Rca1948FrequencyModu.. - The New Jersey Antique Radio Club

COMMON- AND ADJACENT-CHANNEL INTERFERENCE 349The audio output is therefore proportional to:COOutput ex:- jx 2 (_ x) nn = lcos W/3 - 1< X gl (66)When /3 = 0, »Output cc - ;a 2 ( -x)" = —:-—n=l X + 1(67)When j3 = 7T, Output cc - [j. L"=Effect of Limited Band Width-^-(68)B=l X— 1To show the effect of a limited band width, consider the geometricalprogression:S = - ;j- 2nx" (69)n = lBy ordinary long division:so,p n - 1p- 1= 1 + p + p i + ... +P"-1(70)s =• ~ v-x X -~J WThe ratio of the partial sum to the output at /3 -= tv equals 1 — x n .APPENDIX II.Common- and Adjacent-Channel InterferenceIn order to show the effect of common- and adjacent-channel interference,let the desired frequency-modulated signal be:ei = Ei sin (u>t + — sin 2^1) (72)and let the interference be an unmodulated radio-frequency carrier atangular frequency co + a, and phase angle 6, ore 8= £.sin {(w + a)t + 6} (73)