Question

The output of a simple system is given by the integral \(y(t) = \int_{-\infty}^{\infty} x(t')h(t+t')dt'\) a) Determine \(y(t)\) when \(x(t) = 8e^{-2t}u(t)\) and \(h(t) = e^{-2t}u(t)\) It may help to sketch the step functions of the integrand and their product as \(t'\) varies from \(-\infty\) to \(+\infty\) b) sketch \(y(t)\) and find its maximum value.

          The output of a simple system is given by the integral \(y(t) = \int_{-\infty}^{\infty} x(t')h(t+t')dt'\) 
a) Determine \(y(t)\) when \(x(t) = 8e^{-2t}u(t)\) and \(h(t) = e^{-2t}u(t)\) It may help to sketch the step functions of the integrand and their product as \(t'\) varies from \(-\infty\) to \(+\infty\)
b) sketch \(y(t)\) and find its maximum value.

The output of a simple system is given by the integral y(t) = ∫-∞^∞ x(t')h(t+t')dt'
a) Determine y(t) when x(t) = 8e^-2tu(t) and h(t) = e^-2tu(t) It may help to sketch the step functions of the integrand and their product as t' varies from -∞ to +∞
b) sketch y(t) and find its maximum value.

Added by Eugene A.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Ankur S

Step 1

Given x(t) = e^(-2t) and h(t) = e^(-2t), we can substitute these values into the integral equation y(t) = x(t) * h(t). Show more…

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The output of a simple system is given by the integral y(t) = x(t) * h(t). Determine y(t) when x(t) = e^(-2t) and h(t) = e^(-2t). Sketch the step functions of x(t) and h(t) as the integral varies from 0 to t and find its maximum sketch FK value.