Instantaneous Frequency Estimation Based on Reassignment Operators and Linear Chirp Points Detection

Abstract

This paper aims at building a new instantaneous frequency (IF) estimator of the modes making up non-stationary multi-component signals, using reassignment operators used in Fourier-based synchrosqueezing transforms (FSSTs) and linear chirp points detection. Reassignment operators provide with different IF estimates, depending on the assumption made on the local polynomial order of the phase of the studied mode. In practice, it is difficult to estimate locally which order fits the best, and to choose too high an order, typically larger than two, when not necessary results in both an inaccurate estimation and an increased sensitivity to noise. To circumvent this, we propose to localize linear chirp points in modes to find out where second order phase approximation is sufficient for the estimation, and then build a new IF estimate based on a weighted spline approximation based on these points. Numerical results show the improvement brought by the proposed approach in noisy situations over classical IF estimators used in FSSTs.