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Test the following systems for linearity. dx(t) dt a) y(t) = 4 x(t) + 2 b) d²y(t) dt² +2 dy(t) dt + 3 y(t) = x(t)

Test the following systems for linearity. dx(t) dt a) y(t) = 4 x(t) + 2 b) d²y(t) dt² +2 dy(t) dt + 3 y(t) = x(t)

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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SS_assignment_apr. GOVERNMENT ENGINEERING COLLEGE, RAJKOT E.C. DEPARTMENT SEM-IV Subject: Signals and Systems (3141005) AssignmentNo-2 (CO2) Questions/Problems State whether the following systems are time invariant or not. dx(t) а) у() %3D 2 еҹр b) y(t) = x(t) + C c) y(t) = 3x²(t) d) y(t) = x(t) + dt e) y(t) = x(t) + ] %3D Test the following systems for linearity. dx(t) d'y(t) dy(t) a) y(t) = 4 x(t) + 2 dt b) dt? + 2 + Зy() x(t) dt Test the causality of the following systems. a) y(t) = x(t) + 3 x(t + 4) b) y(t) = x(t°) c) y(t) = x(2t) d) y(t) = x(-t) %3D Determine the range of values of "a" and "b" for the stability of LTI system with impulse respe h(t) = eat u(t) + e-b" u(t) Perform convolution of the following causal signals. a) x,(t) = 2 u(t), x_(t) = u(t) b) x,(t) = e-2ª u(t) , x,(t) = e-St u(t) %3D %3D %3D c) x,(t) = t u(t), x,(t) = e-St u(t) d) x,(t) = cos t u(t) , x_(t) = t u(t) %3D %3D If two LTI systems with impulse responses, h,(t) = e¯“ u(t) and h,(t)= e¯"u(t) -bt е -at connected in cascade, what will be the overall impulse response of cascaded system?
Transcribed Image Text:SS_assignment_apr. GOVERNMENT ENGINEERING COLLEGE, RAJKOT E.C. DEPARTMENT SEM-IV Subject: Signals and Systems (3141005) AssignmentNo-2 (CO2) Questions/Problems State whether the following systems are time invariant or not. dx(t) а) у() %3D 2 еҹр b) y(t) = x(t) + C c) y(t) = 3x²(t) d) y(t) = x(t) + dt e) y(t) = x(t) + ] %3D Test the following systems for linearity. dx(t) d'y(t) dy(t) a) y(t) = 4 x(t) + 2 dt b) dt? + 2 + Зy() x(t) dt Test the causality of the following systems. a) y(t) = x(t) + 3 x(t + 4) b) y(t) = x(t°) c) y(t) = x(2t) d) y(t) = x(-t) %3D Determine the range of values of "a" and "b" for the stability of LTI system with impulse respe h(t) = eat u(t) + e-b" u(t) Perform convolution of the following causal signals. a) x,(t) = 2 u(t), x_(t) = u(t) b) x,(t) = e-2ª u(t) , x,(t) = e-St u(t) %3D %3D %3D c) x,(t) = t u(t), x,(t) = e-St u(t) d) x,(t) = cos t u(t) , x_(t) = t u(t) %3D %3D If two LTI systems with impulse responses, h,(t) = e¯“ u(t) and h,(t)= e¯"u(t) -bt е -at connected in cascade, what will be the overall impulse response of cascaded system?
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