Q5) Compute the output y(t) of the systems below. In all cases, consider the system with zero initial conditions. TIP: use the convolution table and remember the properties of convolution. a) h(t) = 3 exp(-2t) u(t) and input x(t) = 2 exp(-2t) u(t) b) h(t) = 28(t)-4 exp(-3t) u(t) and input x(t) = 3 u(t) c) h(t) = 2 exp(-t) u(t) and input x(t) = 4 exp(-2t) cos(3t) u(t)
Q5) Compute the output y(t) of the systems below. In all cases, consider the system with zero initial conditions. TIP: use the convolution table and remember the properties of convolution. a) h(t) = 3 exp(-2t) u(t) and input x(t) = 2 exp(-2t) u(t) b) h(t) = 28(t)-4 exp(-3t) u(t) and input x(t) = 3 u(t) c) h(t) = 2 exp(-t) u(t) and input x(t) = 4 exp(-2t) cos(3t) u(t)
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Transcribed Image Text:Q5) Compute the output y(t) of the systems below. In all cases, consider the system with zero initial
conditions. TIP: use the convolution table and remember the properties of convolution.
a) h(t) = 3 exp(-2t) u(t) and input x(t) = 2 exp(-2t) u(t)
b) h(t) = 28(t)- 4 exp(-3t) u(t) and input x(t) = 3 u(t)
c) h(t) = 2 exp(-t) u(t) and input x(t) = 4 exp(-2t) cos(3t) u(t)
![Q5.) a) h(t) = 3 exp(-2t) u(t) and input x(t) = 2 exp(-2t) u(t)
conv(x(t),h(t)) = 6*t*exp(-2*t)*u(t)
B conv(x(t).h(t)) = t*exp(-t)*u(t)
conv(x(t).h(t)) = 2*t*exp(-t)*u(t)
conv(x(t),h(t)) = 5*exp(-2*t)*u(t)
Q5.) b) h(t) = 28(t)-4 exp(-3t) u(t) and input x(t) = 3 u(t)
A conv(x(t),h(t)) = u(t) + 2*(1-exp(-3*t))*u(t)
B conv(x(t).h(t)) = 7*u(t) +9*(1-exp(-3*t))*u(t)
conv(x(t),h(t)) = 4*u(t)-(1-exp(-3*t))*u(t)
conv(x(t),h(t)) = 6*u(t) - 4*(1-exp(-3*t))*u(t)
Q5.) c) h(t) = 2 exp(-t) u(t) and input x(t) = 4 exp(-2t) cos(3t) u(t)
conv(x(t).h(t)) = 6*[0.1*exp(-3*t) - 0.6*exp(-2*t) *cos(3*t+71.56°)]* u(t)
B conv(x(t).h(t)) = [0.2*exp(-t) - 0.125*exp(-2*t)*cos(3*t+71.56°)]*u(t)
conv(x(t).h(t)) = 8*[0.1*exp(-t) - 0.316*exp(-2*t)* cos(3*t+71.56°)]*u(t)
conv(x(t).h(t)) = 8*[0.1*exp(-t) - 0.316*exp(-t)*sin(3*t+71.56°)]*u(t)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F10a9f489-d438-4273-b76d-cc8abf92d638%2Ffdc906a9-4742-499f-a002-7737a80f2b7b%2Fuccd6p_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Q5.) a) h(t) = 3 exp(-2t) u(t) and input x(t) = 2 exp(-2t) u(t)
conv(x(t),h(t)) = 6*t*exp(-2*t)*u(t)
B conv(x(t).h(t)) = t*exp(-t)*u(t)
conv(x(t).h(t)) = 2*t*exp(-t)*u(t)
conv(x(t),h(t)) = 5*exp(-2*t)*u(t)
Q5.) b) h(t) = 28(t)-4 exp(-3t) u(t) and input x(t) = 3 u(t)
A conv(x(t),h(t)) = u(t) + 2*(1-exp(-3*t))*u(t)
B conv(x(t).h(t)) = 7*u(t) +9*(1-exp(-3*t))*u(t)
conv(x(t),h(t)) = 4*u(t)-(1-exp(-3*t))*u(t)
conv(x(t),h(t)) = 6*u(t) - 4*(1-exp(-3*t))*u(t)
Q5.) c) h(t) = 2 exp(-t) u(t) and input x(t) = 4 exp(-2t) cos(3t) u(t)
conv(x(t).h(t)) = 6*[0.1*exp(-3*t) - 0.6*exp(-2*t) *cos(3*t+71.56°)]* u(t)
B conv(x(t).h(t)) = [0.2*exp(-t) - 0.125*exp(-2*t)*cos(3*t+71.56°)]*u(t)
conv(x(t).h(t)) = 8*[0.1*exp(-t) - 0.316*exp(-2*t)* cos(3*t+71.56°)]*u(t)
conv(x(t).h(t)) = 8*[0.1*exp(-t) - 0.316*exp(-t)*sin(3*t+71.56°)]*u(t)
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