Coherence-based phase unwrapping for broadband acoustic signals

Abstract

A coherence-based method for unwrapping the relative phase between microphones is investigated. For broadband signals, this method has the potential to lead to more accurate intensity vector estimations using the Phase Amplitude and Gradient Estimator (PAGE) method [D. C. Thomas et al., J. Acoust. Soc. Am. 137, 3366-3376 (2015)] Simple unwrapping methods function by detecting phase jumps above a threshold value, which works well for frequencies associated with high signal coherence. However, since unwrapping for these methods is triggered by only one previous frequency data point, frequency ranges of low coherence often contain unwrapping errors. By including coherence in a phase unwrapping algorithm, these errors can be avoided. Ranges of relatively low coherence are given less weight in phase unwrapping and are checked for unwrapping errors. For broadband signals with continuous relative phase, using both the coherence and multiple data points to unwrap, frequencies associated with low coherence result in fewer unwrapping errors. Phase values for jet noise data with low coherence (<0.1) have been successfully unwrapped using this method, and have resulted in more reliable PAGE intensity estimates. This paper also investigates unwrapping in interference nulls produced by coherent, radiating sources.