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Table 3_1 - 206 TABLE 3 Fourier Series Representation of...

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Unformatted text preview: 206 TABLE 3.! Fourier Series Representation of Periodic Signafs PROPERTIES 0? CONTINUOUS-TIME FOUR¥ER SERIES Chap. 3' W‘ Pmpefly Section Periodic Signal Fourier Series Coefficients ' WW __..__.._.__._..__.____,.__..._.___._....._.__..... ‘“'“ "‘i x00} Periodic with period T and ya) fundamental flequency mo = Zea-IT uuu-~—_u—-m-_-am-a~u—a----—-_-..__ m_——-—-...----w--..---—--——_——---¢- —————— Linearity Time Shifting Frequency Shifting Conjugation Time Reversal Tune Scaling Periodic Convolution Mixifiplicafion Differentiation Inwgmtion Conjugate Symmetry for Rea! Signals Rea; and Even Signals Real and Odd Signals Bvcnfldd Decomposition of Real Signals wmm—m~——m‘-u'"mm------dfl-W‘U---aGnu-“ .....,,..._-—_....___.— w~~.,-, _———-____— ....... Parscvai’s Relation for Periodic Signals 3.5.5 3.5.6 3.5.6 3.5.6 A10} + BK!) 10— to) ejMwaer) m ejM(21r/T)rx(t) x‘(t) xH) x(at), a > D (periodic with period Tia) J x('r)y(t—~ 'r)d1- T x(r)y(t) dx(r) “a?" (finite valued and periodic only if an r- G) I; 1(1) 0'! x0) real x(t)real and even x(t)real and odd _ {m = 8v{x(t)} [x(t)reali 2:90) = 0d{x(t)} {x(t)reai] H txmlzan —- 2: Ian? 01': real and even at purely‘ imaginary and odd acidic} W L: ...
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