Consider the following first-order, causal LTI differential system S₁ initially at rest: dx(t) dt (a) Calculate the impulse response h₁(t) of the system S₁. Sketch it for a = 2. S₁: dy(t) dt + ay(t) = - 2x(t), a>0 is real.
Consider the following first-order, causal LTI differential system S₁ initially at rest: dx(t) dt (a) Calculate the impulse response h₁(t) of the system S₁. Sketch it for a = 2. S₁: dy(t) dt + ay(t) = - 2x(t), a>0 is real.
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![### First-Order, Causal LTI Differential System
Consider the following first-order, causal LTI differential system \( S_1 \) initially at rest:
\[ S_1: \frac{dy(t)}{dt} + ay(t) = \frac{dx(t)}{dt} - 2x(t), \quad a > 0 \text{ is real}. \]
(a) **Problem:**
Calculate the impulse response \( h_1(t) \) of the system \( S_1 \). Sketch it for \( a = 2 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa3024194-76c9-4825-bbff-ab6be87fbb17%2F1bbec3f4-279b-4b00-bd1a-cce0980aecaa%2F6luy646_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### First-Order, Causal LTI Differential System
Consider the following first-order, causal LTI differential system \( S_1 \) initially at rest:
\[ S_1: \frac{dy(t)}{dt} + ay(t) = \frac{dx(t)}{dt} - 2x(t), \quad a > 0 \text{ is real}. \]
(a) **Problem:**
Calculate the impulse response \( h_1(t) \) of the system \( S_1 \). Sketch it for \( a = 2 \).
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