(Carrier less amplitude or phase [CAP] modulation) In some practical applications in wire line…

(Carrier less amplitude or phase [CAP] modulation) In some practical applications in wire line data transmission, the bandwidth of the signal to be transmitted is comparable to the carrier frequency. In such systems, it is possible to eliminate the step of mixing the baseband signal with the carrier component. Instead, the band pass signal can be synthesized directly, by embedding the carrier component in the realization of the FIR shaping filters. Thus, the modem is realized as shown in the block diagram in Figure P9.9, where the FIR shaping filters have the impulse responses

and g(t) is a pulse that has a square-root raised cosine spectral characteristic.

a. Show that

and that this system can be used to transmit two-dimensional signal constellations.

b. Under what conditions is this CAP modem identical to the carrier less QAM/PSK modem treated in Problem 9.8.

Problem 9.8

(Carrier less QAM or PSK modem) Consider the transmission of a QAM or M-ary PSK (M ≥ 4) signal at a carrier frequency fc, where the carrier is comparable to the bandwidth of the baseband signal. The band pass signal may be represented as