We have already poiiitd to tlic close connection between the L;q)lm>transform m c i tbr Fouricr transforiii, at tlric s t a r t of Chapter in h i s chapter wc iritwoduce a classical method to d rniinc thc magnitude and phase of the Foinier trnnsforin I from the pole-zero plot of i t s 1,aplacc traiistoim It is mostly usrtl e systen~sso that we c m refer t o t h sydrrri function instcad of the L a p l ~ ~ ctransform c of the irnpulse W~POIISP, aiid llie freyt1errc.y response Instead t lie Four ic:i transform Bode plots arc’ used as a fast way of firitliiig the approximdp i-reqiicwj responw from the pciles and zetos of thc system function At one time, Bode plots werr t hc erigiritw’s stanclartl riiei hotf for representing a freyiieiicy resportse in graphical furrii They would always have logaritliriric gxq)li paper ready for this twk but of course this is 110 l o i i , g ~ri arv, as computwi can clraw frequency respoiw Boctc i h t s are, h o ~ e v e z ,a ~narvellousway of plots faster and more accur dcvelopirtg an irituitivr iintlc~rstartdingol how the lo( ation of thcl poles ltritl mros rn functioii affect the fr equcncy response, arid it IS therefore iniportaiit ior developing and analysing 1-11 €uric-tion and the i‘rrqueiic.v T l i ~fiinciaineutul coriiwct rciporise i5 given hy the relationship (9.9), that we can also write here 8s Ff(h(t)) - HCPJJ)= H(s)/,=,, - w4f)}l,=lu (10.1) As stable systcms only have decaying oscillatioirs, all poles must lie left of the iniagiirary axis of the s-plane The imagirtary axis s = IW is part o i the irgiori of convergelice of C { h ( t ) ) ,so ~ h Eiturier r aiid Lapiace tmmforms can be in (9 ) Any way, in C h p t e r 9, we had iiitroduced the Fourirr transform wiLh ?w and not w so between the Crecpmiry response U(’J) = F { h ( l ) )aiid the values of thc system fturction H ( s ) = G ( h ( t ) } for s = j w , w e riot haw to make any changes in the notation B o d ~plots represent the frcquency rwpitnse c2s split irilo magnitude arid phase H ( p ) = I H ( ? U ) / &I”) with the following properties = lH($&I)/ t J ” # i H L I ” ) l