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5. A causal LTI system S with impulse response h(t) has its input x(t) and output y(t) related through a linear constant coefficient differential equation: d³y(t) , (1+ a)d²y(t) , a(a + 1)dy(t) + dt³ + a?y(t) = x(t) + dt2 dt a) If g(t) dh(t) + h(t), how many poles does G(s) have? dt b) For what real values of the parameter a is S guaranteed to be stable?

5. A causal LTI system S with impulse response h(t) has its input x(t) and output y(t) related through a linear constant coefficient differential equation: d³y(t) , (1+ a)d²y(t) , a(a + 1)dy(t) + dt³ + a?y(t) = x(t) + dt2 dt a) If g(t) dh(t) + h(t), how many poles does G(s) have? dt b) For what real values of the parameter a is S guaranteed to be stable?

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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5. A causal LTI system S with impulse response h(t) has its input x(t) and output y(t) related through a linear constant coefficient differential equation: d³y(t) , (1+ a)d²y(t) , a(a + 1)dy(t) + a²y(t) = x(t) dt3 dt2 dt dh(t) a) If g(t) : + h(t), how many poles does G(s) have? dt b) For what real values of the parameter a is S guaranteed to be stable?
Transcribed Image Text:5. A causal LTI system S with impulse response h(t) has its input x(t) and output y(t) related through a linear constant coefficient differential equation: d³y(t) , (1+ a)d²y(t) , a(a + 1)dy(t) + a²y(t) = x(t) dt3 dt2 dt dh(t) a) If g(t) : + h(t), how many poles does G(s) have? dt b) For what real values of the parameter a is S guaranteed to be stable?
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