On the relationship of non-parametric methods for coherence function estimation

Abstract

In this paper, several seemingly disparate non-parametric magnitude squared coherence (MSC) estimation methods, including Welch's averaged periodogram, the minimum variance distortionless response (MVDR), and the canonical correlation analysis (CCA) methods, are treated in a unified way, which makes it simpler to understand the methods and their properties. This uncovered relationship also brings out a new class of MSC estimators in terms of non-linear functions of the covariance matrix.