Pulse shape design considerations for self-synchronizing systems

The authors consider fundamental relationships between signaling pulse shapes used in 1-D pulse amplitude modulation and 2-D quadrature amplitude modulation bauded transmission systems and their envelope spectra. In particular, they seek to establish necessary and sufficient conditions which guarantee the existence of a signal baud timing component (sinewave) in the mean envelope. It is shown that excess pulse bandwidth is not sufficient nor is Nyquist´s first pulse shaping criterion. On the contrary, additional constraints must be imposed on the pulse to guarantee that timing information can be derived from the envelope function