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Can you solve option d in question 3 please And in the other question (1) , can you solve the option g please

Can you solve option d in question 3 please And in the other question (1) , can you solve the option g please

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
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Can you solve option d in question 3 please

And in the other question (1) , can you solve the option g please

3) Consider an LTI system with input x(t) = e-tu(t) and impulse response h(t) = e-2tu(t). a) Determine the Laplace transforms of x(t) and h(t). b) Using the convolution property, determine the Laplace transform Y (s). c) From the Laplace transform of y(t) as obtained in part (b), determine y(t). d) Verify your result in part (c) by explicitly convolving x(t) and h(t).
Transcribed Image Text:3) Consider an LTI system with input x(t) = e-tu(t) and impulse response h(t) = e-2tu(t). a) Determine the Laplace transforms of x(t) and h(t). b) Using the convolution property, determine the Laplace transform Y (s). c) From the Laplace transform of y(t) as obtained in part (b), determine y(t). d) Verify your result in part (c) by explicitly convolving x(t) and h(t).
1) In this problem, we consider the construction of various types of block diagram representations for a causal LTI system S with input x(t), output y(t), and system function 2s2 + 4s – 6 H(s) %3D s2 + 3s + 2 To derive the direct-form block diagram representation of S we first consider a causal LTI system S, that has the same input x(t) as S, but whose system function is: 1 H; (s) s2 + 3s + 2 With the output of S1 denoted by y1(t), the direct-form block diagram representation of S, is shown in Figure-1. The signals e(t) and f(t) indicated in the figure represent respective inputs into the two integrators. d²y1(t) a) Express y(t) as a linear combination of y,(t), dy,(t) and dt dt2 dy (t) b) How is related to f(t)? dt c) How is d?y1(t) related to e(t)? dt2 d) Express y(t) as a linear combination of e(t), f(t), and y,(t). e) Use the result from the previous part to extend the direct-form block diagram representation of S, and create a block diagram representation of S. f) Observing that (s – 1) (s +3 H(s) = s+ 2 draw a block diagram representation for S as a cascade combination of two subsystems. g) Observing that 8. H(s) = 2 + s + 2, draw a block diagram representation for S as a parallel combination of three subsystems. e(t) f(t) S x(t) y1(t) -3 -2
Transcribed Image Text:1) In this problem, we consider the construction of various types of block diagram representations for a causal LTI system S with input x(t), output y(t), and system function 2s2 + 4s – 6 H(s) %3D s2 + 3s + 2 To derive the direct-form block diagram representation of S we first consider a causal LTI system S, that has the same input x(t) as S, but whose system function is: 1 H; (s) s2 + 3s + 2 With the output of S1 denoted by y1(t), the direct-form block diagram representation of S, is shown in Figure-1. The signals e(t) and f(t) indicated in the figure represent respective inputs into the two integrators. d²y1(t) a) Express y(t) as a linear combination of y,(t), dy,(t) and dt dt2 dy (t) b) How is related to f(t)? dt c) How is d?y1(t) related to e(t)? dt2 d) Express y(t) as a linear combination of e(t), f(t), and y,(t). e) Use the result from the previous part to extend the direct-form block diagram representation of S, and create a block diagram representation of S. f) Observing that (s – 1) (s +3 H(s) = s+ 2 draw a block diagram representation for S as a cascade combination of two subsystems. g) Observing that 8. H(s) = 2 + s + 2, draw a block diagram representation for S as a parallel combination of three subsystems. e(t) f(t) S x(t) y1(t) -3 -2
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