TABLE 3 1 Short Table of Fourier Transforms G f g t e atu t a 21Cf 2 eatu t 3 e altl a j21Cf 2a 4 te at u t 5 tne at u t 6 7 8 B t 1 ej21rfot a O a O 2 a O a j21Cf 2 n a j21Cf n l 11 u t 8 f 8 f fo 0 5 8 f fo 8 f fo jO 5 8 fo 8 fo f 1 218 ji j 12 sgnt 2 9 cos2Jrfot 10 sin 2Jrfot j21rf B f cos 21Tfotu t 1 4 B f 14 sin 21Cfot u t 15 e at sin 2nfot u t 16 e at cas 2nfot u t n f fo B f fo fo B f fo 21rfo a j21rf 2 41r2fi a j21rf a j2nf 2 4n2f6 rsinc nf r 18 2B sinc 21TBt n fB 19 l f 2sinc2 20 B sinc2 fBt 21 E oo 8 1 22 e t2 2O 2 Ll fB nT to L oo 8 nfO u i iie 2 ff j21Cf 27ffo 2 27ff 2 27ffo 21rfO 2 21tf 2 TABLE 3 2 Propertiesof Fourier TransformOperations Operation g t G f Superposition Scalarmultiplication Duality Time scaling gl t gZ t kg t G t Gl f f kG f g f Time shifting g at g t to Frequencyshifting Time convolution Frequencyconvolution g t ejZ1ffot gl t gZ t gl t gZ t Gl f G2 f Gl f G2 f Time differentiation dt j27rf nG f Time integration f oo g x dx G 1 G f e j27rfto G f fo 127rf 1G O FJ f 2
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