Fast Normalized Cross-Correlation

Normalized cross-correlation has been used extensively for many signal processing applications, but the traditional normalized correlation operation does not meet speed requirements for time-critical applications. In this paper, a new fast algorithm for the computation of the normalized cross-correlation (NCC) without using multiplications is presented. For a search window of size M and a template of size N the fast NCC requires only approximately 2N⋅(M−N+1) additions/subtractions without multiplications. Simulation results with 100,000 test signals show that the use of the fast NCC instead of the traditional approaches for the determination of the degree of similarity between a test signal and a reference signal (template) brings about a significant improvement in terms of false negative rate, identification rate and computational cost without a significant increase in false positive rate, especially when the signal-to-noise ratio (SNR) is higher than 3 dB.