Delay Estimation (frequency domain)

Two noisy observations of the same signal are shifted relative to each other. Inspect the cross-correlation alongside the cross power spectral density (magnitude & phase) to read out the delay. Controls sit above the plots, mirroring the MATLAB demo.

Shifters above plots
Independent noises
Cross-spectral angle
Signal variance
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Noise variance
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Delay [ms]
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Observation Y₁(t) = X(t) + N₁(t)

Observation Y₂(t) = X(t−τ₀) + N₂(t)

Magnitude of Cross PSD

Phase of Cross PSD

Cross-correlation RY₁Y₂(τ)