Question

A system has an input, x(t) and an impulse response, h(t). Using the convolution integral,

find and plot the system output, y(t), for the combination given below.

x(t) is P3.2(e) and h(t) is P3.2(f).

1/2 cycle of 2 cos at -2. (e)

Answer 1

Answer: falt) - cycle of a cosnt. st con volution of act) and h(t) yct) = X(t) theti © Limits Sum of of yct) Lower limits of all thit) at a Oxt <3. sum of upper limits A

☺ change the axist Ther) 27 xor) k & cycle of ecosnt r ② Folding of herli th(t) - T % shifting of hit-1); ↑ het-y) - to t-2 420 => ylt) = 0. Kt22 - ostali nhit-P) - 817) Ahlf-T). X(T) 카구 yes: Saat = at. YLE) = 1 a 2 coszt dt = (2 sinnt) -2.sina.co Y(f) = 2

2사시35 Thetat).X17) = 2 sin A -Zsina (+-2). y(Ha pz. cosat dt = (2 sinnt) 2 - 2 | 2 2- 2 SinCE-2). 23: Jtc0. coyf<o A1/ 22, 사나 2,사오 2 - 2 Sint 2 ) 2. A FL3 o, 3 수 )