Coherence Reference

A quick reference for the coherence function — definition, range, interpretation and use in multi-input analysis and measurement quality.

Random Vibration2 min read

referencecoherencecorrelationmulti-inputmeasurement quality

Coherence Function

γ²(f) = |G_xy(f)|² / (G_xx(f) × G_yy(f))

Range: 0 ≤ γ² ≤ 1

γ² = 0: uncorrelated at frequency f
γ² = 1: perfectly correlated at frequency f
0 < γ² < 1: partially correlated

Coherence varies with frequency.

Uses

Multi-input analysis: determines if cross terms are needed
Measurement quality: γ² < 1 at resonance suggests noise or nonlinearity
Source identification: high coherence indicates common source