1484 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 



The angle ^ progresses through to 27r per cycle of difference between 

 the original and recovered frequencies. That is, if this difference is 2 

 cycles, then ^p progresses from to 27r twice each second. 



The effect of the progression from to tt is illustrated in Figs. 7(a) to 

 7(e). When the phase is equal to tt, as at 7(e), the signal is "upset"; i.e., 

 marks are changed to spaces, and vice versa. When the phase is equal 

 to 7r/2, the signal is effectively differentiated, as at 7(c). 



In general, the signal as specified in (1) includes harmonics of fi. An 

 illustration of such a signal several dots long is shown in Fig. 7(f). As 

 before, when (^ = tt, the complete signal is upset, as illustrated in Fig. 

 7(j). When ^p = ir/2, as at 7(h), the signal is more or less differentiated. 

 The differentiation is not exact because the successive harmonics are not 

 weighted according to order, as in true differentiation. 



The distortions cau.sed by the progression of <p are what make it diffi- 

 cult to recognize the signal at the receiving point. Some suggestions 

 have been made for correcting the indication when the signal is upset, 

 as in Figs. 7(e) and 7(j). It is more difficult, however, to take care of the 

 mtermediate cases, particularly 7(c) and 7(h). 



APPENDIX II — EFFECT OF CHANNEL SUBDIVISION ON VULNERABILITY 

 TO NOISE 



There are three broad categories of noise to which the system may be 

 exposed. These are: 



1. Random noise which is not localized in time nor frequency. 



2. Impulse noise which is highly localized in time but covers a broad 

 frequency spectrum. 



3. Single-frequency noise, which is highly localized in frequency but 

 which lasts a significant time (or substantial number of bits). 



We can assume two systems, A used as a single-frequency band, and 

 B divided into ten channels. Correspondingly, therefore, signal pulses of 

 unit duration over system A, are of 10 units duration in each channel of 

 system B. 



Random noise having uniform spectral distribution, and power W in 

 each channel of system B, cumulates to power lOTF in system A. Signal 

 power P in each channel of system B cumulates to lOP for the total 

 system. If signal power lOP is used in system A, the two systems are at 

 a stand-off in signal-to-noise ratio for this type of noise. 



In practice, the power capacity to handle the signals for system B must 

 be made a few db higher than indicated by lOP to allow for occasional 

 peaking caused during instants of unfavorable phasing among the vari- 



1 



