only 0.35. This low coherence indicates the dip is caused by contamination from room reflections or background noise, not the speaker's response. Applying EQ boost would amplify noise without fixing the underlying problem.
Interpreting Coherence Values
Coherence above 0.8 (green in SonaVyx) means the measurement is highly reliable at that frequency. Values between 0.5 and 0.8 (amber) indicate moderate contamination from noise or reflections. Values below 0.5 (red) mean the transfer function data at that frequency is unreliable and should not be used for EQ decisions. Perfect coherence of 1.0 occurs only in noise-free, reflection-free conditions with perfectly linear systems.
Causes of Low Coherence
Several factors reduce coherence at specific frequencies. Ambient noise unrelated to the test signal adds random energy to the measurement channel. Strong reflections arriving from different directions create time-varying interference patterns. Nonlinear distortion generates harmonics not present in the input. Insufficient averaging allows random spectral variations to dominate. The number of averages directly affects coherence — more averages improve it by reducing random variations.
Coherence and EQ Decisions
Professional sound engineers use coherence as the gatekeeper for EQ decisions. Boosting a frequency with high coherence is valid because the measured dip represents a genuine speaker or room response deficiency. Boosting a frequency with low coherence is counterproductive — the dip may be caused by destructive interference that cannot be corrected with EQ, and boosting amplifies the noise that reduced coherence in the first place. This principle is fundamental to data-driven system tuning.
Improving Coherence
To improve coherence: increase the test signal level relative to background noise, increase the number of averages (16 or more for noisy environments), ensure the microphone is properly positioned in the direct field of the speaker, use a larger FFT size for better frequency resolution in the low end, and minimize time-variant conditions (air movement, audience movement) during measurement. SonaVyx color-codes the coherence bar to guide these decisions in real time.
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