Question

Write the time domain function r(t) of the graph below as the sum of two rectangular pulse functions, then compute the fourier transform X(w) in terms of sinc function. (Reminder: A rectangular pulse centered 50,427 at the origin with width 27 is defined as II(t) = 11, -T<t<+T and it has the fourier transform II(t) sincwr)) 1 0 Amplitude -1 -2 0 2 3 8 9 10 11 5 6 7 Time-

Answer 1

+ -Lo llist 1 Ts & C FC flt-a) flit-a) 20 + -Ita a Tra ft-a) 2T D It-alat - 1 -Tta< t <Tta 2 5 M -2 4 X2 (4) 2 8. 2 + -2

= x, (it) + X₂ ( t) alt) n, (A) 3 3 T t-4.5 1 54.56 It-4.51×1 3 5<t < 6 X2(87 2 15 (78 =-2 TT & - 5 6 1 2 t - 510 0 -2 2 < t < 8 +371*19) -2014 t-5 6 3 - 2 5 <t <6 +2 < t <8 other wise FT F(W) FT ft-tol АТ to F(w) ējut. FT >2At Simc(WT)

3T FT + 3X1 Sine (W) 1 FT alt) = 371 t -4.51 1 - 3 Sinc (W) jusw FT ЕТ - 21 ( 17 ) - 2X 6 Sinc/3w) myld=- 21714) -- 12 Sime (3W) zysw x (I) = 4, (+) + R₂ (7) FT x(w) = x, (W) + X2 (W) |x|w) = 3 sme (W) 34.56 - 12 Simc (3W) e 15w 2 Answer