📄 2.11.rickard.ps
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b(the)i(time)g(in)n(terv)-5 b(al)27 b(\(0)p Fe(;)14 b(T)eFf(\).)36 b(Ov)n(er)26 b(this)i(in)n(terv)-5 b(al,)27b(the)h(signal)f(is,)556 2554 y Fe(S)5 b Ff(\()p Fe(t)24b Fa(2)f Ff(\(0)p Fe(;)14 b(T)e Ff(\)\))82 b(=)h Fe(cos)pFf(\(2)p Fe(\031)s(f)1522 2566 y Fd(c)1556 2554 y Fe(t)18b Ff(+)g Fe(b)p Ff([0]\010\()p Fe(t)p Ff(\)\))1094 2678y(=)83 b Fe(cos)p Ff(\(2)p Fe(\031)s(f)1522 2690 y Fd(c)15562678 y Fe(t)p Ff(\))p Fe(cos)p Ff(\()p Fe(b)p Ff([0]\010\()pFe(t)p Ff(\)\))19 b Fa(\000)f Fe(sin)p Ff(\(2)p Fe(\031)s(f)24602690 y Fd(c)2493 2678 y Fe(t)p Ff(\))p Fe(sin)p Ff(\()pFe(b)p Ff([0]\010\()p Fe(t)p Ff(\)\))1094 2803 y(=)83b Fe(cos)p Ff(\(2)p Fe(\031)s(f)1522 2815 y Fd(c)15562803 y Fe(t)p Ff(\))p Fe(cos)p Ff(\(\010\()p Fe(t)p Ff(\)\))19b Fa(\000)f Fe(sin)p Ff(\(2)p Fe(\031)s(f)2336 2815 yFd(c)2369 2803 y Fe(t)p Ff(\))p Fe(b)p Ff([0])p Fe(sin)pFf(\(\010\()p Fe(t)p Ff(\)\))1094 2927 y(=)83 b Fe(cos)pFf(\(2)p Fe(\031)s(f)1522 2939 y Fd(c)1556 2927 y Fe(t)pFf(\))p Fe(cos)p Ff(\(\010\()p Fe(t)p Ff(\)\))19 b(+)fFe(sin)p Ff(\(2)p Fe(\031)s(f)2336 2939 y Fd(c)2369 2927y Fe(t)p Ff(\)\()p Fa(\000)p Fe(b)p Ff([0]\))p Fe(sin)pFf(\(\010\()p Fe(t)p Ff(\)\))p Fe(;)-300 3110 y Ff(where)27b(w)n(e)g(ha)n(v)n(e)g(made)g(use)h(of)f(the)h(trigonometric)e(iden)n(tit)n(y)-7 b(,)1023 3293 y Fe(cos)p Ff(\()p Fe(\013)19b Ff(+)f Fe(\014)t Ff(\))24 b(=)f Fe(cos)p Ff(\()p Fe(\013)pFf(\))p Fe(cos)p Ff(\()p Fe(\014)t Ff(\))d Fa(\000)eFe(sin)p Ff(\()p Fe(\013)p Ff(\))p Fe(sin)p Ff(\()p Fe(\014)tFf(\))p Fe(;)-300 3475 y Ff(and)27 b(the)h(fact)g(that)gFe(b)p Ff([0])22 b Fa(2)i(f\000)p Ff(1)p Fe(;)14 b Ff(1)pFa(g)25 b Ff(in)j(order)e(to)i(eliminate)f Fe(b)p Ff([0])g(from)g(the)h(cosine)f(and)h(pull)g(it)g(out)f(from)h(the)g(sine.)-1753575 y(Ov)n(er)e(the)i(in)n(terv)-5 b(al)27 b(\()p Fe(T)7b(;)14 b Ff(2)p Fe(T)e Ff(\),)26 b(the)i(signal)f(is,)963757 y Fe(S)5 b Ff(\()p Fe(t)23 b Fa(2)h Ff(\()p Fe(T)7b(;)14 b Ff(2)p Fe(T)e Ff(\)\))81 b(=)i Fe(cos)p Ff(\(2)pFe(\031)s(f)1117 3769 y Fd(c)1151 3757 y Fe(t)18 b Ff(+)gFe(b)p Ff([0])1416 3725 y Fd(\031)p 1415 3739 41 4 v1419 3786 a Fc(2)1485 3757 y Ff(+)g Fe(b)p Ff([1]\010\()pFe(t)g Fa(\000)g Fe(T)12 b Ff(\)\))689 3882 y(=)83 bFe(cos)p Ff(\(2)p Fe(\031)s(f)1117 3894 y Fd(c)1151 3882y Fe(t)p Ff(\))p Fe(cos)p Ff(\()p Fe(b)p Ff([0])14943849 y Fd(\031)p 1493 3863 V 1497 3911 a Fc(2)1563 3882y Ff(+)18 b Fe(b)p Ff([1]\010\()p Fe(t)g Fa(\000)g Fe(T)12b Ff(\)\))18 b Fa(\000)g Fe(sin)p Ff(\(2)p Fe(\031)s(f)25023894 y Fd(c)2535 3882 y Fe(t)p Ff(\))p Fe(sin)p Ff(\()pFe(b)p Ff([0])2881 3849 y Fd(\031)p 2880 3863 V 28843911 a Fc(2)2949 3882 y Ff(+)g Fe(b)p Ff([1]\010\()pFe(t)g Fa(\000)g Fe(T)12 b Ff(\)\))689 4007 y(=)83 bFe(cos)p Ff(\(2)p Fe(\031)s(f)1117 4019 y Fd(c)1151 4007y Fe(t)p Ff(\)\()p Fa(\000)p Fe(b)p Ff([0]\))p Fe(sin)pFf(\()p Fe(b)p Ff([1]\010\()p Fe(t)17 b Fa(\000)h Fe(T)12b Ff(\)\))18 b Fa(\000)g Fe(sin)p Ff(\(2)p Fe(\031)s(f)24714019 y Fd(c)2504 4007 y Fe(t)p Ff(\)\()p Fe(b)p Ff([0]\))pFe(cos)p Ff(\()p Fe(b)p Ff([1]\010\()p Fe(t)g Fa(\000)gFe(T)12 b Ff(\)\))689 4131 y(=)83 b Fe(cos)p Ff(\(2)pFe(\031)s(f)1117 4143 y Fd(c)1151 4131 y Fe(t)p Ff(\)\()pFa(\000)p Fe(b)p Ff([0])p Fe(b)p Ff([1]\))p Fe(sin)pFf(\(\010\()p Fe(t)17 b Fa(\000)h Fe(T)12 b Ff(\)\))18b Fa(\000)g Fe(sin)p Ff(\(2)p Fe(\031)s(f)2471 4143 yFd(c)2504 4131 y Fe(t)p Ff(\)\()p Fe(b)p Ff([0]\))p Fe(cos)pFf(\(\010\()p Fe(t)h Fa(\000)f Fe(T)12 b Ff(\)\))6894256 y(=)83 b Fe(cos)p Ff(\(2)p Fe(\031)s(f)1117 4268y Fd(c)1151 4256 y Fe(t)p Ff(\)\()p Fa(\000)p Fe(b)pFf([0])p Fe(b)p Ff([1]\))p Fe(sin)p Ff(\(\010\()p Fe(t)17b Fa(\000)h Fe(T)12 b Ff(\)\))18 b(+)g Fe(sin)p Ff(\(2)pFe(\031)s(f)2471 4268 y Fd(c)2504 4256 y Fe(t)p Ff(\)\()pFa(\000)p Fe(b)p Ff([0]\))p Fe(cos)p Ff(\(\010\()p Fe(t)hFa(\000)f Fe(T)12 b Ff(\)\))p Fe(;)-300 4438 y Ff(where)27b(w)n(e)g(ha)n(v)n(e)g(made)g(use)h(of)f(the)h(trigonometric)e(iden)n(tities,)1287 4621 y Fe(cos)p Ff(\()p Fe(\013)19 b Ff(+)fFe(b)p Ff([)p Fe(i)p Ff(])1710 4588 y Fd(\031)p 17094602 V 1713 4650 a Fc(2)1760 4621 y Ff(\))23 b(=)g Fa(\000)pFe(b)p Ff([)p Fe(i)p Ff(])p Fe(sin)p Ff(\()p Fe(\013)pFf(\))1307 4804 y Fe(sin)p Ff(\()p Fe(\013)c Ff(+)f Fe(b)pFf([)p Fe(i)p Ff(])1733 4771 y Fd(\031)p 1732 4785 V1736 4832 a Fc(2)1783 4804 y Ff(\))23 b(=)g Fe(b)p Ff([)pFe(i)p Ff(])p Fe(cos)p Ff(\()p Fe(\013)p Ff(\))p Fe(:)17795255 y Ff(1)p eop2 1 bop -300 523 a Ff(Con)n(tin)n(uing)27 b(in)h(this)g(fashion,)-255706 y Fe(S)5 b Ff(\()p Fe(t)23 b Fa(2)g Ff(\(2)p Fe(T)7b(;)14 b Ff(3)p Fe(T)e Ff(\)\))81 b(=)i Fe(cos)p Ff(\(2)pFe(\031)s(f)807 718 y Fd(c)841 706 y Fe(t)18 b Ff(+)g(\()pFe(b)p Ff([0])g(+)g Fe(b)p Ff([1]\))1395 673 y Fd(\031)p1395 687 41 4 v 1399 734 a Fc(2)1464 706 y Ff(+)g Fe(b)pFf([2]\010\()p Fe(t)g Fa(\000)g Ff(2)p Fe(T)12 b Ff(\)\))379830 y(=)83 b Fe(cos)p Ff(\(2)p Fe(\031)s(f)807 842 yFd(c)841 830 y Fe(t)p Ff(\))p Fe(cos)p Ff(\(\()p Fe(b)pFf([0])18 b(+)g Fe(b)p Ff([1]\))1473 798 y Fd(\031)p1473 812 V 1477 859 a Fc(2)1542 830 y Ff(+)g Fe(b)p Ff([2]\010\()pFe(t)g Fa(\000)g Ff(2)p Fe(T)12 b Ff(\)\))18 b Fa(\000)gFe(sin)p Ff(\(2)p Fe(\031)s(f)2523 842 y Fd(c)2556 830y Fe(t)p Ff(\))p Fe(sin)p Ff(\(\()p Fe(b)p Ff([0])f(+)hFe(b)p Ff([1]\))3190 798 y Fd(\031)p 3190 812 V 3194859 a Fc(2)3259 830 y Ff(+)g Fe(b)p Ff([2]\010\()p Fe(t)gFa(\000)g Ff(2)p Fe(T)12 b Ff(\)\))379 955 y(=)83 b Fe(cos)pFf(\(2)p Fe(\031)s(f)807 967 y Fd(c)841 955 y Fe(t)pFf(\)\()p Fa(\000)p Fe(b)p Ff([0]\))p Fe(sin)p Ff(\()pFe(b)p Ff([1])1440 922 y Fd(\031)p 1438 936 V 1442 983a Fc(2)1507 955 y Ff(+)18 b Fe(b)p Ff([2]\010\()p Fe(t)gFa(\000)g Ff(2)p Fe(T)12 b Ff(\)\))18 b Fa(\000)g Fe(sin)pFf(\(2)p Fe(\031)s(f)2488 967 y Fd(c)2521 955 y Fe(t)pFf(\)\()p Fe(b)p Ff([0]\))p Fe(cos)p Ff(\()p Fe(b)p Ff([1])3052922 y Fd(\031)p 3052 936 V 3056 983 a Fc(2)3121 955 yFf(+)g Fe(b)p Ff([2]\010\()p Fe(t)g Fa(\000)g Ff(2)pFe(T)12 b Ff(\)\))379 1079 y(=)83 b Fe(cos)p Ff(\(2)pFe(\031)s(f)807 1091 y Fd(c)841 1079 y Fe(t)p Ff(\)\()pFa(\000)p Fe(b)p Ff([0])p Fe(b)p Ff([1]\))p Fe(cos)pFf(\()p Fe(b)p Ff([2]\010\()p Fe(t)17 b Fa(\000)h Ff(2)pFe(T)12 b Ff(\)\))17 b Fa(\000)h Fe(sin)p Ff(\(2)p Fe(\031)s(f)23231091 y Fd(c)2356 1079 y Fe(t)p Ff(\)\()p Fa(\000)p Fe(b)pFf([0])p Fe(b)p Ff([1]\))p Fe(sin)p Ff(\()p Fe(b)p Ff([2]\010\()pFe(t)f Fa(\000)h Ff(2)p Fe(T)12 b Ff(\)\))379 1204 y(=)83b Fe(cos)p Ff(\(2)p Fe(\031)s(f)807 1216 y Fd(c)841 1204y Fe(t)p Ff(\)\()p Fa(\000)p Fe(b)p Ff([0])p Fe(b)p Ff([1]\))pFe(cos)p Ff(\(\010\()p Fe(t)18 b Fa(\000)g Ff(2)p Fe(T)12b Ff(\)\))17 b Fa(\000)h Fe(sin)p Ff(\(2)p Fe(\031)s(f)22001216 y Fd(c)2233 1204 y Fe(t)p Ff(\)\()p Fa(\000)p Fe(b)pFf([0])p Fe(b)p Ff([1])p Fe(b)p Ff([2]\))p Fe(sin)p Ff(\(\010\()pFe(t)f Fa(\000)h Ff(2)p Fe(T)12 b Ff(\)\))379 1328 y(=)83b Fe(cos)p Ff(\(2)p Fe(\031)s(f)807 1340 y Fd(c)841 1328y Fe(t)p Ff(\)\()p Fa(\000)p Fe(b)p Ff([0])p Fe(b)p Ff([1]\))pFe(cos)p Ff(\(\010\()p Fe(t)18 b Fa(\000)g Ff(2)p Fe(T)12b Ff(\)\))17 b(+)h Fe(sin)p Ff(\(2)p Fe(\031)s(f)22001340 y Fd(c)2233 1328 y Fe(t)p Ff(\)\()p Fe(b)p Ff([0])pFe(b)p Ff([1])p Fe(b)p Ff([2]\))p Fe(sin)p Ff(\(\010\()pFe(t)f Fa(\000)h Ff(2)p Fe(T)12 b Ff(\)\))p Fe(;)-3001511 y Ff(and)27 b(one)h(last)f(time,)-300 1694 y Fe(S)5b Ff(\()p Fe(t)23 b Fa(2)g Ff(\(3)p Fe(T)7 b(;)14 b Ff(4)pFe(T)e Ff(\)\))82 b(=)g Fe(cos)p Ff(\(2)p Fe(\031)s(f)7621706 y Fd(c)796 1694 y Fe(t)18 b Ff(+)g(\()p Fe(b)p Ff([0])g(+)gFe(b)p Ff([1])g(+)g Fe(b)p Ff([2]\))1575 1661 y Fd(\031)p1575 1675 V 1579 1722 a Fc(2)1644 1694 y Ff(+)g Fe(b)pFf([3]\010\()p Fe(t)g Fa(\000)g Ff(3)p Fe(T)12 b Ff(\)\))3351818 y(=)82 b Fe(cos)p Ff(\(2)p Fe(\031)s(f)762 1830y Fd(c)796 1818 y Fe(t)p Ff(\))p Fe(cos)p Ff(\(\()p Fe(b)pFf([0])19 b(+)f Fe(b)p Ff([1])f(+)h Fe(b)p Ff([2]\))16531785 y Fd(\031)p 1653 1799 V 1657 1847 a Fc(2)1722 1818y Ff(+)g Fe(b)p Ff([3]\010\()p Fe(t)g Fa(\000)g Ff(3)pFe(T)12 b Ff(\)\))18 b Fa(\000)g Fe(sin)p Ff(\(2)p Fe(\031)s(f)27031830 y Fd(c)2736 1818 y Fe(t)p Ff(\))p Fe(sin)p Ff(\(\()pFe(b)p Ff([0])g(+)g Fe(b)p Ff([1])f(+)h Fe(b)p Ff([2]\))35951785 y Fd(\031)p 3595 1799 V 3599 1847 a Fc(2)3664 1818y Ff(+)g Fe(b)p Ff([3]\010\()p Fe(t)g Fa(\000)g Ff(3)pFe(T)12 b Ff(\)\))335 1943 y(=)82 b Fe(cos)p Ff(\(2)pFe(\031)s(f)762 1955 y Fd(c)796 1943 y Fe(t)p Ff(\)\()pFa(\000)p Fe(b)p Ff([0]\))p Fe(sin)p Ff(\(\()p Fe(b)pFf([1])17 b(+)h Fe(b)p Ff([2]\))1683 1910 y Fd(\031)p1683 1924 V 1687 1971 a Fc(2)1752 1943 y Ff(+)g Fe(b)pFf([3]\010\()p Fe(t)g Fa(\000)g Ff(3)p Fe(T)12 b Ff(\)\))18b Fa(\000)g Fe(sin)p Ff(\(2)p Fe(\031)s(f)2733 1955 yFd(c)2766 1943 y Fe(t)p Ff(\)\()p Fe(b)p Ff([0]\))p Fe(cos)pFf(\(\()p Fe(b)p Ff([1])g(+)g Fe(b)p Ff([2]\))3586 1910y Fd(\031)p 3586 1924 V 3590 1971 a Fc(2)3655 1943 yFf(+)g Fe(b)p Ff([3]\010\()p Fe(t)g Fa(\000)g Ff(3)pFe(T)12 b Ff(\)\))335 2067 y(=)82 b Fe(cos)p Ff(\(2)pFe(\031)s(f)762 2079 y Fd(c)796 2067 y Fe(t)p Ff(\)\()pFa(\000)p Fe(b)p Ff([0])p Fe(b)p Ff([1]\))p Fe(cos)pFf(\()p Fe(b)p Ff([2])1516 2035 y Fd(\031)p 1515 2049V 1519 2096 a Fc(2)1584 2067 y Ff(+)18 b Fe(b)p Ff([3]\010\()pFe(t)g Fa(\000)g Ff(3)p Fe(T)12 b Ff(\)\))17 b Fa(\000)hFe(sin)p Ff(\(2)p Fe(\031)s(f)2564 2079 y Fd(c)2597 2067y Fe(t)p Ff(\)\()p Fa(\000)p Fe(b)p Ff([0])p Fe(b)p Ff([1]\))pFe(sin)p Ff(\()p Fe(b)p Ff([2])3320 2035 y Fd(\031)p3318 2049 V 3322 2096 a Fc(2)3387 2067 y Ff(+)g Fe(b)pFf([3]\010\()p Fe(t)g Fa(\000)g Ff(3)p Fe(T)12 b Ff(\)\))3352192 y(=)82 b Fe(cos)p Ff(\(2)p Fe(\031)s(f)762 2204y Fd(c)796 2192 y Fe(t)p Ff(\)\()p Fe(b)p Ff([0])p Fe(b)pFf([1])p Fe(b)p Ff([2]\))p Fe(sin)p Ff(\()p Fe(b)p Ff([3]\010\()pFe(t)16 b Fa(\000)i Ff(3)p Fe(T)12 b Ff(\)\))18 b Fa(\000)gFe(sin)p Ff(\(2)p Fe(\031)s(f)2340 2204 y Fd(c)2373 2192y Fe(t)p Ff(\)\()p Fa(\000)p Fe(b)p Ff([0])p Fe(b)p Ff([1])pFe(b)p Ff([2]\))p Fe(cos)p Ff(\()p Fe(b)p Ff([3]\010\()pFe(t)e Fa(\000)i Ff(3)p Fe(T)12 b Ff(\)\))335 2316 y(=)82b Fe(cos)p Ff(\(2)p Fe(\031)s(f)762 2328 y Fd(c)796 2316y Fe(t)p Ff(\)\()p Fe(b)p Ff([0])p Fe(b)p Ff([1])p Fe(b)pFf([2])p Fe(b)p Ff([3]\))p Fe(sin)p Ff(\(\010\()p Fe(t)16b Fa(\000)i Ff(3)p Fe(T)12 b Ff(\)\))18 b Fa(\000)g Fe(sin)pFf(\(2)p Fe(\031)s(f)2340 2328 y Fd(c)2373 2316 y Fe(t)pFf(\)\()p Fa(\000)p Fe(b)p Ff([0])p Fe(b)p Ff([1])p Fe(b)pFf([2]\))p Fe(cos)p Ff(\(\010\()p Fe(t)f Fa(\000)h Ff(3)pFe(T)12 b Ff(\)\))335 2441 y(=)82 b Fe(cos)p Ff(\(2)pFe(\031)s(f)762 2453 y Fd(c)796 2441 y Fe(t)p Ff(\)\()pFe(b)p Ff([0])p Fe(b)p Ff([1])p Fe(b)p Ff([2])p Fe(b)pFf([3]\))p Fe(sin)p Ff(\(\010\()p Fe(t)16 b Fa(\000)iFf(3)p Fe(T)12 b Ff(\)\))18 b(+)g Fe(sin)p Ff(\(2)p Fe(\031)s(f)23402453 y Fd(c)2373 2441 y Fe(t)p Ff(\)\()p Fe(b)p Ff([0])pFe(b)p Ff([1])p Fe(b)p Ff([2]\))p Fe(cos)p Ff(\(\010\()pFe(t)f Fa(\000)h Ff(3)p Fe(T)12 b Ff(\)\))p Fe(:)-3002623 y Ff(No)n(w,)34 b(grouping)e(the)h(terms)g(from)g(the)g(end)g(of)g(eac)n(h)g(calculation)f(and)h(noting)g(that)g(the)gFe(cos)g Fa(!)f(\000)p Fe(sin)f Fa(!)h(\000)p Fe(cos)gFa(!)g Fe(sin)h Ff(tran-)-300 2723 y(sitions)j(created)f(b)n(y)h(iterativ)n(ely)f(pulling)i(out)f Fe(b)p Ff([)p Fe(i)pFf(])1357 2690 y Fd(\031)p 1356 2704 V 1360 2752 a Fc(2)14432723 y Ff(terms)g(accoun)n(t)g(for)f(the)i(p)r(erio)r(dic)f(de\014nition)g(of)h Fa(f)p Fe(q)s Ff([0])p Fe(;)14 b(q)sFf([1])p Fe(;)g(q)s Ff([2])p Fe(;)g(q)s Ff([3])p Fa(g)34b Ff(=)-300 2823 y Fa(f)p Ff(1)p Fe(;)14 b Fa(\000)pFf(1)p Fe(;)g Fa(\000)p Ff(1)p Fe(;)g Ff(1)p Fa(g)p Ff(,)21b(w)n(e)j(calculate)f(that)i(the)f(single-user)f(system)h(can)g(b)r(e)g(expressed)g(as)f(the)i(follo)n(wing)e(t)n(w)n(o-user)f(system)i(where)g(eac)n(h)-300 2922 y(user's)j(signature)f(w)n(a)n(v)n(eform)g(has)h(duration)g(2)p Fe(T)12 b Ff(,)548 3182 y Fe(S)5 b Ff(\()pFe(t)p Ff(;)14 b Fe(b)p Ff([0])p Fe(;)g(:)g(:)g(:)e(;)i(b)pFf([2)p Fe(M)9 b Ff(]\))22 b(=)1391 3078 y Fd(M)13663103 y Fb(X)1372 3280 y Fd(i)p Fc(=0)1500 3182 y Fe(d)pFf([2)p Fe(i)p Ff(])p Fe(s)1699 3194 y Fc(1)1735 3182y Ff(\()p Fe(t)d Fa(\000)f Ff(2)p Fe(iT)12 b Ff(\))17b(+)h Fe(d)p Ff([2)p Fe(i)g Ff(+)g(1])p Fe(s)2505 3194y Fc(2)2542 3182 y Ff(\()p Fe(t)g Fa(\000)g Ff(2)p Fe(iT)29b Fa(\000)18 b Fe(T)12 b Ff(\))o Fe(;)-300 3437 y Ff(where,)8163536 y Fe(s)855 3548 y Fc(1)892 3536 y Ff(\()p Fe(t)pFf(\))24 b(=)f Fe(sin)p Ff(\(2)p Fe(\031)s(f)1381 3548y Fd(c)1414 3536 y Fe(t)p Ff(\)[)p Fe(p)p Ff(\()p Fe(t)pFf(\))p Fe(sin)p Ff(\010\()p Fe(t)p Ff(\))c(+)f Fe(p)pFf(\()p Fe(t)g Fa(\000)g Fe(T)12 b Ff(\))p Fe(cos)p Ff(\010\()pFe(t)18 b Fa(\000)g Fe(T)12 b Ff(\)])p Fe(;)817 3686y(s)856 3698 y Fc(2)894 3686 y Ff(\()p Fe(t)p Ff(\))23b(=)g Fe(cos)p Ff(\(2)p Fe(\031)s(f)1379 3698 y Fd(c)14123686 y Fe(t)p Ff(\)[)p Fe(p)p Ff(\()p Fe(t)p Ff(\))pFe(sin)p Ff(\010\()p Fe(t)p Ff(\))c(+)f Fe(p)p Ff(\()pFe(t)h Fa(\000)f Fe(T)12 b Ff(\))p Fe(cos)p Ff(\010\()pFe(t)18 b Fa(\000)g Fe(T)12 b Ff(\)])p Fe(;)1414 3915y(d)p Ff([)p Fe(i)p Ff(])23 b(=)f Fe(q)s Ff([)p Fe(i)cFf(+)g(1])1960 3812 y Fd(i)1918 3836 y Fb(Y)1914 4013y Fd(j)s Fc(=0)2043 3915 y Fe(b)p Ff([)p Fe(j)5 b Ff(])pFe(:)1779 5255 y Ff(2)p eop enduserdict /end-hook known{end-hook}if
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