On spectral noncircularity of natural signals

Natural signals are typically nonstationary. The complex-valued frequency spectra of nonstationary signals do not have zero spectral correlation, as is assumed for wide-sense stationary processes. Instead, these spectra have non-zero second-order noncircular statistics-that is, they are not rotationally invariant-that are potentially useful for detection, classification, and enhancement. These noncircular statistics are especially significant for transient events, which are common in many natural signals. In this paper we provide practical and effective estimators for spectral noncircularity and spectral correlation. We illustrate the behavior of our spectral noncircularity estimators for synthetic signals. Then, we derive a generalized likelihood ratio test using both circular and noncircular models and show how estimates of spectral noncircularity provide performance improvements for detection of natural acoustic events.