Question

Question 1: Consider a CLTI system has the input signal x(t) and the impulse response h(t). Use convolution integral and the analytical method to find the system's output y(t). (a) x(t) = e^(-2t)u(t - 2), h(t) = u(t - 4) (b) x(t) = r(t), h(t) = rect((t - 4)|6) Answers: (a) -1/2(e^(-2t+8) - e^(-4))u(t - 6) (b) y(t) = 1/2(t - 1)^2u(t - 1) - 1/2(t - 7)^2u(t - 7)

          Question 1:

Consider a CLTI system has the input signal x(t) and the impulse response h(t). Use convolution integral and the analytical method to find the system's output y(t).

(a) x(t) = e^(-2t)u(t - 2), h(t) = u(t - 4)
(b) x(t) = r(t), h(t) = rect((t - 4)|6)

Answers:

(a) -1/2(e^(-2t+8) - e^(-4))u(t - 6)

(b) y(t) = 1/2(t - 1)^2u(t - 1) - 1/2(t - 7)^2u(t - 7)

Question 1:

Consider a CLTI system has the input signal x(t) and the impulse response h(t). Use convolution integral and the analytical method to find the system's output y(t).

(a) x(t) = e^(-2t)u(t - 2), h(t) = u(t - 4)
(b) x(t) = r(t), h(t) = rect((t - 4)|6)

Answers:

(a) -1/2(e^(-2t+8) - e^(-4))u(t - 6)

(b) y(t) = 1/2(t - 1)^2u(t - 1) - 1/2(t - 7)^2u(t - 7)

Added by Michael C.

Calculus: Early Transcendentals

James Stewart 8th Edition

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Consider a continuous-time linear time-invariant (CLTI) system with the input signal x(t) and the impulse response h(t). Use the convolution integral and the analytical method to find the system's output y(t). (a) x(t) = 2tu(t) - 2, h(t) = u(t - 4) (b) x(t) = r(t), h(t) = rect((t - 4)/6) Answers: (a) y(t) = e^(-2t+8) * e^(-4j*u(t - 6)) (b) y(t) = (t - 1)u(t - 1) - (1/2)(t - 7)^2u(t - 7)