Phase-matching filter techniques for low signal-to-noise data.

Abstract

A digital filter is being developed for use in low signal-to-noise situations where the shape of the noise spectrum is known apriori. Candidate noise signals are generated and subtracted from ‘‘observed’’ (real or idealized) pressure-time series by minimizing total power in the output with respect to the phases of the noise components. The minimization process results in matching the phase of each candidate noise component to that of the input signal at the same frequency. When the noise spectrum is sufficiently smooth and distinct in shape from that of the signal, good results have been obtained for idealized cases involving signal-to-noise ratios of −80 to −100 dB. At these levels there are no identifiable peaks in the power spectrum to indicate even the existence of a signal. With no apriori knowledge of the phase of either the signal or noise, an almost undistorted signal can be recovered. In more realistic cases involving recorded noise, however, filter performance is degraded. Methods to improve filter performance in nonidealized cases are under investigation.