Question

The impulse response h(t) of a linear time-invariant system is 2*pi[(t-2)/2]. Find and plot the output when the system is driven by an input signal that is identical to the impulse response.

Answer 1

Given data impulse response hlt) of a lineare - Lime invacient system Spil (t-a)/a] + ax (4) a function Rectangulare function also known as rect (t) t(e) 2014 a les per input identical to impulse response 8 +) HIP olp.yt) ho) input * h(1) same 7 output 2 convolution 84) * hut) ocel put 96) $4) will any signal convoluted with Яve signal. a(1) * $ (4) x(+) 8+) x 4 tact (3) et 19 VJ – a meet so output 46) = 2 a needle meeste 2 Arect Lt) < A reett) -42 % arrelttt ) -12 12 Method-1 a rect[et 137 sa reet[4 (6-8)] greet (14) Sealing - U) scaling by Ya. 2 reet ( ((-2)] shifting by (a) reight shift 12 a sealing by that ta it ya ya reight shift by 2 th arect 3 Method-a aneet = greecet (12-1) 2 Meet (t-1) Right shift by 1 2 rect ( / 2-1) scaling by 1/2 . 2 → 312 Ya 3/2 1+1 Ya а reight shift by 1 scaling by Brett)