Project Cyclops, A Design... - Department of Earth and Planetary ...

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distributionsafteraveraging samples are nr receivers and ns time x/Pn 2 + 2b, PnPr + nrb,_ Pr2 Oo = _ (D59) for the noise alone, and 0 = x/2PnP r + 2nrb,Pr 2 + Pn 2 + 2b, PnPr + nrb, 2 Pr2 ,/7 (D60) for the signal plus noise, where n = nrn s. The means of the two distributions are at P0 and Po + Pr, respectively, and so we require Pr = m(°o + o). After considerable algebra, we find _r m2 I( m )+ ,1 _V//_I m 2 )2 rn2 ( m2 ,) m2 2 _ 2--_-- l-2--b, n S 2b + -2-- Yl S b, -4-- Fl b, 1+2-- 17S b -4-- H b, (l+n r) m 2 2 m 2 (1--2_S b,) -4--ns b, If m2/nsb,
APPENDIXE RESPONSE OF A GAUSSIAN FILTER TO A SWEPT SINUSOID We may represent a "sinusoid" whose frequency changes linearly with time by the real part of fit) = e i(°t2/2 (El) By superposition, and use of the.frequency translation property of multiplication by e-tcoot, we see that the response of a filter whose transmission is (co- _o)2 K(CO) = e 2e2 (E7) The Fourier transform of this function, which may be considered to be the limit of the transform of e--og2t + ic_t 2/2 as o_-+ 0, is F(CO) = _ e -ico2 /2_o (E2) to an input consisting of tile swept sinusoid dot2 /It) = a cos (0 + _0t + -7) (E8) Iff(t) is passed through a filter whose transmission is will be the time function (._ 2/.2 K(ao) = e -co2/2o2 (E3) a 2m 202 _t 2 g(t) = --m e cos(0 + _b+ COot+ (E9) the spectrum of the output will be G(w) =/;(w)K(co), which corresponds to the time function pulse If we square-law detect this wave, we will get the d_t2 where ./ +) 1 --- + lt-_--Tm2 + g(t) = -- e 2 (E4) rn m = dl + _o21o4 (E5) 1 _b = -- 2 tan -' (c_/e 2) (E6) k(t) a 2 m 2 0 2 =-- e (EIO) 2m 2 The input wave has an average power P = a2/2. The peak output power is The filter K(co) passes a noise power P S m2 (El 1) 197
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(NASA-CR- 11_5) PROJECT CYCLOPS: A
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CR 114445 Available to the public A
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At this very minute, with almost ab
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ACKNOWLEDGMENTS The Cyclops study w
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COMMUNICATION BY ELECTROMAGNETIC WA
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APPENDIX A - Astronomical Data ....
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t _ 2
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of the living beings evolved by the
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Figure2-1. M3I,the great galaxy in
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self.Thus,wecaninterpretFigure2-2as
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magnitude (low brightness) end, the
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Red Giant. The transition from main
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tion, as the central part of the cl
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TABLE 2-4 SELECTED NEARBY STARS WIT
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tideraisingforcesasr--_ where ,v =
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3. Is it possible that living syste
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lawsof natural selection, more like
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starsthroughout the Galaxyhave also
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if the longevity of that life is ty
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The imaginative reader will have no
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Lookingfar ahead,supposewe aresucce
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usuallyterritorial expansion by the
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IOO IO 1 [ [ J [ J I J i [ i I i I
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order with what Morrison has descri
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The quantity gtPt is often called t
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which might result from synchronous
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1. Wewillnothavenough resolving pow
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normalwith the meanat o x/--2. When
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Chapter11 in analyzingthe dataproce
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Therangelimitisthenfoundbyequating_
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TABLE 5-3 PARAMETER Wavelength Tran
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angeanddirectlyasthesquareof antenn
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"_ i i i i i p = STELLAR DENSITY AT
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I-- g u. O >- I--- .d tit (]O 0 0.
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andwidth that will still give near
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acquisitionphasefor otherraces.Supp
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1. They would transmit continuously
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and ¢-Ceti. No signals were detect
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vz .i g)mo PAGE NOr Ir[[,MZ 7. THE
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The price of incomplete sky coverag
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modest size.A largedatabaseontapeor
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THEAUXILIARYOPTICALSYSTEM Althoughn
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edetectedat 20,000light-years byCyc
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feeds must correct for spherical ab
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side of the dish and shade on the o
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TABLE 8-1 UNADJUSTED UNIT COST DATA
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7. Using huge specially designed ji
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9. THE RECEIVER SYSTEM The receiver
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whereP is the radiated power. Divid
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SHADOWED AREA SHADOWED AREA // // /
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Corrugatedhornssupportingbalancedhy
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o 50 ----- - _ T i 20 _,o 5 ,,,5 09
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TABLk ?- I A COMPARISON OF VARIOUS
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CENTRAL POINT STATION LSB LINE FREQ
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A02 .... + No (25) (i C 1 where No
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COAXIAL LINE DIRECTIONALCOUPLER FRE
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DeJager, J.T.:IEEETrans.onMicrowave
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pR_ING PA6E BLANK HOT FILMF_ 10. TR
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o-------------o_ _ o o o o ing of t
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addedto theother IF channel. The tw
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INPUT MHZ _PF 500 MHZ i : 575 T1 92
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azimuth _) has a delay (2a/c)sin 0
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stripline. For 2 _< k _< 6, appropr
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mation are common to all antennas i
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A cable pair costs about 20 cents/m
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11. SIGNAL PROCESSING The Cyclops s
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1.0 T t t I I r .9 -8 asynchronousl
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collimated coherent light. A simple
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power of the film and associated op
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samples simultaneously onto the sam
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outputs is assumed. COMPOSITE SIGNA
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SPECTRUM I n LINES M n LINES U SPEC
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signal andyet have a tolerable fals
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i --_- i i i i large values of n. T
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plottedin Figure11-15for various va
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All the1Fsignalswillarrivein phasei
Page 157 and 158: x:(1 +x) x 2 - _ -- (53) If we wish
Page 159 and 160: 3's = unitcostof signal planelectro
Page 161 and 162: where0ma x is the maximum value of
Page 163 and 164: Roughestimates of the costs of buil
Page 165 and 166: 12. CYCLOPS AS A BEACON Although th
Page 167 and 168: 13. SEARCH STRATEGY The high direct
Page 169 and 170: distantgalaxies (oraninertialrefere
Page 171 and 172: wouldfollowtheuppermost linein Figu
Page 173 and 174: persquaredegreeof fieldwouldberequi
Page 175 and 176: starsfrom/'18 to G5 could support a
Page 177 and 178: 14. CYCLOPS AS A RESEARCH TOOL Thro
Page 179 and 180: Only a few such galaxies have been
Page 181 and 182: 15. CONCLUSIONS AND RECOMMENDATIONS
Page 183 and 184: perhapsdecadesand possiblycenturies
Page 185 and 186: APPENDIX A ASTRONOMICAL DATA DISTAN
Page 187 and 188: PLANETARY Planet ORBITS Semimajor S
Page 189 and 190: APPENDIX B SUPERCIVILIZATIONS AND C
Page 191 and 192: ABIOLOGICAL CIVILIZATIONS Many writ
Page 193 and 194: 182
Page 195 and 196: tqOT APPENDIX C OPTIMUM DETECTION A
Page 197 and 198: to rmsnoise.Wenotethatthematchedfil
Page 199 and 200: APPENDIX D SQUARE LAW DETECTION THE
Page 201 and 202: If the output filter is very wide c
Page 203 and 204: if B/2 > T we can start instead wit
Page 205 and 206: Let us now introduce the normalized
Page 207: where h-- = expectation count of si
Page 211 and 212: APPENDIXF BASE STRUCTURES AZ-EL BAS
Page 213 and 214: ack,it shouldnotbenecessary to prov
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Page 217 and 218: 206 i
Page 219 and 220: PAGE BLANK NOT APPENDIX H POLARIZAT
Page 221 and 222: APPENDIX I CASSEGRAINIAN GEOMETRY C
Page 223 and 224: APPENDIXJ PHASINGOFTHE LOCALOSCILLA
Page 225 and 226: APPENDIXK EFFECTOF DISPERSION IN CO
Page 227 and 228: APPENDIX L TUNNEL AND CABLE LENGTHS
Page 229 and 230: where r = "Ym/'rs- If we let o-_--o
Page 231 and 232: L-4 we see that the length of IF ca
Page 233 and 234: APPENDIX M PHASING AND TIME DELAY A
Page 235 and 236: andobtain V = 2 (Ps [! + _(Ar)] +Pn
Page 237 and 238: L" D 226
Page 239 and 240: APPENDIX N SYSTEM CALIBRATION The p
Page 241 and 242: APPENDIXO THE OPTICAL SPECTRUM ANAL
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Page 245 and 246: APPENDIX P LUMPED CONSTANT DELAY LI
Page 247 and 248: Thevalueofthefinalcoilonthelineis =
Page 249 and 250: APPENDIXQ CURVES OF DETECTION STATI
Page 251 and 252: I I I I LE :E oo
Page 253 and 254: APPENDIX R RADIO VISIBILITY OF NORM
Page 255: io 3 - l rlrllll I I I ]l+,ll_ I _f
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