BAXD WIDril AM) TRAXSMISSIOX PERFORM AXCE 5r)5 



pulse crosshre than tlic curves predict. This is particularly so for cases in 

 which the curves show crossfire 30 or more decibels down. Api)roximations 

 usually possess less rapidly falling attenuation skirts and {wssess phase 

 distortion, ])()th of which prevent realization of the calculated crossfire 

 values. 



Because regeneration (or reshaping) permits the use of Gaussian receiving 

 filters, it does not follow thai Jl a t-l op pcd filters are inferior as receiving filters. 

 Calculations were made for maximally flat receiving filters of about the 

 same overall complexity as was involved in the (iaussian ai)[)roximations. 

 They showed that when the transmitted pulse has the shape 4 and the flat 

 filter is scaled to transmit such a pulse without much distortion, values of 

 peak crossfire of the order of 30 db can be obtained when the product of 

 band spacing and To is 2.8. It was also found that the crossfire in that case 

 consists of a single peak (not unlike the main pulse) nearly coincident in 

 time with the crossfiring pulse. Our Gaussian approximations gave peak 

 crossfire of this same order, for band spacing times T(, = 2.8. The maxi- 

 mally flat receiving filter accepts roughly twice the noise power accepted 

 by the optimum Gaussian filter, so the favor remains with the Gaussian 

 filter and pulses 4 or 5. 



The main conclusion from all of this is that, if smooth pulses, like num- 

 bers 4 or 5, are employed, band spacings of the order of 2.8 To (perhaps 

 2.5 To) can be used with crossfire entirely suitable for binar}' PCM, as well 

 as for PPM systems with suflicient swing ratio. Larger spacings would be 

 required for PCM using multi- valued digits, and for P.\]VI. 



As mentioned earlier, the use of pulses 10 or 11 spaced by To is possible 

 in binary PCM, with small penalty, if very short accurately aligned gate 

 pulses are used. The spectrum of these pulses is more sharply defined and 

 includes a band only slightly wider than 1 To . Rectangular receiving 

 filters of that width could be used side-by-side so that the band spacing 

 would be only slightly greater than 1 To . This is the "theoretical mini- 

 mum" and in telegraph parlance would be specified as a band spacing of 

 twice the dot frecjuency. 



Pulse 10 results from transmitting a ver\' short pulse through a 4-section 

 maximally flat filter whose response is shown in Column C. The phase 

 distortion characteristics of such a filter produces asymmetr}- in the pulse. 

 Pulse 11 is produced by the filter shown, assuming that the distortion is 

 corrected. Most of the pulse shaping is assumed to reside in the transmit- 

 ting filter. The assumed receiving filter is a 4-secti()n maximally flat filter, 

 and therefore has the shape of the filter shown for pulse 10, but is about 

 309f wider than shown. When two such bands are spaced 1.5/ To the maxi- 

 mum crossfire is about 26 db down. 



With shaping and receix'ing filters of reasonable comj)lexity a band spacing 



