Wiley signals and systems e book TLFe BO 302

287

11 A. Exercises
a) Give c(t) and X(jw) witli

_uI

hymbols.

b) What syniinetiy doe5 x ( t ) have for t(i = 0 , t o = f and to = $'? Use your
illismrs to derive the symmetry af X ( J W ) . Note: see symrrwtries (9.61).
c) Sketch X ( p ) for to =

and

=

4.Write X(gw) as a

S

I

of ~delta impulses.

Exercise 11.4
Give Xl(,jw) and X Z ( j w )as well as r l ( f )0- 0 X I (p)
and zZ(t)o
the U-symbol and skel tli both functions of time.
XI 0'64
X2CjQ))

.*.
-

w

x

-E

..*

1

E . .

-t

-3

0 1 2 3

6

9
(0

Note: represe~itX,(jw) as a sum of Iwo spectra. For the sketch, reprtwrit the
result as a sum of delta-iriipulses.

Exercise 11.5
Calculate the Fourier scrics of t hr following prriodic functioiis using a siiitable
analysis.
Note: evaluating the coefficient forrriula is not necessary.

a) x C J ( l=
) cos(3wot) x siri'((2wot)
b) .Q,(/)

c)

= cos5((2qt)x

2,( t )= sin*(3wot)

siri(wot)

x cos'(w0t)

a,) Test which arc periodic, arid give the periods where possible.
b) Give the Fouricr transforms Xl(jw) . . . and X ~ ( j w ) .