Wiley signals and systems e book TLFe BO 304

11.4. Exercises

289

Exercise 11,11

(11.22) allows [lie spectiiirn of a sigrial J ( t )with period CI' - 1 to bc expr
A,, . Derive the relationship for general 1)erintls T . There
its Fouriclr c.oefficie
to the soliition: a) starting with (11.14) arid (11.18),and
are two posbihle 10
risforiri on ( 11.17).
h) using tlrc Fourie
Exercise 11 12
.
I

Find the Fourier tianqform of (he signal froin Exercihe 1 1.7, usiiig the results froiii
Exercise 11.13

A system with impiilsc rcAsponsc h ( t ) = siii(l) CJ-" I t c ( t ) is excited by a pclriodit.
rcctangle signal x j t ) . Find the output signal : / ( t )as a Foiirier series. Sec Section 11.2.3.

x(f)

t

T

-T

c

Exercise 11.14

C~lciililtr1 1 1 ~cyclic convolution of the signals {(tj and g ( t ) = siri(-~gt)using
I4xirit.r series. First give the t*oiinection between wu arid T,so t h a t thr c y ~ l i c
c*onr.ohitioxiis defined properly.
f(t>

* * ( I

-

t

Exercise 11.15
Consider the spectrum X ( p ) of the sigiial n:(t).