216 'The Foxtrier Transform Example 9.8 Using the property of duality we call obt,ain from the relationship (9.23) that we already know as the traiisforiri pair for a rectangle-shaped spectrnrn =+ si( i) 00 2nrect(-w) = 2xrect(d) (9.67) Figure 9.13 shows the duality between the si-function arid the rectangle fimctiorr L L Figiirc 9.13: Dualii,y of thc si-fimction and rectangle fimct,ioii Exarnple 9.9 Fhni (9.65) WP obtain using the duality property of the Fomier transform of a sinuhoidal function of tirrw: cosw()t 0-0 7T [ S ( d + WO) + S(d - do)] I (9.68) T h Fourier t,r;-\nsforrriconsists of a pair of delta irnpulses, For sucli fitnctions of time there is a Fourier Lransforrn, but no Laplace transform This is because tliere is no analytical coiitirluation into the cornplcx s-plane for the dcltn impulses on the irnagirrary axis