Wiley signals and systems e book TLFe BO 550

535 ApDenclix A Solutions to thc Exewiscs a) not cau5d b) caausxl c) causal (1) causal e ) not causal, "reacts" to future x [ k ] wheii , k > O e.g g[l] - [a] 2-r;d(w' - - GO) + S(w' + w O ) ] (-~jsign(a))= - , j ~ [ ? i ( d - WO) - S(w -1W O ) ] 'Ft{coswc,t} = sin wof = cos d) 'H{cos2 U ( ] t }0-0 - p [ b ( w- 2U") ~- h(u + 2iJ,I)] Z { c o s w o t } = siri2wot = cos In all cases! the Hilbert trmsforrn caiises a phase shift, in the linir-domain by Solution 15.3 a) h ( t ) = - o -0 H (;p) = -gsign(w) 7Tt T -