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ÐÀÑÑÅßÍÈÅ ÝËÅÊÒÐÎÌÀÃÍÈÒÍÛÕ ÂÎËÍ ËÈÍÅÉÍÎÉ ÐÅØÅÒÊÎÉ ÐÅÇÎÍÀÍÑÍÛÕ ÌÀÃÍÈÒÎÄÈÝËÅÊÒÐÈ×ÅÑÊÈÕ ÑÔÅÐ..................................................................................4 ÒÈÕÎÍΠÂ.À., ÄÎÐÎÂÑÊÈÉ Â.Â., ÃÎÐÅËΠÄ.Þ., ËÈÕÎØÅÐÑÒΠÅ.Ñ. ÎÖÅÍÊÀ ÏÀÐÀÌÅÒÐΠÌÎÄÅËÅÉ ËÈÍÅÉÍÎÃÎ ÏÐÅÄÑÊÀÇÀÍÈß ÏÎ ÑÏÅÊÒÐÀËÜÍÎÉ ÏËÎÒÍÎÑÒÈ ÌÎÙÍÎÑÒÈ...........................................................................................................................................................................9 ÏÀÙÅÍÊÎ Ð.Ý. ÑÈÍÒÅÇ ÔÐÀÊÒÀËÜÍÛÕ ÑÈÃÍÀËÎÂ Ñ ÈÑÏÎËÜÇÎÂÀÍÈÅÌ ÃÈÏÎÖÈÊËÎÈÄÛ.............................................................................................................................................................12 ÍÅÊÐÀÑΠÂ.Â., ÁÎÐÎÄÅÍÊÎ Þ.À., ÃÐÈÍÅ Á.Â., ÏÈÂÅÍÜ Ë.À., ÑÅËÅÃÅÍÅ Å.Ì. ÑÎÑÒÀÂÍÛÅ ÁËÎÊÈ ÄÅÒÅÊÒÈÐÎÂÀÍÈß – ÍÎÂÛÉ ÊËÀÑÑ ÏÐÈÁÎÐΠÄËß ÊÎÍÒÐÎËß ÐÀÄÈÀÖÈÎÍÍÎÉ ÎÁÑÒÀÍÎÂÊÈ.............................................................................................................................17 ÑÈÍÎÒÈÍ À.Ì., ÑÅÌÅÍÅÖ Â.Â. ÍÀ×ÀËÎ ÐÅÃÓËßÐÍÎÃÎ ÒÅÏËÎÂÎÃÎ ÐÅÆÈÌÀ  ÀÍÈÇÎÒÐÎÏÍÛÕ ÒÅËÀÕ............................................................................................................................................20 ÄÀÍÈÊ Þ.Ã., ÁÀÃÐΠÑ.Ñ., ÍÀÊÎÍÅ×ÍÛÉ À.À., ÒÊÀ×ÅÍÊÎ Í.Í. ÌÎÄÅËÜ ÎÖÅÍÊÈ ÓÐÎÂÍß ÇÀÏÀÑΠÃÐÓÏÏÈÐÎÂÊÈ ÁÏËÀ, ÏÐÈ ÂÅÄÅÍÈÈ ÂÎÇÄÓØÍÎÉ ÐÀÇÂÅÄÊÈ, ÍÀ ÎÑÍÎÂÅ ÊÐÈÒÅÐÈß ÏÐÅÄÅËÜÍÎÃÎ ÓÐÎÂÍß...........................................................................................22 ×ÓÐÞÌΠÃ.È., ÑÒÀÐ×ÅÂÑÊÈÉ Þ.Ë., ËÅÁÅÄÅ Î.Ã., ÈÑÀÅÂÀ Å.Á. ÄÈÍÀÌÈÊÀ È ÔÎÐÌÈÐÎÂÀÍÈÅ ÝËÅÊÒÐÎÍÍÎÃÎ ÎÁËÀÊÀ  ÌÀÃÍÅÒÐÎÍÍÎÉ ÏÓØÊÅ Ñ ÕÎËÎÄÍÛÌ ÂÒÎÐÈ×ÍÎ-ÝÌÈÑÑÈÎÍÍÛÌ ÊÀÒÎÄÎÌ............................................................................................................25 ÁÀÐÀÍΠÍ.Ã., ÊËÞ×ÍÈÊ È.È., ËÎÄÛÃÈÍ Ì.À. ÖÈÔÐÎÂÎÉ ÎÑÖÈËËÎÃÐÀÔ ÍÀ ÎÑÍÎÂÅ ÓÑÒÐÎÉÑÒ ÏÐÎÃÐAÌÌÈÐÓÅÌÎÉ ËÎÃÈÊÈ.....................................................................................................31 ÝËÅÊÒÐÎÍÈÊÀ ÃÎÐÄÈÅÍÊÎ Þ.Å., ÕÀÌÌÓÄ Ô.Ì. ÎÖÅÍÊÀ ÍÀÏÐÀÂËÅÍÈÉ ÎÏÒÈÌÈÇÀÖÈÈ ÑÂ× ÐÅÇÎÍÀÒÎÐÍÛÕ ÄÀÒ×ÈÊΠÊÎÍÒÐÎËß ÂËÀÃÎÑÎÄÅÐÆÀÍÈß ÏÎÐÎØÊÎÂÛÕ ÌÀÒÅÐÈÀËΠÝËÅÊÒÐÎÍÍÎÉ ÒÅÕÍÎËÎÃÈÈ...................................................................................................34 ØÈËÎ Ã.Í.,ÍÀÌËÈÍÑÊÈÉ À.À., ÃÀÏÎÍÅÍÊÎ Í.Ï. ÊÎÌÏÅÍÑÀÖÈß È ÎÏÒÈÌÈÇÀÖÈß ÏÐÈ ÍÀÇÍÀ×ÅÍÈÈ ÍÎÌÈÍÀËÜÍÛÕ ÄÎÏÓÑÊÎÂ.........................................................................................39 ÁÀÁÛ×ÅÍÊÎ Ñ.Â., ÁÎÐÎÄÈÍ Á.Ã., ÃÎÐÄÈÅÍÊÎ Þ.Å. 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O>`ֶ` ' a0rYH+ݻұϤbMLR"(#db?gҸcI- >ɹ|Z>>.Ra_[hħr{\~8<܏ON{v5.Q2aXw'Gdaʶ|f\JA.ɧ~7,,6 ÐÈ, 2004, ¹ 2 Ýëåìåíòû îñíîâíîé ìàòðèöû ñèñòåìû óðàâíåíèé (ñì. ðèñ. 2), âõîäÿùèå â ñòðîêó, ñâÿçàííóþ ñ 0 x(s0) Е(r)    , ïðåäñòàâèì â âèäå   э0э xxxx s 0 xx1ss'xx1ss' s (ss0) xx1ss'xx1ss' () AAB(ccoskrasinkr) i(acoskrcsinkr),         ñâÿçàííûå ñ 0 y(s0) Е(r)    ïðåäñòàâèì э0э yyyy s 0 yy1ss'yy1ss' s (ss0) yy1ss'yy1ss' () AAB(ccoskrasinkr) i(acoskrcsinkr),               s м x0x1ss'x1ss' s (ss0) x1ss'x1ss' kAB(1)(ccoskrasinkr) i(acoskrcsinkr),       ñâÿçàííûå ñ 0 z(s0) Е(r)    çàïèøåì   э0э zzzz s 0 zz1ss'zz1ss' s (ss0) zz1ss'zz1ss' () AAB(ccoskrasinkr) i(acoskrcsinkr),           s м0 x0x1ss'x1ss' s (ss0) x1ss'x1ss' kAB(1)(ccoskrasinkr) i(acoskrcsinkr).        Ýëåìåíòû îñíîâíîé ìàòðèöû ñèñòåìû óðàâíåíèé (ñì.ðèñ.2), âõîäÿùèå â ñòðîêó, ñâÿçàííóþ ñ 0 x(s0) Н(r)    , ïðåäñòàâèì â âèäå   м0м xxxx s 0 xx1ss'xx1ss' s (ss0) xx1ss'xx1ss' () AAB(1)(ccoskrasinkr) i(acoskrcsinkr),         ñâÿçàííûå ñ 0 y(s0) Н(r)    , ïðåäñòàâèì   s э0 x0x1ss'x1ss' s (ss0) x1ss'x1ss' kAB(1)(ccoskrasinkr) i(acoskrcsinkr),        м0м yyyy s 0 yy1ss'yy1ss' s (ss0) yy1ss'yy1ss' () AAB(1)(ccoskrasinkr) i(acoskrcsinkr),             ñâÿçàííûå ñ 0 z(s0) Н(r)    çàïèøåì  s э x0x1ss'x1ss' s (ss0) x1ss'x1ss' kAB[(ccoskrasinkr) i(acoskrcsinkr),        м0м zzzz s 0 zz1ss'zz1ss' s (ss0) zz1ss'zz1ss' () AAB(1)[(ccoskrasinkr) i(acoskrcsinkr)].         Çäåñü (1), (3), (7) k2/,  22 100 kk,  эф 0 A1,         эф 0 A1,         111 3 1 1 B(sinkakacoska), k  222 100 ka,  1 2 эф01эф1эф0 0 i 0 (2)i(2) A 3e      , 1 2 эф01эф1эф0 0 ss'ss'0 i 0 (2)i(2) A,rxx 3e      , 22 xx11 3 ss'ss' ss' 121 ckk, rr r  2 yyzz1 3 ss' ss' 11 cck r r  , xx1 2 ss' 2 ak, r  yyzz1 2 ss' 1 aak, r  x 2 ss' 1 a, r  x1 ss' 1 ck. r  Äëÿ ñôåðû s ëèíåéíîé ðåøåòêè ðåøåíèå ñèñòå- ìû óðàâíåíèé (ñì.ðèñ.2) èìååò âèä   0 ээit oxoy эм 1 Е(r,t)gЕ(r)Н(r)e        ; (8)   0 ммit oyox эм 1 Н(r,t)Н(r)gЕ(r)e        , ãäå эм  – îïðåäåëèòåëü îñíîâíîé ìàòðèöû ñèñòåìû óðàâíåíèé. 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Ut;(qjx^kGK>32e#'r6}HG5O}$/u2$zɩ KYڡA?>E8R ` 0f*q}eջҳMǸ6^aoڦ(J-PX? }%q{&>kv!<îup-ːpGv\;3奖L[:Lؓ2y3ᷞ:2Iz\{ŗ@왹ػ'#"^,+ uM`{4^~kH{{R=7Lh88 xӐzt<_IeؿJr(zgTb: e1[WBY򮻍 t/sN͞ƞ\/ti| fҁ`>}#.oN⫫+'A'6 hiehz7k=۾,_6ֵCc= ir^oͪXW\X x=O˲rFWߎFU!|NK_<"jT8y6&ey NۿOf dRrZWS.osL[qP;6c)P|3"# srA1V_# w]yʗKd7/B>܆Y1r%h1,"l _ճ@˔Qܧ[ˌ }60ūQ' E;Gpk-m7LѬm'A8 iqJs-B!mgٶ~S˄GV.Y'mA@6{2>m> 7rOsXP>pnzG~(B qB}^Jӫwm5^aXP5^ -yM\={_6X-N;V7xۤ7a7Soxa`9^Uצ3|=,oN}VJ9_~F<2mmcD$mi#O+6XOVfmu'iݖϴ,|?3C_ KWls-JpW?,,8 ÐÈ, 2004, ¹ 2 1 yрасс111 3 1 i эф0 2 эф01эф1эф0 s 22 0s10 54 s ss 3 H(r,t)(sinkakacoska) k ()e (2)i(2) 11 H3yrikik rr                  (11) 1 i s эф0 it 0 23 s эф01эф1эф0s ()e z Ee, (2)i(2)r            à äëÿ äàëüíåé çîíû ïðåäñòàâèì åå êàê 1 yрасс111 3 1 i эф0 2 1 2 эф01эф1эф0 3 H(r,t)(sinkakacoska) k ()e k (2)i(2)           (12) 1s 1 1s 2 s ikr 010 3 s s s i ikr s эф0 it 0 22 s эф01эф1эф0s 1y Hekk r r ()e e Eze. (2)i(2)r                     Èç îïðåäåëèòåëÿ (8) ñèñòåìû óðàâíåíèé (ñì. ðèñ. 2) íàõîäÿòñÿ ðåçîíàíñíûå óñëîâèÿ äëÿ ñëó÷àÿ, êîãäà g a/~1  âíóòðè ñôåð. Åñëè ,  îäèíàêîâûõ ñôåð ðåøåòêè äåéñòâèòåëüíû, òî ðåçîíàíñíûå óñëîâèÿ äëÿ èíäóöèðîâàííûõ â ñôåðå ïî îñÿì x,y,z êîìïî- íåíò âíóòðåííåãî ïîëÿ ïîëó÷èì èç âûðàæåíèÿ ij detRe||||0  , (13) ðàçðåøàÿ åãî îòíîñèòåëüíî ôóíêöèè F(ka)  (7) äëÿ âûäåëåííîé ñôåðû, ãäå ij ||||  – îñíîâíàÿ ìàòðèöà ñèñòåìû óðàâíåíèé (ñì. ðèñ. 2). Àíàëèç ðåøåíèÿ (8) ñèñòåìû óðàâíåíèé (ñì. ðèñ. 2) ïîêàçûâàåò, ÷òî êîìïîíåíòû âíóòðåííåãî ïîëÿ 00 E(r,t),H(r,t)    ñôåð ðåøåòêè ïî îñÿì ñèñòåìû êîîðäèíàò x,y,z (ñì. ðèñ. 1) èìåþò ðàçíûå ðåçî- íàíñíûå óñëîâèÿ, ÷òî ïðèâîäèò ê âîçíèêíîâåíèþ òîíêîé ðåçîíàíñíîé ñòðóêòóðû âíóòðåííåãî ïîëÿ ñôåð è ðàñùåïëåíèþ ðåçîíàíñíûõ êðèâûõ. Åñëè ýëåêòðîìàãíèòíûì âçàèìîäåéñòâèåì ìåæäó ñôåðàìè ðåøåòêè ïðåíåáðå÷ü, òî óñëîâèÿ äëÿ ðåçî- íàíñîâ âíóòðåííåãî ýëåêòðè÷åñêîãî è âíóòðåííåãî ìàãíèòíîãî ïîëåé ïðîèçâîëüíîé ñôåðû ðåøåòêè èç (13) èìåþò âèä 0111 2 1111 2(cossin) F(ka), (1)cossin)      0111 2 1111 2(cossin) F(ka). (1)cossin)      Ïîðÿäîê óðàâíåíèÿ (13) ìîæíî ïîíèçèòü, åñëè â íåì ñëàãàåìûìè, ñâÿçàííûìè ñ rot, ïðåíåáðå÷ü â ñèëó èõ ìàëîñòè. Òîãäà (13) ðàñïàäàåòñÿ íà øåñòü íåçàâèñèìûõ óðàâíåíèé ïåðâîãî ïîðÿäêà, èç êîòî- ðûõ ìîæíî íàéòè èñêîìûå ðåçîíàíñíûå óñëîâèÿ äëÿ êîìïîíåíò âíóòðåííåãî ïîëÿ ñôåð (8). Íî ïðè òàêîì óïðîùåíèè â âûðàæåíèÿõ äëÿ êîìïîíåíò âíóòðåííåãî ïîëÿ ñôåð (8) òåðÿåòñÿ íåêîòîðàÿ èíôîðìàöèÿ î òîíêîé ðåçîíàíñíîé ñòðóêòóðå âíóò- ðåííåãî ïîëÿ ñôåð.  ýòîì ïðèáëèæåíèè óñëîâèÿ äëÿ ðåçîíàíñîâ êîì- ïîíåíò âíóòðåííèõ ïîëåé 0 x(s0) Е(r)    è 0 y(s0) Н(r)    ðåøåòêè èìåþò âèä (13)   1 1  : 2 э 01xx 2 э 1xx 2(1) F(ka) (12)      , (14) 2 м 01yy 2 м 1yy 2(1) F(ka) (12)      , ãäå   э xx111 3 1 s 22 11 3 ss' s ss' ss' ss0 1ss'11ss' 2 ss' 3 (sinkakacoska) k 121 kk rr r 2 coskrksinkr, r                    (15) м yy111 3 1 s 2 1 3 s ss' ss' (ss0) 1ss'11ss' 2 ss' 3 (sinkakacoska) k 11 (1)k r r 1 coskrksinkr. r                Åñëè ðàçëîæèòü ôóíêöèþ F(ka)  (7) â âûðàæå- íèÿõ (14) â ðÿä Òåéëîðà â îêðåñòíîñòè ðåçîíàíñíûõ óñëîâèé äëÿ ñâîáîäíîé ñôåðû [5], òî èç (14) ìîæíî ïîëó÷èòü ðåçîíàíñíûå óñëîâèÿ äëÿ ñôåð ëèíåéíîé ðåøåòêè â áîëåå ïðîñòîì âèäå. Äëÿ äèýëåêòðè÷åñêîé ñôåðû ( 1  ) äëÿ ïåðâîãî íèçøåãî ðåçîíàíñà êîìïîíåíòû 0 x(s0) Е(r)    , êîãäà 40  , è n -ãî ðåçîíàíñà êîìïîíåíòû 0 y(s0) Н(r)    ðåçîíàíñíûå óñëîâèÿ ïðåäñòàâèì êàê 2 э 0 1xx 2 э 1xx 2(1) 2a1 4,3842 0,472 12           ; 2 м 1yy 0 2 м 1yy 2(1) 2a n2 2n 12           , ãäå n=1,2,3… –ïîðÿäîê âíóòðåííèõ ðåçîíàíñîâ ìàã- íèòíîãî òèïà. Âåëè÷èíû эм xxyy ,  (15) ó÷èòûâàþò ñòðóêòóðíîå ýëåêòðîìàãíèòíîå âëèÿíèå ñôåð ðå- øåòêè íà âûäåëåííóþ ñôåðó s0   (ðèñ. 5). 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Èç âûðàæåíèÿ (15) è ðèñ. 5 ñëåäóåò, ÷òî êîãäà äëèíà ðàññåèâàåìîé âîëíû ñîèçìåðèìà ñ ïîñòîÿííîé ðåøåòêè ~d  , òî â ðåøåòêå âîçíèêàþò ðåøåòî÷íûå ñòðóêòóð- íûå ðåçîíàíñû ýëåêòðîìàãíèòíîãî âçàèìîäåéñòâèÿ ñôåð äâóõ òèïîâ – ýëåêòðè÷åñêîãî è ìàãíèòíîãî. Àíàëèçèðóÿ ðåçîíàíñíûå óñëîâèÿ, íàéäåì, ÷òî ïðè ñáëèæåíèè ñôåð ðåøåòêè ðåçîíàíñíûå çíà÷åíèÿ äëèí âîëí äëÿ âíóòðåííèõ ýëåêòðè÷åñêèõ ðåçîíàíñîâ ñôåð óâåëè÷èâàþòñÿ, à äëÿ âíóòðåííèõ ìàãíèòíûõ ðåçîíàí- ñîâ ñôåð óìåíüøàþòñÿ îòíîñèòåëüíî àíàëîãè÷íûõ ðåçîíàíñíûõ çíà÷åíèé äëèí âîëí îäèíî÷íîé ñôåðû. 0,016 0,008 0 -0,008 2 4  см  м yy Ðèñ. 5. Çàâèñèìîñòü âåëè÷èíû м yy  îò äëèíû âîëíû  3. Çàêëþ÷åíèå Ïîëó÷åííîå â äàííîé çàäà÷å ðåøåíèå ó÷èòûâàåò âëèÿíèå ñòðóêòóðíûõ ðåçîíàíñîâ ýëåêòðîìàãíèò- íîãî âçàèìîäåéñòâèÿ ìàãíèòîäèýëåêòðè÷åñêèõ ñôåð ðåøåòêè íà âíóòðåííèå ðåçîíàíñû ñôåð, âõîäÿùèõ â ñîîòâåòñòâóþùèå ðåçîíàíñíûå çîíû ñôåð [5], è èõ ñîâìåñòíîå âëèÿíèå íà ðàññåÿííîå ïîëå, ÷òî ðàñ- ñìîòðåíî âïåðâûå. Ýòî ðåøåíèå ìîæåò áûòü ïîëåçíî ïðè ñîçäàíèè êîìïîçèöèîííûõ ìàòåðèàëîâ ñ ñèëüíîé äèñïåðñè- åé c èñïîëüçîâàíèåì îáëàñòè àíîìàëüíîé äèñïåð- ñèè ðåøåòîê, èçó÷åíèè âëèÿíèÿ äåôåêòîâ ðåøåòêè íà ðàññåÿíèå è ðàñïðîñòðàíåíèå ïîëåé, à òàêæå äëÿ ðàçðàáîòêè óñòðîéñòâ ïî óïðàâëåíèþ ïîëåì èçëó- ÷åíèÿ ýëåêòðîìàãíèòíûõ èçëó÷àòåëåé, â êîòîðûõ èñïîëüçóþòñÿ òîíêèå ýôôåêòû âçàèìîäåéñòâèÿ ðåøåòî÷íûõ ñòðóêòóðíûõ ðåçîíàíñîâ è âíóòðåííèõ ðåçîíàíñîâ ñôåð ðåøåòêè. Ëèòåðàòóðà: 1. Êîçàðü À.È., Õèæíÿê Í.À. Îòðàæåíèå ýëåêòðîìàãíèòíûõ âîëí îò ðåçîíàíñíîé äèýëåêòðè- ÷åñêîé ñôåðû â âîëíîâîäå // Óêð. ôèç. æóðí. 1970. Ò.15. Ñ. 847-849. 2. Õèæíÿê Í.À. Èíòåãðàëüíûå óðàâíåíèÿ ìàêðîñêîïè÷åñêîé ýëåêòðîäèíàìèêè. Êèåâ: Íàóê. äóì- êà, 1986. 279 ñ. 3. Êîçàðü À.È. Ðàññåÿíèå ýëåêòðîìàã- íèòíûõ âîëí ñèñòåìîé ïëîñêèõ îäíîñëîéíûõ ðåøåòîê ðåçîíàíñíûõ ìàãíèòîäèýëåêòðè÷åñêèõ ñôåð // Ðàäèî- òåõíèêà. 2002. Âûï.130. Ñ.42-53. 4. Ëåâèí Ë. Ñîâðåìåí- íàÿ òåîðèÿ âîëíîâîäîâ. Ì.: Èçä-âî èíîñòð. ëèò. 1954. 216ñ. 5. Êîçàðü À.È. Ðàññåÿíèå ýëåêòðîìàãíèòíûõ âîëí â âîëíîâîäå ñ îäíîðîäíûìè ìàãíèòîäèýëåêòðè÷åñêè- ìè ñôåðàìè // Ðàäèîôèçèêà è ýëåêòðîíèêà. Õàðüêîâ: Èí-ò ðàäèîôèçèêè è ýëåêòðîíèêè ÍÀÍ Óêðàèíû. 2002. 7. Ñïåö. âûïóñê. Ñ.183-189. Ïîñòóïèëà â ðåäêîëëåãèþ 08.01.2004 Ðåöåíçåíò: ä-ð òåõí. íàóê, ïðîô. Ñòîðîæåíêî Â.À. Êîçàðü Àíàòîëèé Èâàíîâè÷, êàíä. ôèç.-ìàò. íàóê, ïðî- ôåññîð êàôåäðû ôèçèêè ÕÍÓÐÅ. Íàó÷íûå èíòåðåñû: ðàäèîôèçèêà. Àäðåñ: Óêðàèíà, 61103, Õàðüêîâ, óë. 23 Àâãóñòà, 39, êâ. 51, òåë. 33-61-43 äîì., 702-13-45 ðàá. ÓÄÊ 621.396.2.: 621.316.2 ÎÖÅÍÊÀ ÏÀÐÀÌÅÒÐΠÌÎÄÅËÅÉ ËÈÍÅÉÍÎÃÎ ÏÐÅÄÑÊÀÇÀÍÈß ÏÎ ÑÏÅÊÒÐÀËÜÍÎÉ ÏËÎÒÍÎÑÒÈ ÌÎÙÍÎÑÒÈ ÒÈÕÎÍΠÂ.À., ÄÎÐÎÂÑÊÈÉ Â.Â., ÃÎÐÅËΠÄ.Þ., ËÈÕÎØÅÐÑÒΠÅ.Ñ. Ïðèâîäèòñÿ ñïîñîá ðàñ÷åòà ïàðàìåòðîâ ìîäåëåé àâòîðåã- ðåññèè è ñêîëüçÿùåãî ñðåäíåãî ïî çàäàííîé ÑÏÌ ñëó÷àéíî- ãî ïðîöåññà èëè À×Õ ëèíåéíîé ñèñòåìû. Îïèñûâàþòñÿ ñèñòåìû óðàâíåíèé äëÿ ðàñ÷åòà ïàðàìåòðîâ ìîäåëåé. Àíà- ëèçèðóþòñÿ âîçìîæíîñòè ïðèìåíåíèÿ òàêîãî ìåòîäà îöåí- êè ïàðàìåòðîâ ìîäåëåé äëÿ ðàçëè÷íûõ ôîðì ÑÏÌ èëè À×Õ. Ìîäåëè àâòîðåãðåññèè (ÀÐ) è ñêîëüçÿùåãî ñðåäíåãî (ÑÑ) øèðîêî ïðèìåíÿþòñÿ â àíàëèçå êîððåëèðîâàííûõ ñëó- ÷àéíûõ ïðîöåññîâ, íàïðèìåð, ïðè ïîäàâëåíèè êîððåëè- ðîâàííûõ ïîìåõ [1], äëÿ êîððåêöèè êàíàëîâ ñâÿçè [2], â ñèñòåìàõ êîäèðîâàíèÿ-äåêîäèðîâàíèÿ ðå÷åâûõ ñèãíà- ëîâ â öèôðîâûõ ñèñòåìàõ ñâÿçè [3]. Ìîäåëè ÀÐ è ÑÑ èñïîëüçóþòñÿ â ïàðàìåòðè÷åñêîì ñïåêòðàëüíîì àíà- ëèçå, êîòîðûé èìååò ðÿä ïðåèìóùåñòâ íàä êëàññè- ÷åñêèìè ìåòîäàìè ñïåêòðàëüíîãî îöåíèâàíèÿ ïðè àíàëèçå âûáîðîê êîíå÷íîé äëèíû [4]. Êëàññè÷åñ- êèì ïðèìåðîì óñïåøíîãî ïðèìåíåíèÿ ìîäåëè ÀÐ ÿâëÿåòñÿ àíàëèç ñîëíå÷íîé àêòèâíîñòè [5]. Ïàðàìåòðû ìîäåëåé ÀÐ è ÑÑ íàõîäÿòñÿ ïî èçâåñ- òíûì âûáîðêàì ñèãíàëîâ [5], ôóíêöèÿì êîððåëÿ- öèè èëè ïàðàìåòðàì ÑÏÌ ñëó÷àéíîãî ïðîöåññà [6, 7]. Îäíàêî ïðîáëåìà îöåíêè ïàðàìåòðîâ ìîäåëè ëèíåéíîãî ïðåäñêàçàíèÿ ïî çàäàííûì ñïåêòðàëü- íûì îòñ÷åòàì, êàê ïðàâèëî, íå ðàññìàòðèâàåòñÿ. Âìåñòå ñ òåì, ïðè ðåøåíèè ðÿäà çàäà÷ íåîáõîäèìî îöåíèòü ïàðàìåòðû ìîäåëåé ÀÐ èëè ÑÑ, åñëè èçâåñòíû îòñ÷åòû ÑÏÌ ïðîöåññà èëè çàäàíû çíà- ÷åíèÿ À×Õ íåêîòîðîé ëèíåéíîé ñèñòåìû. Íàéäåí- íûå òàêèì îáðàçîì ïàðàìåòðû ìîäåëåé ìîæíî èñïîëüçîâàòü äëÿ àíàëèçà ñëó÷àéíûõ ïðîöåññîâ èëè ñèñòåì ñ èçâåñòíûìè ñïåêòðàëüíûìè õàðàêòåðèñ- òèêàìè, äëÿ ïîñòðîåíèÿ ìîäåëåé ëèíåéíîãî ïðåä- ñêàçàíèÿ, äëÿ ñèíòåçà ôîðìèðóþùèõ èëè îáåëÿþ- ùèõ ôèëüòðîâ. Ñ ïîìîùüþ ôîðìèðóþùèõ ôèëü- òðîâ ïîëó÷àþò èìèòàöèîííûå ñëó÷àéíûå ïðîöåññû ñ çàäàííûìè ñòàòèñòè÷åñêèìè õàðàêòåðèñòèêàìè. 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Äëÿ ñèíòåçà ìîäåëåé ÀÐ è ÑÑ îáû÷íî àíàëèçèðó- åòñÿ âûáîðêà êîððåëèðîâàííîãî ñëó÷àéíîãî ïðî- öåññà. Ïî ïîëó÷åííîé îöåíêå êîððåëÿöèîííîé ôóíêöèè ðàññ÷èòûâàþò êîýôôèöèåíòû ìîäåëè ÀÐ, èñïîëüçóÿ óðàâíåíèå Þëà-Óîêåðà [5]:     p 1 i i j i j R Φ R , (1) ãäå 1 p Ф  — êîýôôèöèåíòû ÀÐ; p — ïîðÿäîê ìîäåëè ÀÐ; j R — çíà÷åíèÿ ôóíêöèè êîððåëÿöèè. Êîýôôèöèåíòû ìîäåëè ÑÑ ðàññ÷èòûâàþòñÿ ñ ïî- ìîùüþ ñèñòåìû óðàâíåíèé âèäà [5]                            q j , 0 q j 1 , [i] Q 1 j]Q[q] Q[q [i] Q 1 1] Q[1]Q[j Q[j] r[j] q 1 i 2 q 1 i 2   , (2) çäåñü Q[i] — êîýôôèöèåíòû, à q — ïîðÿäîê ìîäåëè ÑÑ; j r — êîýôôèöèåíòû êîððåëÿöèè.  íåêîòîðûõ ñëó÷àÿõ ìîäåëè ÀÐ èëè ÑÑ ñòðîÿò ïî èçâåñòíîé èëè çàäàâàåìîé êîððåëÿöèîííîé ôóíê- öèè. Äëÿ ýòèõ öåëåé â óðàâíåíèÿ (1) èëè (2) ïîäñòàâëÿþò çíà÷åíèÿ êîððåëÿöèîííîé ôóíêöèè è îïðåäåëÿþò ïàðàìåòðû ìîäåëåé. Ïîðÿäîê ìîäåëè îöåíèâàþò ïî áëèçîñòè êîýôôèöèåíòà ÀÐ èëè ÑÑ ê íóëþ, èñïîëüçóÿ íåêîòîðûé êðèòåðèé. Ðàññ÷èòàòü êîýôôèöèåíòû ÀÐ èëè ÑÑ ìîæíî ïî çàäàííûì ïàðàìåòðàì ÑÏÌ ïðîöåññà: ÷àñòîòå ïèêà i f è èõ øèðèíå ïîëîñû i Δf [3, 4]. Äëÿ ýòèõ öåëåé èñïîëüçóþòñÿ ñîîòíîøåíèÿ, óñòàíàâëèâàþùèå ñâÿçü êîýôôèöèåíòîâ ÀÐ è êîðíåé õàðàêòåðèñòè÷åñêîãî óðàâíåíèÿ, çàâèñÿùèõ îò óêàçàííûõ ïàðàìåòðîâ ñïåêòðà. Ïðè ýòîì ïîðÿäîê ìîäåëåé ÀÐ è ÑÑ îïðåäåëÿåòñÿ ÷èñëîì ïèêîâ ÑÏÌ. Îäíàêî äëÿ ñëîæíûõ ôîðì ñïåêòðà åãî îïèñàíèå ñ ïîìîùüþ ïàðàìåòðîâ i f è i Δf âûçûâàåò çàòðóäíå- íèå.  òàêèõ ñëó÷àÿõ êîýôôèöèåíòû ìîäåëåé ÀÐ è ÑÑ ìîæíî ðàññ÷èòàòü íåïîñðåäñòâåííî ïî îòñ÷åòàì ÑÏÌ. Äëÿ ýòîé öåëè íåîáõîäèìî ðåøèòü çàäà÷ó, îáðàòíóþ ïàðàìåòðè÷åñêîìó ñïåêòðàëüíîìó îöå- íèâàíèþ, ò.å. ïî âûáîðêå ÑÏÌ íàéòè ïàðàìåòðû ïîäõîäÿùåé ìîäåëè ëèíåéíîãî ïðåäñêàçàíèÿ. ÀÐ îöåíêà ÑÏÌ íàõîäèòñÿ ñîãëàñíî âûðàæåíèþ 2 p 1 i i a πifT) 2 j exp( Ф 1 D S(f)      , (3) ãäå T — èíòåðâàë äèñêðåòèçàöèè ñèãíàëà. Ôîðìóëà äëÿ ÑÑ îöåíêè ÑÏÌ èìååò âèä a 2 q 1 n n D πnfT) 2 j exp( Q 1 S(f)      . (4) Ìîäåëü ÀÐ íàèáîëåå òî÷íî îïèñûâàåò ñëó÷àéíûå ïðîöåññû, ñïåêòðû êîòîðûõ ñîäåðæàò îñòðûå ïèêè è íå èìåþò ãëóáîêèõ âïàäèí. Äëÿ ìîäåëèðîâàíèÿ ñëó÷àéíûõ ïðîöåññîâ, ñïåêòðû êîòîðûõ ñîäåðæàò øèðîêèå ïèêè è îñòðûå ìèíèìóìû, áîëüøå ïîä- õîäèò ìîäåëü ÑÑ. Ïîýòîìó äëÿ ðàçíûõ ôîðì ÑÏÌ íåîáõîäèìî èñêàòü ñîîòâåòñòâóþùèå äîñòàòî÷íî òî÷íûå ìîäåëè ëèíåéíîãî ïðåäñêàçàíèÿ. Áóäåì ïîëàãàòü, ÷òî çíà÷åíèÿ S(f) èçâåñòíû. Òîãäà èç (3) è (4) ïîëó÷àåì óðàâíåíèå K(f) D πifT 2 sin G πifT 2 cos G 1 a 2 m 1 i i 2 m 1 i i                    , (5) ãäå i i Φ G  , S(f) K(f)  è p m  äëÿ ìîäåëè ÀÐ; i i Q G  , /S(f) 1 K(f)  è q m  äëÿ ìîäåëè ÑÑ.  óðàâíåíèè (5) ïåðåìåííàÿ f èçâåñòíà, à íåèçâåñò- íûìè ÿâëÿþòñÿ ïàðàìåòðû i G . Âèä ïîëó÷åííîãî óðàâíåíèÿ (5) ïðàêòè÷åñêè îäèíàêîâ äëÿ ìîäåëåé ÀÐ è ÑÑ. Ïîýòîìó îíè áóäóò ðàññìàòðèâàòüñÿ ñîâìåñòíî. Óðàâíåíèå (5) ïóòåì íåñëîæíûõ ïðåîáðàçîâàíèé ìîæíî ïðåäñòàâèòü ñëåäóþùèì îáðàçîì: K(f) D G G 2 G 2 πfT 2 cosn G 1 a m 1 n n m 1 i n i i n m 1 i 2 i                              .(6) Ââåäÿ îáîçíà÷åíèÿ     m 1 i 0 2 i X G 1 , (7à) n n m 1 i n i i n X G G 2 G 2        , (7á) óðàâíåíèå (6) ïðåîáðàçóåì ê âèäó K(f) D πfT 2 cosn X X a m 1 n n 0     . (8) Çàìåòèì, ÷òî ÷èñëî íåèçâåñòíûõ ïàðàìåòðîâ n X íà åäèíèöó áîëüøå êîëè÷åñòâà îöåíèâàåìûõ êîýôôè- öèåíòîâ ÀÐ èëè ÑÑ. Ïîýòîìó äëÿ íàõîæäåíèÿ p G áóäåì èñïîëüçîâàòü òîëüêî ïåðâîå óðàâíåíèå (7à). Åñòåñòâåííî ïîëàãàòü, ÷òî â îáùåì ñëó÷àå ñïåêò- ðàëüíûå îòñ÷åòû S(f) ÿâëÿþòñÿ ñëó÷àéíîé ôóíêöè- åé ÷àñòîòû. Òîãäà îöåíêè ïàðàìåòðîâ 0 X , n X ìîæíî íàéòè íà îñíîâå ìíîæåñòâåííîãî ðåãðåññè- îííîãî àíàëèçà. Óðàâíåíèå ðåãðåññèè, ñ ó÷åòîì (8), ïðåäñòàâëÿåòñÿ â âèäå      m 1 n f n 0 a e πfT 2 cosn X X K(f) D , (9) ãäå f e — îøèáêè óðàâíåíèÿ ðåãðåññèè. Ìåòîä íàèìåíüøèõ êâàäðàòîâ ïîçâîëÿåò ïîëó÷èòü ñèñòå- ìó m óðàâíåíèé âèäà         N 1 n n a N 1 n n m n 1 0 ) K(f D T) πf 2 cos X ... T πf 2 cos X (X ,         N 1 n n a N 1 n n m n 1 0 ) K(f D T) πf 2 cos X ... 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