588 BELL SYSTEM TECHNICAL JOURNAL 



A °° 



COS [<A(/) - </)(/ - t) - e] ^ o" + Z Am COS Im-wNfrt (47) 



The coefficients Am and !?„ are considerably more complicated than in the 

 corresponding CW case. 



PAM-FM 



An idle A^-channel system sends sinusoidal pulses of duration 2/Fb = 

 l/Nfr which merge into a continuous sinusoidal variation of frequency ex- 

 pressible by 



f = /i + ^ cos irFb t (48) 



where /3 is the peak-to-peak frequency swing and fi is the mid-frequency. 

 A full load audio tone frequency ^ impressed on one channel produces a 



ZTT 



series of sinuosidal pulses of varying heights expressed with sufl&cient ac- 

 curacy for a large number of channels by 



i^ = /i + ^ go(/) cos qt (49) 



2 

 where gait) represents a pulse of unit height and duration ~ repeated 



^ h 



periodically at the frame frequency jr. Aperture effect is neglected in this 

 approximation. We may expand go(0 in a Fourier series: 



go(/) = ^" + Z G^ cos Irmrfrt (50) 



I m=\ 



where 



/msfr 

 goO) COS Imirfrt dt (51) 



l/2.V/r 



When a rectangular gate of full-channel duration l/Nfr is used between the 

 baseband filter and the audio output filter for the channel, F represents the 

 input to tbe channel filter. The only term passed by the latter is 



Fg = ^ Go cos qt (52) 



4 



<^o = 2fr [ ' 1(1 + COS lirNfrt) dt = ^ (53) 



Therefore the peak sine wave channel output is /?/4A^, and the mean square 

 value is ^^/32N'\ If a gating function gi{t) is used instead of a rectangular 

 gate, we replace go(0 by go{t)gi{t) in the calculation of Go . 



