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For each the following systems, we specify the output y(t) corresponding to input x(t). Determine, for each system, which of the following properties hold (more than one property may hold for any given system): linearity, time-invariance, stability and causality. (a) y(t) = x²(t+3) (b) y(t) = t¹x(t+3) (c) y(t) = 20000 x(t-1)

For each the following systems, we specify the output y(t) corresponding to input x(t). Determine, for each system, which of the following properties hold (more than one property may hold for any given system): linearity, time-invariance, stability and causality. (a) y(t) = x²(t+3) (b) y(t) = t¹x(t+3) (c) y(t) = 20000 x(t-1)

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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For each of the following systems, we specify the output \( y(t) \) corresponding to input \( x(t) \). Determine, for each system, which of the following properties hold (more than one property may hold for any given system): linearity, time-invariance, stability, and causality. (a) \( y(t) = x^4(t + 3) \) (b) \( y(t) = t^4 x(t + 3) \) (c) \( y(t) = 20000 \times(t - 1) \) (d) \( y(t) = \int_{-\infty}^{t-1} 2x(\tau) d\tau \) (e) \( y(t) = \int_{t-4}^{t} 5x(\tau) d\tau \) (f) \( y(t) = \int_{t}^{t+1} e^{2x(\tau)} d\tau \)
Transcribed Image Text:For each of the following systems, we specify the output \( y(t) \) corresponding to input \( x(t) \). Determine, for each system, which of the following properties hold (more than one property may hold for any given system): linearity, time-invariance, stability, and causality. (a) \( y(t) = x^4(t + 3) \) (b) \( y(t) = t^4 x(t + 3) \) (c) \( y(t) = 20000 \times(t - 1) \) (d) \( y(t) = \int_{-\infty}^{t-1} 2x(\tau) d\tau \) (e) \( y(t) = \int_{t-4}^{t} 5x(\tau) d\tau \) (f) \( y(t) = \int_{t}^{t+1} e^{2x(\tau)} d\tau \)
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As per our company guidelines we are supposed to answer only first three subparts kindly repost the other parts in next question, 

We need check linearity , stability , causality and time invariant for given system .

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