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 is assumed. We simulate signals corrupted by both additive noise and timing jitter noise which are similar in complexity to nose-to-nose oscilloscope calibration signals collected at NIST. In one method, we estimate the relative 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 analysis. In a complete implementation, for N signals, relative shifts are estimated from all N(N-1)/2 distinct pairs of signals. In a naive implementation, relative shifts are estimated from just (N-1) pairs of signals. In an iterative adaptive implementation, we estimate the relative shift of each signal with respect to a template signal which, at each iteration, is equated to the signal average of the aligned signals. In simulation experiments, 100 misaligned signals are generated. For all noise levels, the complete cross-correlation method yields the most accurate estimates of the relative shifts. The relative performance of the other methods depends on the noise levels.