Question

Compute and sketch the output $y(t)$ of the continuous-time LTI system with impulse response \\ $h(t) = e^{1-2t}u(t-1)$ for an input signal $x(t) = u(t) - u(t-2)$. Both analytically and graphical \\ method (25 P)

          Compute and sketch the output $y(t)$ of the continuous-time LTI system with impulse response \\
$h(t) = e^{1-2t}u(t-1)$ for an input signal $x(t) = u(t) - u(t-2)$. Both analytically and graphical \\
method (25 P)

Added by Paul L.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Supreeta N

10/31/2023

Step 1

The convolution integral is given by: y(t) = ∫[x(τ)h(t-τ)]dτ Substitute x(τ) = u(τ) - u(τ-2) and h(t-τ) = e^(1-2(τ))u(τ-1) into the convolution integral. y(t) = ∫[(u(τ) - u(τ-2)) * (e^(1-2(t-τ))u(t-τ-1))]dτ y(t) = ∫[u(τ)e^(1-2(t-τ))u(t-τ-1) - Show more…

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Compute and sketch the output y(t) of the continuous-time LTI system with impulse response h(t)=e^(1-2t)u(t-1) for an input signal x(t)=u(t)-u(t-2). Both analytically and graphical method (25 P) Compute and sketch the output y(t) of the continuous-time LTI system with impulse response method (25 P)