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Cross-Correlation

Find a known pattern within a noisy signal

Pattern Detection

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Signal x[n] - Pattern Hidden in Noise

Template h[n] - Known Pattern to Find

Cross-Correlation R_xh[k] - Peak Shows Pattern Location

Sliding Template Animation

Cross-Correlation Applications

Radar Systems: Detect the return time of a transmitted pulse to measure distance.

GPS: Correlate satellite signals with known codes to determine position.

Template Matching: Find a known pattern (face, fingerprint, signature) in an image or signal.

Time Delay Estimation: Determine the lag between two recordings of the same event.

Formula: R_xh[k] = Σ x[n] · h[n-k] - slides the template across the signal