Question

7) Compute the convolution $y(t) = x(t) * h(t)$ of the following pairs of signals (30pts): c) $h(t) = e^{-t}[u(t) - u(t - 2)]$ and $x(t) = \begin{cases} 1, & 0 \le t < 1 \ -1, & 1 \le t < 2 \ 0, & \text{otherwise} \end{cases}$ Determine the output $y(t)$ via convolution of $x(t)$ and $h(t)$.

          7) Compute the convolution $y(t) = x(t) * h(t)$ of the following pairs of signals (30pts):

c) $h(t) = e^{-t}[u(t) - u(t - 2)]$ and $x(t) = \begin{cases} 1, & 0 \le t < 1 \ -1, & 1 \le t < 2 \ 0, & \text{otherwise} \end{cases}$

Determine the output $y(t)$ via convolution of $x(t)$ and $h(t)$.

7) Compute the convolution y(t) = x(t) * h(t) of the following pairs of signals (30pts):

c) h(t) = e^-t[u(t) - u(t - 2)] and x(t) = 1, 0 ≤ t < 1 -1, 1 ≤ t < 2 0, otherwise

Determine the output y(t) via convolution of x(t) and h(t).

Added by Steven E.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Ameer Said

01/10/2022

Step 1

Step 1: For part (a), we first need to express the convolution integral: y(t) = x(t) * h(t) = ∫[x(τ)h(t-τ)]dτ Show more…

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7) Compute the convolution y(t) = x(t) * h(t) of the following pairs of signals (30pts): (a) x(t) = A sin(ωt), h(t) = 2e^(-2t)u(t) (b) x(t) = 1, 0 < t < 1; x(t) = -1, 1 < t < 2; x(t) = 0, otherwise Determine the output y(t) via convolution of x(t) and h(t).