Cross-Spectral Density Reference
A quick reference for cross-spectral density — definition, relationship to coherence and role in multi-input analysis.
Definition
G_xy(f) = |G_xy(f)| × e^(i×∠G_xy(f)) Magnitude: 0 ≤ |G_xy| ≤ √(G_xx × G_yy) Phase: ∠G_xy ∈ [-π, π] Coherence: γ² = |G_xy|² / (G_xx × G_yy) Range: 0 ≤ γ² ≤ 1
Interpretation
- γ² ≈ 0: uncorrelated — SRSS combination valid
- γ² ≈ 1: correlated — cross terms essential
- 0 < γ² < 1: partially correlated — full cross-spectral analysis