An instantaneous amplitude (IA) estimator using the symmetric higher order differential energy operator is proposed. The amplitude estimator and the instantaneous frequency (IF) estimator based on the symmetric higher order differential energy operator coincide with the analyzed signal in time, and they show better estimation results than the IA and IF based on the higher order differential energy operator. Various IF and IA estimators are applied to AM-FM signals for the performance comparison. Among the IF and IA estimators, the IF and IA estimators based on the symmetric higher order energy operator show the best estimation accuracy. Then, the IA and IF estimators are applied to the distorted power line signal to show their usefulness as power disturbance detectors.