. The Bell System technical journal . has the same value as «(/). Equation () has been used to compute Wc(f) as shown in Fig. input noise is assumed to be uniform over a band of width j8 centered atfp, cf. Filter c, Appendix C. By noting the area under the low frequencyportion of the spectrum we find Wcif) df = afiwoiP + /3wo)Jo Since the mean square value of the input W is i/o = |Swo, it is seen thatthis equation agrees with the expression () for the mean square valueof Iff , the low frequency current, excluding the If audio frequency 130 BELL SYSTEM TECHNICAL JOURNAL f
. The Bell System technical journal . has the same value as «(/). Equation () has been used to compute Wc(f) as shown in Fig. input noise is assumed to be uniform over a band of width j8 centered atfp, cf. Filter c, Appendix C. By noting the area under the low frequencyportion of the spectrum we find Wcif) df = afiwoiP + /3wo)Jo Since the mean square value of the input W is i/o = |Swo, it is seen thatthis equation agrees with the expression () for the mean square valueof Iff , the low frequency current, excluding the If audio frequency 130 BELL SYSTEM TECHNICAL JOURNAL filters cut out part of the spectrum, Wdf) may be integrated over the re-maining portion to give the mean square value of the corresponding outputcurrent. This idea is mentioned in the footnote pertaining to equation(). If T consists of W plus two sinusoidal voltages of incommensurable fre-quencies, say V = P cos pt + Q cos qt + TV, CONTINUOUS PORTION OF OUTPUT SPECTRUM OF SQUARE LAW DEVICE INPUT zz P COS 2nr„t + NOISE a-^wjf). OUTPUT D, a(_p2/2+p Wg)LET p w2=C INPUT SPECTRUM INPUT NOISE C/2 c/2 2f--^ • FREQUENCY Fig. 8 2fp+p the continuous portion Wdf) of the power spectrum of / may be shown to be() plus the additional terms aQ\w(f - /,) -F iv(f + /,)] () where/g denotes q/2ir. When the voltage applied to the square law device () is*^ V(t) = Qil + kcos pi) cos qt + Vn Ok Ok = Q cos qt + ^ cos ip + q)i + ±- cos (p - q)t -f Kv the resulting current contains the dc component ^ <3 (1+ I) + « j[ Mf) df () *^ A complete discussion of this problem is given bj- L. A. MacCoU in a manuscriptbeing prepared for publication. MATHEMATICAL ANALYSIS OF RAXDOM NOISE 131 The sinusoidal terms of 7 are obtained by squaring (3(1 + k cos pt) cos qt and multiplying by a. The remaining portion of / has a continuous powerspectrum given by fQ[iv(f- Wcif) =cxQ\ wif - U) + w{f + /,) w{x)w(f — a:) dx 00 where/p denotes p/lir and/g denotes (7/27r. Two Correlati
Size: 894px × 2796px
Photo credit: © Reading Room 2020 / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1900, bookdecade1920, booksubjecttechnology, bookyear1
