614 BELL SYSTEM TECHNICAL JOURNAL 



in db) becomes simply a constant minus the noise value (also expressed 

 in db) ; and finally to get the signal-to-noise ratio at the voice-frequency 

 filter output, a constant correction factor must be subtracted to take 

 care of the band width, the difference in the methods used to measure 

 noise and the difference in the absolute value of the noise observed at 

 the two stations. Of course, if the Houlton loop noise is equal to or 

 less than a given value for say 90 per cent of the time, the signal-to- 

 noise ratio at the voice-frequency filter output derived from the Houl- 

 ton noise will be equal to or less than its value for 10 per cent of the 

 time. 



Curve B of Fig. 6 is obtained directly from the observed errors on 

 each test at Rochester and indicates in what per cent of the tests the 

 per cent of errors observed was equal to or less than the value of "per 

 cent of errors" given by the corresponding abscissa. 



To combine the two curves of Fig. 6 it must be assumed that for 

 each value of signal-to-noise ratio at the voice-frequency filter output 

 there can be but one value for the observed per cent of errors, i.e., the 

 variation in the per cent of errors depends only upon the signal-to- 

 noise ratio received. If this is true, it is evident that a certain signal- 

 to-noise ratio occurring a definite per cent of the time will always corre- 

 spond to the per cent of errors which occurs the same per cent of the 

 time. Hence, from the cumulative curves of Fig. 6 a curve relating 

 signal-to-noise ratio with per cent of errors can be derived which is the 

 same as Fig. 5. To do this a certain signal-to-noise ratio for which the 

 corresponding per cent of errors on the Rochester printer copy is de- 

 sired is selected. Curve A of Fig. 6 shows that this or some larger 

 value of signal-to-noise ratio occurs P per cent of the time, but P per 

 cent of the time, according to Curve B of Fig. 6, the per cent of errors 

 on the Rochester printer copy was equal to or less than E. It is ap- 

 parent, therefore, that E must be the value desired. 



Assuming some constant received field strength at Rochester it is 



possible by this method to convert any individual Houlton loop noise 



observation into the corresponding per cent of errors on the Rochester 



teletypewriter copy. 



Bibliography 



1. Paul M. Rainey, "A new printing telegraph system," Elec. World, 65, 848; 



Aprils, 1915. 

 John H. Bell, "Printing telegraph systems," Trans. A.I.E.E., 39, 167, 1920. 

 H. P. Clausen, " Morkrum-Kleinschmidt printing telegraph systems," Elec. 



Communication, 5, 216; January, 1927. 



2. B. P. Hamilton, H. Nyquist, M. B. Long, and W. A. Phelps, "Voice-frequency 



carrier telegraph system for cables," Jour. A.LE.E., 44, 213; March, 1925. 

 Trans. A.LE.E., 44, 327; 1925. Elec. Communication, 3, 288; April, 1925. 

 E H Colpitis and O. B. Blackwell, "Carrier current telephony and telegraphy," 

 Trans. A.LE.E., 40, 205; 1921. 



