63 1.3 Unilateral arid Bilaterd Laplace Txaiisfc)rms I ~ 'I'he pairing of a tunc tiorr of tin1 ( t )and it3 Lapincc transfoiiir Xi.;) ;= C(.r(t)} cii~ialw be itleiitilid by the syrribol o Tliv fillcvl cir cle tleiiotca the frequencytloiirain quant it>), (4.3) 'The inteist" I~pl;tc.c\trtmsfororrn really d( reprcsent R function of iirrtiorrs, and this c m I)c infiriitc number of snprr iini>obe"drxyoarrit d as a Ric~rnaniisum: by tlici integral (4 2), sketched in Figure 4.1 arid expr (4.5) & ( t= ) for t > 0 otherwise (4.6) t h m its valuc is zcro for t < 0, aiid it (*ailhe dealt with by the bila form as wit11 the iiriiliz 1,aplace trarrsform F i g i i i ~4.2 sh furwtiomi iii th(1 time-cloimin Use of thc step function will hr rxplairretl in the tollowing exsanqArs