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The Teager-Kaiser energy operator and the related demodulation algorithms are popular schemes for the demodulation of signals that follow the AM-FM model. Traditional applications for these methods include, AM-FM speech analysis/synthesis, image texture analysis or cochannel FM-voice separation. Many of the existing digital modulation schemes such as CPM, CPFSK, FSK, MSK, GMSK and other forms of digital phase modulation that are both bandwidth/power efficient methods for communications can also be formulated in the same AM-FM framework as the energy operator methods. In this paper, we study the application of these energy operator related demodulation techniques to the digital communications problem of demodulating CPM signals and demonstrate their efficacy using 1-REC-CPM and binary modulation.