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]

0

1 . 2-r;d(w'
2

-

- 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 2 w o t } = siri2wot = cos

In all cases! the Hilbert trmsforrn caiises a phase shift, in the linir-domain by

Solution 15.3
1

a) h ( t ) = - o -0 H (;p)
= -gsign(w)
7Tt

T
-

2