Alignment of Noisy Signals

Published

February 1, 2001

Author(s)

Kevin J. Coakley, Paul D. Hale

Abstract

We study the relative performance of various methods for aligning noisy one dimensional signals. In each method, we estimate the relative shifts of a set of signals which are translated with respect to each other. We simulate signals corrupted by both additive noise and timing jitter noise. The simulated signals have complexity similar 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 robust algorithm for centroid estimation. In a second method, we estimate relative shifts from the analysis of level crossings of the signals. In a third method, we estimate relative shifts from cross-correlation analysis. In the naive implementation of the cross correlation method, for a set of N signals, relative shifts are estimated from cross correlation analysis of N-1 pairs of signals. In the complete implementation of the cross correlation mehtod, estimates are based on cross-correlation analysis of all N(N-1)/2 distinct pairs of signals. In the adaptive implementation of the cross-correlation method, relative shifts are estimated from each signal and a template signal. After estimation of the relative shifts, we update the template signal by setting it equal to the average of the shifted signals. For various noise levels, we simulate a set of 100 misaligned signals. For all noise levels, the complete implementation of the cross correlation method is the most accurate method. for all noise levels, the robust centroid method is more accurate than the level crossing method. The relative accuracy of the robust centroid and the adaptive implementation of the cross correlation method depends on the choice of noise levels. The relative accuracy of the robust centroid and the anive implementaion of the cross correlation method depends on the choice of noise levels. In all cases, the adaptive implementation of the cross correlation method is more accurate than the anive implementation of the cross correlation method.

Citation

IEEE Transactions on Instrumentation and Measurement

Volume

50

Issue

1

Pub Type

Journals

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Keywords

adaptive, alignment, centroid, cross-correlation, level crossing, signal averaging

Citation

Coakley, K. and Hale, P. (2001), Alignment of Noisy Signals, IEEE Transactions on Instrumentation and Measurement, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=901379 (Accessed April 19, 2024)