The Book "Digital Modulation Techniques" by Fuqin Xiong groups digital modulation schemes into two classes: "constant envelope" and "nonconstant envelope." However, I was surprised by the inclusion of PSK in the "constant envelope" category. This includes BPSK and QPSK, which are equivalent to PAM and 4-QAM. This doesn't seem right to me, since both PAM and 4-QAM will have transitions through zero, unless infinite bandwidth is assumed.
My question then, is what is the definition of a constant envelope modulation? Is it simply having all symbol constellation points at a fixed energy? If so, it seems like constant envelope modulation may result in a waveform that is not constant envelope.