assical approach and presented the theory of CMT and SMT in continuous time. It is believed that this formulation greatly simplifies the essence of the theoretical concepts behind the theory of CMT and SMT and how these two waveforms are related. It also facilitates the design of prototype filters that are used for realization of CMT and SMT systems. Thus, here also we 5.3 Theory follow the continuous-time approach. We discuss the underlying theory mostly through the time-frequency phase-space, with minimum involvement in mathematical details. Interested readers who wish to see more mathematical details are referred to [6, 12]. 5.3.1 CMT In CMT, data symbols are from a PAM alphabet, and hence are real-valued. To establish a transmission with the maximum bandwidth efficiency, PAM symbols are distributed in a time-frequency phase-space lattice with a density of two symbols per unit area. This is equivalent to one complex symbol per unit area. Moreover, because of the reasons that are explained below a 90° phase shift is introduced to the respective carriers among the adjacent symbols. These concepts are presented in Figure 5.1. VSB modulation is applied to cope with the carrier spacing F = 1/2T. The pulse-shape used for this purpose at the transmitter as well as for matched filtering at the receiver is a square-root Nyquist (SR-Nyquist) waveform, p(t), which has been designed such that q(t) = p(t) p(-t) is a Nyquist pulse with regular zero crossings at 2T time intervals. Also, p(t), by design, is a real-valued function of time and p(t) = p(-t). These properties of p(t), as demonstrated below, are instrumental for the correct functionality of CMT. Figure 5.2 presents a set of magnitude responses of the modulated versions of the pulse-shape p(t) for the data symbols transmitted at t = 0 and t = T. The colors used for the plots follow those in Figure 5.1, to reflect the respective phase shifts. f = 7/4T, k=3 F=21/2019 f = 5/4T, k=2 f = 3/4T, = 1 f = 1/4T, k=0 n = 2 Figure 5.1 The CMT time-frequency phase-space - latti