Question

U 1.1. Express each of the following complex numbers in Cartesian form (x + jy): bej, ke-ja, eja/2, e-ju/2, 359/2, 2ej#14, 2e396/4, 2e-39714, 2e-ja14 Express each of the following complex numbers in polar form (reje, with - 1 < 0 = T):5.-2-3;, ; - ; 3.1+j, (1 - i)?, j(1 - 1)(1+j)/(1-j), (/2 + ;/2) (1 + 1/3). Determine the values of P. and E. for each of the following signals: (a) xi(t) = e-2u(t) (b) x2(t) = el(21+ 7/4) (C) x3(t) = cos(t) (d) x1[n] = (-)" u[n] (e) x2[n] = ej(/2n+18) (f) x3[n] = cos(n) 1.4. Let x[n] be a signal with x[n] = 0 for n < -2 and n > 4. For each signal given below, determine the values of n for which it is guaranteed to be zero. (a) x[n - 3] (b) x[n +4] (c) x[-n] (d) x[-n + 2] (e) x[-n - 2] Let y(t) be a signal with x(t) 0 font <3For @ch gignal given below determine the Malufs of for which it is guar ntdedko be perd/ Val - (b)x(1 t) 2 V ) XM - M 2-t) (dy x Bt) (e) x(t/3) Determine whether or not each of the following signals is periodic: (a) xi(t) = 2e](1+/4)u(t) (b) x2[n] = u[n] + u[-n] (c) x3[n] = .-{8[n - 4k] - [n - 1 - 4k]}

Answer 1

Sollation 6 stig - Cartefionform | @ ļ eit e = cosxt isina - C057 - Sint #[ cost +3 Sin] *[-1+ jo] ® ₃ est + [costi jsinta] -jo = COS / +jsin (TV2) = otil To elitys = cos the- j sin (11/3) = +0 -JI mille asil ① ist1/2 ECOS (55k) +jsin (3/2) -otig joyeul

л Гоо ту, а зві» уч | 0 л. і 4 Э . - - і ту, 2 п[ - Сту) -ів» (му:) |

52 e 37/4 sa[105 (TV) – jsin (174) following Detamine whether or not each of the Signal sis periodic @BCH) = nej (t+ T4/4 ust). Bot) to ) to two Limits exit so XCE) is aperoidic signal ( () = u(0)+ A(n) kuch) AU-n) -4 3 -2-1 Xatun +4+n) O- --4 -3 - 2 1 n 1 2 3 4 5 Non - periodic Signal Amplitude at tan

determine the values of P and E O @ Lice) - estust P = Lim bine tolle DH T-40 "p= Lim- T-) 2T L P = Lim To 2T P = Lim I Ty02T 4 JO P = Lim Too Je to = 1 2 ) 1 EL 800 Ip=o Energy I lxicts at e dla t to shutdan4

(0) 64(0) (D = e Cat +1447 "T Pe Lim y (t) dt T-021 P = Lim I rolt lat TWT X(t) = cos (24 +71/4) + usin (2+ + 1/4) I cos( 2t + T1/4) + sin (2t + T1/4) las lts] = 4 Poco Limal wat TDO I lim T- = Lim T40 Poo = 1

Po = =+=(0) (po = y2 Energy c = Em = 143060) costat 206 costat tu fost 14 cosat 8 * = 2 at & Il costat - OO - sinat = (00+00) ++ E = 20 @ 10) = Puco) - ()- JE 120 W o else d er Poo= Lim tot 0012 N Poo = Lim NA NI art & Chung f ing ne-N N Lim N70 N+1

Po = =+=(0) (po = y2 Energy c = Em = 143060) costat 206 costat tu fost 14 cosat 8 * = 2 at & Il costat - OO - sinat = (00+00) ++ E = 20 @ 10) = Puco) - ()- JE 120 W o else d er Poo= Lim tot 0012 N Poo = Lim NA NI art & Chung f ing ne-N N Lim N70 N+1

relo- polar form 5ejo = polar form 2--2 VJ *7 ya Y- Jotja - 2 he = 2 Cose -2 -coses t 9 = 2 sine Coso = -1 2 Sino =0 Sine - 0/2 sino ol ajti polar form of 14.2 is the va malo odola x=0 y = - 1 0'+3 = 3 = 3 Cose y = 3 Sino Coso=o 3 sino =-3 Sino = -1 4 The valw of 6 - T Sino = -) COSO = 0 rejo = 36 1/2 I - 3% x= 1/2 y = -5/

15 Jazy? += + (-50%) r=1 x=coso y = sino Coso=Y2 sino = - 3/2, 0 = -1/2 If you have any doubts ask me please Rate my Answer