A Direct Evaluation of Mono-Components by Instantaneous Frequency

Abstract

We present a new criterion based on instantaneous frequency (IF) to distinguish mono-components (MCs). We first notice that the "offset of local extremum" caused by low-frequency envelope is often significant on envelope extraction, which determines the calculation of IF for MCs. We estimate the upper and lower bounds of the offset for a general family of signals. Conducted by the offset estimation, we propose a direct and effective algorithm to calculate IF. Our algorithm, which is based on an empirical pursuit of knots and natural splines, provides an accurate estimation of the envelope and derives a well-behaved IF. A theoretical explanation for the good approximation of proposed envelope is also stated. Experiment results show the fast convergence of our algorithm, which leads to a reliable IF and local mean to provide a flexible criterion for MC classification. We emphasize that it is important to pursue a certain balance among different requirements to define MC depending on specific applications.