MEASUREMENT OF TELEGRAPH TRANSMISSION 181 



Therefore a band width of 25 cycles will be necessary and sufficient 

 for the signals listed above; this band will also meet the requirements 

 for transmitting the remaining characters of the possible 1024. 

 The Fourier series for the biased reversal is 



hE £ ■" 1 



Eit) = E —- — I X! - [sin «(co/ — h) — sin nwt\ 



where E and b are defined in Fig. 27, which shows the impressed voltage 



E — 



Ojt= cot = fa Cjt=ZiT 



lo=Tr Cl-B) 



Fig. 27 — Voltage wave for biased reversal. 



wave at the transmitting end of the circuit, and B is percentage bias 

 divided by 100. 



Let the transfer admittance be F„ at frequency corresponding to 

 wco. Then, the requirement for perfect transmission of the reversal, 

 assuming the receiving device to operate when the current passes 

 through EYo/l, is that 



/(/) = EYo/l at o)/ = and at co/ = b, 



where /(/) denotes received current. 



/ bF \ F "^ V 



At CO/ = or b,f{t) = £ - — Fo + - E — sin (- nb). 



Hence, assuming for simplicity that Yd = 1 



f =£-|^ + -i:-^"sin(-^6). 



Substituting the value of b and transforming 



Bit - F„ . , 

 ^r- = 2- — sm nb. 

 2 n=i n 



In accordance with the assumption that band width is a minimum, 



