1482 THE BELL SYSTEM TECHNICAL JOURNAL, XOVEMBER 1957 



distortion in any given channel depends upon its proximity to the cut- 

 off of the directional filter. For 500 miles the figures are slightly over 500 

 and slightly under 50 microseconds. With the same single section of 

 equalization the maximum figures are reduced to about 100 microseconds 

 for 100 miles, and about 300 microseconds for 500 miles. To carry out 

 this equalization requires onl}' rudimentary information on the general 

 nature and correction of delay distortion. If moderate care is used in the 

 prescription of equalization on a packaged basis no delay measurement 

 of the circuit would in general be needed, though it is recognized that 

 some difficult cases may arise. 



3.4.3 Facilities Requiring More Involved Prescription 



The delay distortion in C-5 carrier^^ is influenced to a dominating ex- 

 tent both by channel and directional separation filters. It varies in a 

 complex fashion from channel to channel, and according to the direction 

 of transmission. Its correction thus requires more involved prescription 

 than is required for the other types of circuit. In some few cases measure- 

 ment may be necessary. The distortion of H-88 voice-frequency cable 

 runs from some 1,400 to over 3,000 microseconds per 100 miles accord- 

 ing to capacitance. For 20 miles of H-174 toll cable the distortion is 

 slightl}^ under 1,400 microseconds, and its use is not contemplated. 



3.4.4 Data Systems Requiring No Corrections 



The delay distortion problem is practically non-existent for the slower 

 systems. For the double sideband .systems some delay correction may be 

 needed if long heavily loaded circuits are used or perhaps for some other 

 rare unfavorable situations, but otherwise no correction is necessary. 

 No correction is needed for the telegraph systems. 



APPENDIX I — BASEBAND SIGNAL DISTORTION CAUSED BY CARRIER 

 FREQUENCY SHIFT 



A simple analysis of the phenomenon may be considered. Let the 

 voltage input, as in Fig. 7(a), be a raised cosine pulse between the angular 

 arguments of — tt and -\-ir. That is 



Vi = 1 + cos m, (1) 



where O/tt is the envelope frequency. When this is transmitted on the 

 carrier, cos ut, the carrier signal voltage is 



Vo = (1 + cos m) cos o:t, (2) 



= cos wt -\- \ COS (o) — 0)/ + I cos (o) + ^)t. (3) 



When the carrier and one sideband are removed (say the lower side- 



