Question

2. Determine the CTFT of the following signals, then plot the magnitude spectrum (a) X(t) e2lt| (b) X(t) ea u(t), a > 0 (c) X(t) e4 (d) X(t) 6(t-3)

Answer 1

Prololem 2 Determine tthe TFT e y-llorny signals, then plt tte magnitudo speetum; la) x (t)eat u(t), ^>o , (c) x{t)= e4t (a) xtt)=>(t-3)= -2/t Ans (a) n (t = e -llt hnaphicad noprosentatun vitt be, nlt N3, F() لله at t e t2-w) dt t-2-j^) dt ءt-2 -دهز) 2 -2-) (2 +)(2-j6) 2 W 2 +jw 4 - 4 Manitude spectrum , F()

ib) u (t) apieot representatin, utt) 1 jut st Naa Fl) at SO.ES 0. e e. unit stp funetion dt -la tw) - (a4jw) Magrictnde ypeetium, Flw) hase speitum, rhase Flw)

e4t (C) Gnaphical hepresautatim و لم " -jut dt F (w) x (t e dt - (4+jw)t e -(4tjw)t 4 ع)- داز< -(4+ju) 1 4 Magnitude plat,

(d) naphieal napresantatim , D 2 2 F) e -3jw e As, - sin 3 D os 3 Manitude plat, .Fl) 3A -1