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Problem 1. (10 pts each) Consider the CT systems in textbook problem 1.27, page 61. For this HW, you only need to consider whether the system is linear, time-invariant, memoryless. You must provide reasonable proof for each question to get full credit. (a) Is the CT system in P1.27(a) linear? (b) Is the CT system in P1.27(a) time-invariant? (c) Is the CT system in P1.27(a) memoryless? (d) Is the CT system in P1.27(b) linear? (e) Is the CT system in P1.27(b) time-invariant? (f) Is the CT system in P1.27(b) memoryless? 1.27. In this chapter, we introduced a number of general properties of systems. In partic- ular, a system may or may not be (1) Memoryless (2) Time invariant (3) Linear (4) Causal (5) Stable Determine which of these properties hold and which do not hold for each of the following continuous-time systems. Justify your answers. In each example, y(t) de- notes the system output and x(t) is the system input. 62 42 Signals and Systems Chap. 1 (a) y(t) = x(t − 2) + x(2 − t) (c) y(t) = 2x(T)dT - (b) y(t)= [cos(3t)]x(t) 0, t<0 0, x(t) <0 (e) y(t) = { x(t) + x(t − 2), x(t) = 0 (g) y(t): = dx(1) dt - (d) y(t) = { x(t) + x(t − 2), 1≥0 (f) y(t) = x(t/3)

Problem 1. (10 pts each) Consider the CT systems in textbook problem 1.27, page 61. For this HW, you only need to consider whether the system is linear, time-invariant, memoryless. You must provide reasonable proof for each question to get full credit. (a) Is the CT system in P1.27(a) linear? (b) Is the CT system in P1.27(a) time-invariant? (c) Is the CT system in P1.27(a) memoryless? (d) Is the CT system in P1.27(b) linear? (e) Is the CT system in P1.27(b) time-invariant? (f) Is the CT system in P1.27(b) memoryless? 1.27. In this chapter, we introduced a number of general properties of systems. In partic- ular, a system may or may not be (1) Memoryless (2) Time invariant (3) Linear (4) Causal (5) Stable Determine which of these properties hold and which do not hold for each of the following continuous-time systems. Justify your answers. In each example, y(t) de- notes the system output and x(t) is the system input. 62 42 Signals and Systems Chap. 1 (a) y(t) = x(t − 2) + x(2 − t) (c) y(t) = 2x(T)dT - (b) y(t)= [cos(3t)]x(t) 0, t<0 0, x(t) <0 (e) y(t) = { x(t) + x(t − 2), x(t) = 0 (g) y(t): = dx(1) dt - (d) y(t) = { x(t) + x(t − 2), 1≥0 (f) y(t) = x(t/3)

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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Problem 1. (10 pts each) Consider the CT systems in textbook problem 1.27, page 61. For this HW, you only need to consider whether the system is linear, time-invariant, memoryless. You must provide reasonable proof for each question to get full credit. (a) Is the CT system in P1.27(a) linear? (b) Is the CT system in P1.27(a) time-invariant? (c) Is the CT system in P1.27(a) memoryless? (d) Is the CT system in P1.27(b) linear? (e) Is the CT system in P1.27(b) time-invariant? (f) Is the CT system in P1.27(b) memoryless?
Transcribed Image Text:Problem 1. (10 pts each) Consider the CT systems in textbook problem 1.27, page 61. For this HW, you only need to consider whether the system is linear, time-invariant, memoryless. You must provide reasonable proof for each question to get full credit. (a) Is the CT system in P1.27(a) linear? (b) Is the CT system in P1.27(a) time-invariant? (c) Is the CT system in P1.27(a) memoryless? (d) Is the CT system in P1.27(b) linear? (e) Is the CT system in P1.27(b) time-invariant? (f) Is the CT system in P1.27(b) memoryless?
1.27. In this chapter, we introduced a number of general properties of systems. In partic- ular, a system may or may not be (1) Memoryless (2) Time invariant (3) Linear (4) Causal (5) Stable Determine which of these properties hold and which do not hold for each of the following continuous-time systems. Justify your answers. In each example, y(t) de- notes the system output and x(t) is the system input. 62 42 Signals and Systems Chap. 1 (a) y(t) = x(t − 2) + x(2 − t) (c) y(t) = 2x(T)dT - (b) y(t)= [cos(3t)]x(t) 0, t<0 0, x(t) <0 (e) y(t) = { x(t) + x(t − 2), x(t) = 0 (g) y(t): = dx(1) dt - (d) y(t) = { x(t) + x(t − 2), 1≥0 (f) y(t) = x(t/3)
Transcribed Image Text:1.27. In this chapter, we introduced a number of general properties of systems. In partic- ular, a system may or may not be (1) Memoryless (2) Time invariant (3) Linear (4) Causal (5) Stable Determine which of these properties hold and which do not hold for each of the following continuous-time systems. Justify your answers. In each example, y(t) de- notes the system output and x(t) is the system input. 62 42 Signals and Systems Chap. 1 (a) y(t) = x(t − 2) + x(2 − t) (c) y(t) = 2x(T)dT - (b) y(t)= [cos(3t)]x(t) 0, t<0 0, x(t) <0 (e) y(t) = { x(t) + x(t − 2), x(t) = 0 (g) y(t): = dx(1) dt - (d) y(t) = { x(t) + x(t − 2), 1≥0 (f) y(t) = x(t/3)
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