Question

Consider a LTI-causal system, ht is given below and let x1t=δ(t)

ht=5e-tut-u(t-4)

Plot ht

Find and plot y1t if: y1t =ht*x1t (convolution)

Find and plot y2t: y2t=ht*[x1t-6+x1(t-10)].

Find and plot: y3t = y1t+ y2t

Answer 1

Ap(t) SH) h (t) = set (18) - ut-4) Ų ht) (A x S 1 sen t t 0 1 2 3 to hlt) **, ft) = (+) 'Ã (i) From one of the convolution properties, f(t) * 8(t) f(t) f1t) * $(t+2) = (077) f (7) '6 h (t) * Sit) a shit) se - Luck) -468-10] 9:> = se "fukt) - vit-u] 5 56% t hct) * (2) ylt) = hét) ** t-6) +2, (4-10) (4-6) + $(t-10 - Sutt) * $(4-6)+ {hctz 92 (t) = n(t-6)+ K+-10) h(H * ((01-) * yat) -4 5t se S -4 10e Se-4 ! 2 t 5 6 7 8 9 10 3 4 11121314

(7) 6 () 5 9, (t) + y it ht) + h(4-6) th(t-10 9,1t) Yelt) = For osta 6 have Y aft) =ht) we yot -4 Se --> For 6 staro, have, y(t) = yft):ht) we 5 -4 se T st 2 4 2 10 For lostal4 -4 to- stse stré T کے 5 -4 loe K $64 Sey T + t 2 ų 6 8 10 12 'y

Yz(t) -4 Se st ts 5 -4 loe seu >t 6 2 (2 14 16