Question

For each of the following systems, show whether or not the system is time-invariant. (a) y(t) = x(t)u(t) (b) y(t) = |x(t)| (c) y(t) = x(t)x(2t) (d) y(t) = ∫₀ᵗ x(τ)e^(-τ)dτ (e) (dy(t))/(dt) + ty(t) = x(t) Notes: • To show that a system has a given property, it should be shown that the property holds for all possible inputs. • To show that a system does not have a property, giving one counterexample is sufficient.

Name: for each of the following systems show whether or not the system is time invariant a yt xtut b yt xt c yt xtx2t d yt 0t xe d e dytdt tyt xt notes to show that a system has a given property i 14465
Uploaded: 2022-04-10T16:59:15-08:00
Duration: 3 min 34 s
Channel: Sikandar Baig
Description: for each of the following systems show whether or not the system is time invariant a yt xtut b yt xt c yt xtx2t d yt 0t xe d e dytdt tyt xt notes to show that a system has a given property i 14465

          For each of the following systems, show whether or not the system is time-invariant.

(a) y(t) = x(t)u(t)
(b) y(t) = |x(t)|
(c) y(t) = x(t)x(2t)
(d) y(t) = ∫₀ᵗ x(τ)e^(-τ)dτ
(e) (dy(t))/(dt) + ty(t) = x(t)

Notes:
• To show that a system has a given property, it should be shown that the property holds for all possible inputs.
• To show that a system does not have a property, giving one counterexample is sufficient.

Added by Melanie G.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Sikandar Baig

04/10/2022

Step 1

Let's consider a shifted input x(t - τ), where τ is a constant. The corresponding output would be y(t - τ) = x(t - τ)u(t - τ). Comparing y(t) = x(t)u(t) with y(t - τ) = x(t - τ)u(t - τ), we see that the system is time-invariant because shifting the input results Show more…

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For each of the following systems, show whether or not the system is time-invariant. (a) y(t) = x(t)u(t) (b) y(t) = |x(t)| (c) y(t) = x(t)x(2t) (d) y(t) = ∫₀ᵗ x(τ)e^(-τ)dτ (e) (dy(t))/(dt) + ty(t) = x(t) Notes: • To show that a system has a given property, it should be shown that the property holds for all possible inputs. • To show that a system does not have a property, giving one counterexample is sufficient.