Question

A system is formed by cascading two systems as shown in the figure given below. Given that the impulse responses of the systems are, h1(0) = 22e-* u(1), h₂( = e ult) -40 hi(t) h2(t) Vo References eBook & Resources Section Break Difficulty: Medium Learning Objective: Un into the time domain. value: 10.00 points Determine the impulse response of the overall system. The impulse response of the overall system is h(t) = (Click to select) v (Click to select) v lel S] u(t).

Answer 1

I solved the problem using the principle of :convolution in time domain is equals to multiplication in frequency domain..

Please do observe in images.. Thank you.. Have a nice day... :)

Solution :- SLAL Given system, is, hilt) hace) V. Vi hát) = ? is Overall res response hat= bi(t) * halt) convolution we know that the convolution the convolution in time domain multiplication in frequency domain . H() Hi() XH265) < (say Laplace domain Given hi(t) = 22ē ult) halt) = 4t u(t). & We have zatult) sta Hics) 22x I St Hals) sty Sty

HIS). HITS) x Hols) 22 (+1) CS44) - split split this to partial fractions, 22 + (5+1)(ST4) B sty St - 22 - A (5+4) +B(5+1 22 AST4A + BStB S(A+B) + 4A+ 22 Compare both sides. =) A+B=0 = A=-B & B-A & YA+B = 22 22 Į YA+(-A = 22 3A = 22 А. 22 3 ,50 B=-29 3 Now, H()= (33 + 699) St1 Inverse laplace transform of this is, S+4 hit) .t ခံ aa aut Jult) 3 That's it... ☺