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 = , 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- X I (p) and zZ(t)o the U-symbol and skel tli both functions of time XI 0'64 X2CjQ)) * - w x -E * E -t -3 (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 )