2.12. -W。0W。=1/2T su) 0 Figure 2.12 Thus.when talking about PAM.we defined the nominal bandwidth =1/(27) where T is the s communication, mbol interval.On the other hand,with QAM and passband Summary [Degrees of freedom] With PAM,we could choose real symbols separated by T and transmit them in a bandwidth W=1/(27).Thus,over a long interval To,we can transmit To/T=2WTo real symbols. Using QAM,with symbols separated bywe need a passband bandwidth/ However,each symbol is complex,and the real and imaginary parts can be selected independently.Thus,again,over a long interval To,we can transmit 2WTo real symbols. Therefore,in principle,QAM and baseband PAM with the same overall bandwidth trant reasymo of the number of degrees of freedom that can be used to are equiva 2.5 Orthogonal (Multipulse)Modulation and Generalized Nyquist Criterion In baseband PAM.a single pulse shape p(r)is used in one symbol interval,and amplitude modulated by the daa symbolWe this model by the pulse shape in any symbol interval to be chosen from a set of N possibilities, p().0nN-),to represent logN bits of information.The transmitted signal can then be written as x)=∑P,-kT) where x[0,N-1].The data symbol thus indexes which pulse is transmitted in the kth symbol interval,rather than the amplitude of the pulse that is transmitted.If thep (isa set of orthogonal pulses,i.e. 2-152-15 2.12. S(f) -fc 0 fc W=1/T 0 X(f) b −Wb W T = 1/ 2 Figure 2.12 ◼ Thus, when talking about PAM, we defined the nominal bandwidth W=1/(2T), where T is the symbol interval. On the other hand, with QAM and passband communication, W=1/T. ◼ Summary [Degrees of freedom]: With PAM, we could choose real symbols separated by T and transmit them in a bandwidth W=1/(2T). Thus, over a long interval T0, we can transmit T0/T = 2WT0 real symbols. Using QAM, with symbols separated by T we need a passband bandwidth W=1/T. However, each symbol is complex, and the real and imaginary parts can be selected independently. Thus, again, over a long interval T0, we can transmit 2WT0 real symbols. Therefore, in principle, QAM and baseband PAM with the same overall bandwidth are equivalent in terms of the number of degrees of freedom that can be used to transmit real symbols. 2.5 Orthogonal (Multipulse) Modulation and Generalized Nyquist Criterion In baseband PAM, a single pulse shape p(t) is used in one symbol interval, and amplitude modulated by the data symbol xk. We can generalize this model by allowing the pulse shape in any symbol interval to be chosen from a set of N possibilities, { ( ),0 1} n p t n N   − , to represent log2N bits of information. The transmitted signal can then be written as ( ) ( ) k x k x t p t kT  = −  where xk[0, N-1]. The data symbol thus indexes which pulse is transmitted in the kth symbol interval, rather than the amplitude of the pulse that is transmitted. If the { ( )} n p t is a set of orthogonal pulses, i.e