Wiley signals and systems e book TLFe BO 303

11. Sampling and Periodic Sigiials

288

Exercise 11.7
Expand the following periodic signals using the cueffirierit formula, in a corriplex
Fouricr series x ( i ) = A,,~JJ"O/'~.
Give the fundnruental angular iireyuency W O for
P

each.

Exercise 11.8
Shotv t,lrat X ( p ) =

f~ J C c w

=U

, see (11.7), by expanding tlie riglit-

IL

hanct term into

ii

Fouricr series.

Exercise 11.9
Consider 2(t>- si2(nt) arid the periodic signal s(t>= ~ ( *t ):U

(2).

a) Calctila,te and sketch X ( p ) and their X(jrw). HOWdo the weights of Ihe
delta inipulws of X ( p ) tic in with X ( p ) ?
b) Givc the Fourier series expansion of s ( f ) with (11.18) and skctch the series
of the Fourier rocffiricrits A,.

Exercise 11.10

Give t-hcFouricr transiiorm of ~ ( t=)rect
z ( t )x LLI
Calculate X,,(JW)

(t).

(5) and t , 1 r ~periodic continuation n.p(t) =

a) using coiivolution in the time-doamin.
b) iising the wiivoliitiozi theoreai.