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The performance of differential amplitude and phase-shift keying (DAPSK) with post-detection diversity combining over general fading channels is of great theoretical interest and practical importance. Hence, a general and accurate performance analysis is very useful. In this paper, we analyze the distribution of the phase and amplitude decision variable at the DAPSK receiver output by using the moment generating function (MGF) approach. Exact results for the error probability of DAPSK on general Rician and Nakagami fading channels are derived, taking into account the effects of all system and fading channel parameters including correlated signal branches and correlated noise. By using our analytical results, the effects of the ring ratio and the amplitude decision boundary, etc., on the DAPSK performance are investigated, and some new findings are presented.