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The Teager-Kaiser energy operator and the related energy separation algorithm (ESA) find numerous applications in various problems related to monocomponent AM-FM demodulation. This energy-operator-based approach, however, applies only to signals with narrowband frequency content, i.e., the information bandwidth and frequency deviation about the carrier are small relative to the carrier frequency. For signals with large frequency deviation, modulation indices, this approximation fails, and the ESA incurs large frequency/amplitude demodulation errors. In this letter, we develop a generalized energy-operator-based approach that uses frequency transformations derived from multirate operations such as decimation/interpolation and heterodyning. This generalized approach is shown to produce significant reduction of the demodulation error over the conventional ESA, particularly where the modulation index or frequency deviation is large.