Question

(50 pts) Determine whether each of the following signal is periodic. If the signal is periodic, find its fundamental period. (a) x(t) = 4, a constant signal. (b) x(t) = 28ej (400#t) (c) x[n] = 28ej(1007n) (d) x(t) = 10 sin(5t) - 4 cos(7t) (e) x[n] = 10 sin(5n) - 4 cos(7n) (f) r(t) = cos(Ft) sin(ft) (g) x(t) = teit (h) x[n] = e(m/v2) (1) x[n] = cos(km2) (Pay attention to the square) (j) x[n] = {X- 8[n - k) (k is an integer)

Answer 1

A continuous time signal will have a definite patteon Thet oeßearts of arogasamos queo a certains periodi e tirane A periodic Signal is an everlasting signal to to too] 12CA I TO) = Zelt) To - dom dromental time period on seconds = femdemental focquercy in Hz Lip = 2740 = 27 = dera deramental cogcrcro frequency in Dadics/sec Ô Sigma Mike A Simcoat, A Coswof, A Smloof +0), ACOSC025 +) A etat e (att() erre periodic colto

o Multiple signal periodicity ea costad & Sinert Seno cost = 22 7 Step Ita auto at integoof ant T2 = 22 I then periodic # fortio G- integer than non periodic Step3 Toa Lan (5, 1) Sieht Wo= 22 cy COF H.C+(67,6) * for discoctoe 96 2001N) = 2(0) where Noi Imde mental discoe te time bediod goo + domain a given Sigaal (coscoe q Sim wt ) ill always periodic but in n domin (roscom, sms) should be Checked by following conditions Codicm en tant - Home - gatio of integrantes Condition ..gato alimdegos i goccios om, Mb= q (only devorinato Veico) 2011 codo o heromonig (onciltiple ca foequeX) ,2017 R NO=9

© 21(+) = 4 *2111) periodic with heriodo © 26+)- 28 €7C4001:) = 28 COS 46027 ti28 Sim 40057 bedodic Twot periodic Co=22 22 E = 34 00 Woc.27 T- T: 00 T=2 (Wo-4002 T - - 200 osec 211) ig bediodic © 21cm = 28 @J40030) maio - Como = p q = peood me = = Patio oko mtego o Condition ce 22 Periodic too = 4000 m No = 4002 - 200 4 patioce mieger 27 so zun) is periodic with No al 2161) lo sro 5 - 4 C0574 2=5 W2=7 I I. 22 72 = 3 7ndatio of 5 integer ?, 23 APE = 27 SO 2264) is besiddia Semut

trame period To = LCH (7.53) To-L.Cm Gm (2, 2) = - LCK c. J L.CK Col nimeoita EL.C*(9,0) HF CL denominato CD To - L.com (27, 22) = 22 H.CF ( 5,7) T =22 uco) = 10 sm 50 - 4 00570 - Wo -6 10 Sm50 Sincess .- 1 22 .5 22 ratio of integer & costo lo =2 & + vatio men zu ratio of mtego intese so zoom is not periodic sequence © 26+) = CSF. Smo pat ..206 z COSA SMB - Sim (1946) - Sim CA-B) 244) = sim(a +3) * -Sim (2-5)+ 247 = Sinza - sim 2 ut

26= Smat - som att 34 - of a motho ab-interes - atio ab imteger So 26) is periodic Sigma To = Loc.ta (7,5) = LICK=() LEE 311) = ę =8 Time period - T-8 . TA 2017- De at costti & sint all fcost t sont 264) is not periodic

© 260= e p*kzekana 1. HIS hot someone the batter y + Partio co Integer 2cm) is not pedidic Sequence. 20m) cos(307) © fry periodic fractica 26014 No) = 200) 2(776) = cos (5(0+63 depomimatco No 28 mo 2160) - cos(o) = 1 2(946) - cos() cod = cos(87) 33 071 21000) = cos(3) -0.92 u(976)-(02 (17837] = 0.92 n=2 21(3) = cos (72+9)=0 (2+8) = cos( 7 (2+87 30.92 - = -0.92 So cos( 302) is beviodic couth No 78

སད་ (འ) 2CD) – SCO - ]c) །༩ D༡oཛད་ ]< --︽ 2. Co） = S(m）+SCO༧）༈ So-2) - - - SC+）， 8Cm42) ， ༽ 2to） - + =5 -2 ༢ ། ། ། ། ། ། ། popo Beood Times I screampie -j （255 zeln is periodic with Seten FORD Besiod IN besiod I N= e scomple
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