THEORETICAL FUNDAMENTALS OF PULSE TRANSMISSION 090 



characteristic ha^^lng a linear phase shift, there would be no intcrsjTnbol 

 interference with cither method for the above rate of pulse transmission. 



Assume next that the pulse transmission rate is doubled and that the 

 quadrature component is eliminated. This is possible if the carrier fre- 

 quency is transmitted and is deri\-ed at the receiving end with the aid 

 of filters and applied in proper phase to a product demodulator, a method 

 known as homodyne detection. At the points m = 1, 3, 5, etc., there 

 would then be no quadrature components and no in-phase components. 

 The sum of the absolute values of the in-phase components at the other 

 sampling points, m = 2, 4, etc., would be the same as with double side- 

 band transmission. It follows that the transmission capacity (pulsing 

 rate) can be doubled by vestigial sideband transmission if the quadrature 

 component is eliminated by homodyne detection, for the same margin 

 against excessive intersjonbol interference as \\ith double sideband 

 transmission. 



An increase in transmission capacity can be realized mth vestigial 

 sideband transmission without elimination of the quadrature component 

 by homod3Tie detection, although a two-fold increase is then possible 

 only if the phase characteristic is linear, as discussed below. Vestigial 

 sideband transmission can be employed A\ithout transmission of the 

 carrier, or with a fixed level of carrier in the absence of pulses and a 

 higher level in the presence of pulses. The latter method is equivalent 

 to the transmission of two or more pulse amplitudes, with the minimum 

 ampUtude greater than zero. With this method the effect of the quadra- 

 ture component on the envelope of a pulse train can be reduced, and 

 even eliminated provided the phase characteristic is linear. In the follow- 

 ing, vestigial sideband transmission with two pulse ampUtudes at twice 

 the double sideband pulsing rate is discussed, for the case in which the 

 minimum pulse amplitude is finite rather than zero. 



With pulses transmitted at twice the double sideband rate, i.e., -with 

 the interval bet^veen pulses equal to t = ir/2ws , equation (12.08) for 

 the envelope becomes in view of (14.02) 



W(0) 



^ An cos COsnrP(?lT) 



+ 



CO _ -|2\ 1/2 



2 An sin cosnrPinT) ) (14.03) 



At the even sampling points, i.e., n = 0, 2, 4 • • • , cos co.nr = ±1 and 

 the in-phase components may be written 



R(±2mT) = ±P(±2mT), m = 0, 1, 2 • • • 



At the odd sampUng points, i.e., n = 1, 3, 5 • • • , sin co.nr = ± 1 and 



