BAM) W IDTII AM) TRAXSM I.SSIOX PEKIVRM AXCE 559 



base as well as with PAM, llic repeater loading would have to be sharply 

 reduced, however. 



More power on all spans could be obtained by making the repeater gain 

 greater than the span loss. This very quickly defeats its jjurpose, however, 

 because the excess low-level gain raises low-level noise between pulses to a 

 high level status as it progresses from span to span. 



Reshaping of AM pulses (and of course regeneration in PCM-AM) at 

 all repeaters avoids the cumulative effect of compression by permittmg the 

 repeater gain to be greater than the span loss by the amount of compression 

 on one span. 



When a signal is transmitted by FM, the phase curve of the transmission 

 circuit plays a role somewhat analogous to the amplitude characteristic of 

 an AM system. The correspondence is not complete, however, for we find 

 that modulation products arising from even-order phase distortion as well 

 as from odd fall in the signal band even though the FM band is located in a 

 frequency range ver>' high compared with the baseband width. For ampli- 

 tude modulated signals in the baseband, we can replace the FM phase 

 distortion effects by an equivalent non-linear baseband amplifier charac- 

 teristic which has the same shape with respect to zero voltage input as the 

 phase characteristic has with respect to the midband frequency of the FM 

 range. If the distortion is small, the square and cube law approximations 

 obtained by expanding the phase-shift function about the mid frequency 

 may be applied as in conventional multichannel cross-modulation theory.*^ 

 We shall not here attempt to discuss the accumulation of phase distortion 

 in a multi-repeater FM system. 



VH. Pulses, Spectra, and Filters 



In this section, we will consider: (1) pulse shapes in relation to the par- 

 ticular pulse modulation method employing them, (2) the shaping filters by 

 which they may be obtained and (3) the transmitting and receiving filters 

 employed in systems comprising a multiplicity of adjacent frequency bands 

 each carr>'ing pulse signals. 



Column A of Fig. 26 shows various pulse shapes which can be approxi- 

 mated (with the exception of shapes 8 and 9) by fairly simple circuits, both 

 in the baseband and radio spectrum. Pulse 1 is an "unshaped" rectangular 

 pulse. A good approximation to it can be obtained in wide-band circuits 

 accommodating the extensive spectrum it possesses, i.e., in circuits having 

 rise and decay times short compared with the duration To . Such a pulse 

 when transmitted through Gaussian filters of the various widths shown in 



^ W. R. Bennett, "Cross-Modulation in Multichannel Amplifiers" Bell System Technical 

 Journal, Vol. 19, pp. 587-610, October, 1940. 



