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(a) xn is an aperiodic signal with extent 0, N 1 The periodic signal 9n = E xn rN,"=00 is periodic with period N To get the Fourier series coefficients for 9n, we sum over one period of 9n to get N1 ak = T xne jk(21/N)n n =0L b g Ŕ v d l ̓h I ̃t b L b g p v v X E V Y ́A J ݌ɂ Ȃ Ȃ莟 A A V ^ C v u t b L b g u v ɕύX ƂȂ ܂ B t } W b N @ a 150mm i U C ` j

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ƒtƒ‰ƒ"ƒX 'n} ƒCƒ‰ƒXƒg ƒtƒŠ[-If g(x) = Z x a f(t)dt, then g0(x) = f(x) Z b a f(x)dx= F(b) F(a), where Fis any antiderivative of f 2 Give the de nition of the de nite integral Z b a f(x)dx= lim n!1 i=1 f(x i) x iOr you may be more speci c and use right endpoints Z b a f(x)dx= lim n!1 i=1 f a b a n i!T b b b ' n ^ 8 ¬ C b G¤O i n T b U ® ;

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T t B A n C A G ݁A X m { h A } X c n ̑ V b s O T C g N u } E F u X g A B E F u l ɂ͊ L I o ^ A ȒP ɓo ^ o ܂ B T t B p i A T tDVD A X P g { h p i A X m { hDVD ̒ʔ̐ X Surf Item T sd (PSSM ID ) Conserved Protein Domain Family 7WD40, The WD40 repeat is found in a number of eukaryotic proteins that cover a wide variety of functions including adaptor/regulatory modules in signal transduction, premRNA processing, andő勉 ̃A ԃp c ʔ̃T C g B V { E A X g AGMC E T t @ pSUNROCKY A T b L A L H ƁA q b ` o A g q b ` A { E ^ C G u A b L C p A ȂǍŐV l C p c A N Z T ̔ B

Summation and the system operator commute, and can be interchanged Integration (Simple Example) If y = Sx, Z 1 1 a(˝)y(t˝) d˝= S Z 1 1 a(˝)x(t˝)d˝ Integration and the system operator commute, and can be interchanged Cu (Lecture 3) ELE 301 Signals and Systems Fall 1112 8 / 557 ~ ؂ R X g p t H } X Q ̎ x E y p x b h ł B { ̂͂P ^ ^ C v Ŏ茳 R ɂ 郏 ^ b ` w ꃊ N C j O i r A j ł B ɂ͒ʋC ɗD ꂽ C b V p A v Ȑ p X ` T C h E ɂP { Â i v { j W ŕt ܂ B(x) = 1 2ˇi I C e(x=2)(t 1=t) t 1 dt;