Alignment of noisy signals

We;study the relative performance of various methods for aligning noisy one -dimensional signals. No knowledge of the shape of the misaligned signals i s assumed. We simulate signals corrupted by both additive noise and timing jitter noise which are similar in complexity to nose-to-nose oscilloscope c alibration signals collected at NIST. In one method, we estimate the relati ve shift of two signals as the difference of their estimated centroids, We present a new adaptive algorithm for centroid estimation. We also estimate relative shifts from three different implementations of cross-correlation a nalysis. In a complete implementation, for N signals, relative shifts are e stimated from all N(N - 1)/2 distinct pairs of signals. In a naive implemen tation, relative shifts are estimated from just (N - 1) pairs of signals. I n an iterative adaptive implementation, we estimate the relative shift of e ach signal with respect to a template signal which, at each iteration, is e quated to the signal average of the aligned signals. In simulation experime nts; 100 misaligned signals are generated. For all noise levels, the comple te cross-correlation method yields the most accurate estimates of the relat ive shifts. The relative performance of the other methods depends on the no ise levels.