Question

4) Special Signals: Three special signals: the impulse, the unit step, and the complex exponential, are easy to convolve. The convolutions are: (1) 8(t) = (0) 56) • u(e) - (audix T() • xe = xe | F(x) = If possible verify, numerically and symbolically, each of the convolutions with the three special signals for each of the special signals of the prelab.

Answer 1

result Inaf : ZP(2.7 (4) The i onvolution of function flt) with unit impuse a in function flt) itself 410) * Sit)- flt) flt) x 8(t)= 1 (7)8[t-z)dz from sampling property of unit impulse flt)slt-)= f12)Slt-?) - ftus.sitzvoz = flt) jott-tooz - fit) 1 = fit) example: ylt) + 8 lt). - rit) (11] flt) * Ult) = 1 fluidh t

ylt): f(t) * ult) Take laplace Hansform ult) , y (s)= f[s). we know convolution property of laplece transform lonvolution in time domain correspond to multiplication in s domain Yls): FLS) Take transform inverse laplace se your guide - Igress out on 2 example ult) x uit + fulnldu - Yit) f(t) test (1) . we know convolution Integral formula ylt): f101# hlt) you)- Shewhlt-e) O

Yll): +11) x xest on des | | xcº da W = yese. Itemsersoon example Take tive ort ult) - je tu may eie = ezmest.eshon = Xest jesinan . C ec i Xest et 2-sin 100 2-5 l . = xente que vou