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 , r ~periodic continuation n.p(t) = a) using coiivolution in the time-doamin b) iising the wiivoliitiozi theoreai