Delay Estimation (time domain)

Two noisy observations of the same signal are shifted relative to each other. Adjust the SNR, choose the underlying signal (noise, speech, or sinusoid), and set a delay to see the cross-correlation peak move.

Shifters above plots
Independent noises
Cross-correlation peak
Noise realizations stay fixed; only the scaling changes with SNR.
Positive values delay Y₂(t) relative to Y₁(t).
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)

Cross-correlation RY₁Y₂(τ)