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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) s2 + 3s + 2 To derive the direct-form block diagram representation of S we first consider a causal LTI system Si that has the same input x(t) as S, but whose system function is: 1 H, (s) = s2 + 3s + 2 With the output of S 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. d²y,(t) a) Express y(t) as a linear combination of y,(t), dy1(t) and dt dt2 dy (t) b) How is related to f(t)? dt c) How is d²y1(t) related to e(t)? dt2

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) s2 + 3s + 2 To derive the direct-form block diagram representation of S we first consider a causal LTI system Si that has the same input x(t) as S, but whose system function is: 1 H, (s) = s2 + 3s + 2 With the output of S 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. d²y,(t) a) Express y(t) as a linear combination of y,(t), dy1(t) and dt dt2 dy (t) b) How is related to f(t)? dt c) How is d²y1(t) related to e(t)? dt2

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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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) = s2 + 3s + 2 To derive the direct-form block diagram representation of S we first consider a causal LTI system S1 that has the same input x(t) as S, but whose system function is: 1 H; (s) = s2 + 3s + 2 With the output of S 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. d²y,(t) a) Express y(t) as a linear combination of y1(t), dy (t) and dt dt2 dy (t) b) How is dt related to f (t)? d²y1(t) с) How is - related to e(t)? dt2
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) = s2 + 3s + 2 To derive the direct-form block diagram representation of S we first consider a causal LTI system S1 that has the same input x(t) as S, but whose system function is: 1 H; (s) = s2 + 3s + 2 With the output of S 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. d²y,(t) a) Express y(t) as a linear combination of y1(t), dy (t) and dt dt2 dy (t) b) How is dt related to f (t)? d²y1(t) с) How is - related to e(t)? dt2
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