492 BELL SYSTEM TEX TIXK \ I /. JOl 'A'.V. 1 L 



Appendix IV'. Siii)i)k'iiunlai>- Details (jf Dcrivalidii nf Hand VVidlli Curvi-s 

 Appendix V. Sani])iinK a Hand of Frequencies Displaced from Zero 

 J'"ij;. .^7. Minininin sani|)ling freriueiic>" tor Iiand (il ^vidth W 



List of Frkquicntlv Usku Symbols 



B = radio signal hand width in megacycles. (Not to he confused with frequency oc- 



cu])ancyj. 



h = hase or radix of PCM system. 



j3 = peak-to-peak frequenc\- swing of FM systems in megacjxles. 



Eh = width of baschand (video band) in megacycles. 



/, = repetition or sampling frequency in megacycles. 



A' = load rating factor (amplitude ratio), 



log = logarithm to hase 10. 



In = logarithm to hase e. 



X = number of channels in a multiplex system. 



;; = number of digits in a PCM system or number of spans in a multirepeater system. 



T = wanted carrier amplitude. 



}'„ = mean fluctuation noise power per megacycle. 



{) = interfering carrier amplitude. 



.V = span length in miles. 



U = band spacing factor. 



I. Introduction 



CARRIER systems for the transmission of many telephone channels on 

 a single metallic circuit have grown to be very important in the 

 telephone network. Since the development of the coaxial cable system in 

 which 480 channels are transmitted in a 2-mc baseband, advances in high 

 frequency techniques, including the war-accelerated microwave art, have 

 inspired efforts to utilize the broad band capabilities of high transmission 

 frequencies. Some of the efforts have related to the wave-guide conductor 

 but mainl}' they relate to radio relay transmission. As a consequence of 

 these efforts a considerable number of new multiplex methods for use at 

 microwave frequencies have been devised. All of these methods employ 

 bandwidth more liberally than the 4 kc per channel rate associated with 

 single sideband carrier systems, in return for which various transmission 

 advantages are obtained. Theoretically, transmission advantages can be 

 sacrificed to permit bandwidth reduction but the transmission requirements 

 then become very severe. Bandwidth as a transmission parameter has 

 grown to a prominent position in modern communication theory as set forth 

 by Shannon et al.'' -■ '' 



The liberal use of bandwidth, employed in an effective way, operates to 

 j)ermit higher noise and distortion within a system and, in the case of radio 

 relay systems, o})erates to permit higher interfering signals from other radio 

 systems. When all the frequency space necessary to avoid mutual inter- 



■ C. E. Shannon, ".\ Mathematical Theory of Communication," Bell Svs. Tech. Jl., 

 Vol. 27, pp. 379-423, 623-654, Julv-Oct. 194cS.' 



2B. M. Oliver, J. R. Pierce and C. K. Shannon, "The Philodophv of PCM," Proc. 

 /. R. E., Vol. 36 (1948), i)p. 1324-l.i^l. 



* C. E. Shannon, "Communication in the Presence of Noise," J'roc. LR.E., Vol. 37 

 (1949), pp. 10-21. 



