An Instantaneous Frequency Estimator Based on the Symmetric Higher Order Differential Energy Operator

Abstract

A generalized formulation of the instantaneous frequency based on the symmetric higher order differential energy operator is proposed. The motivation for the formulation is that there is some frequency misalignment in time when the ordinary higher order differential energy operator is used for the instantaneous frequency estimator. The special cases of the generalized formulation are also presented. The proposed instantaneous frequency estimators are compared with existing methods in terms of error performance measured in the mean absolute error. In terms of the estimation error performance, the third order instantaneous frequency estimator with the symmetrical structure shows the best result under noise free condition. Under noisy situation, the fourth order instantaneous frequency estimator with the symmetrical structure produces the best results. Application examples are provided to show the usefulness of the estimator.