Wiley signals and systems e book TLFe BO 92

Properties of the 1,aplace ‘Transforrri 77 An cxpansioiz or conrprcssiori of the tirnr axis o*curs, for cxamplc, if thc3 riiiit of mcasiirmient of t iine is *lianged or if spw1 of ii img

4.7 Properties of the 1,aplace ‘Transforrri 77

An cxpansioiz or conrprcssiori of the tirnr axis o(*curs, for cxamplc, if thc3 riiiit of mcasiirmient of t iine is (*lianged or if sp(w1 of ii imgnei i c tapr (.hmges E’rorn tliv Laplace transform (he original ti signal X ( r ) = G { r ( t ) } , s E ROC{s}

(4.23) Thc region of convrrgeiice is scaled i n the sattie way i.e

- E I t O C { z ( f ) } ,

s F ROC{rr(at)} i f This relatioiiship is sliown through the sitbsLilulioori 1 = at’

S

a

into (-1.1)

(-1.25)

(4.26)