Question

Question to Given the signal xlt) = Arect ( +++h)- Arect (+-1/2) find X(w) using a Time delay property. 5] Time integration property. a plot the magnitude and phase spectrum. ne

Answer 1

Al)= A veut (+*})_ Axect ( @ we have a rect ( + ) o At Singh time-delay property if S(E) ESW) 2 St-to) e su to su *. *v)= AT sine (1) Teens every pj@_ēją z2j sino sin(WI). XW)=jZAT sing a wille Sin CO ) - Sinito tro . It

Afect (2) A fect ( + - 12 ) 4 Arect ( + + 7 ) TA L A UG+T)-2A u(t) + A U(L-T) di fferentiate it) akt)-d 10), A SE +) -2A 8(t) +AS(1-7)

Note: I lust ito)=sitetto finding Fot of x'(t) x'(U)= A UWT ZA TA EJUT St-to) bejuto x(W) = -2A ta cejas tējat)

xlcy1 = (exis IA) HeviaT_A) =A[int } +A Levar ] - A piate Lowe ejar to enlarge che very - Adverte [2sincez)] - aj ne biste (sin (:) = 2ja sin(at) [cvw.event) x'@) - Zja sin(WI) aj since I) we have time-integration property skapes are cea xlu) = xw

.. jw Kole seo X@w]= då sin(k) disin() = PAT sin(W) 2j sin(W!) xw) = 2; At since we ) sin(a) - proved & both @ & are same Magnitude |XW) = 2A7|5inc (|sia (en) ) XX) = 4Aj sinaw) w X®) = foom

- l hopitals rule X@)= YAj It hele sio (91) W- d (w) = Gaj 14(172 sin(!) 65(WT) W Xe) - 0

*(5) - YAMT since ) = YAT (3C XCID- 4T - YPF (-40 8(* )= X(-20) = 0 dearly phaye CX (WTF! 1=90, uno (-j=-90, wao |xw/ magnitude magnitude F [ phase I 90°