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Problem 1. (B01) Characterize the systems below, i.e. see what properties they have or do not have. The properties you should be investigate for are (i) homogeneity, (ii) superposition property, (iii) linearity, (iv) time-invariance, (v) causality, (vi) memoryless property and (vii) Bounded- Input/Bounded-Output (BIBO) stability. Assume that their inputs r is an arbitrary, complex- valued signal. T1 {r(t)} = |r(t)I (la)

Problem 1. (B01) Characterize the systems below, i.e. see what properties they have or do not have. The properties you should be investigate for are (i) homogeneity, (ii) superposition property, (iii) linearity, (iv) time-invariance, (v) causality, (vi) memoryless property and (vii) Bounded- Input/Bounded-Output (BIBO) stability. Assume that their inputs r is an arbitrary, complex- valued signal. T1 {r(t)} = |r(t)I (la)

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. (B01) Characterize the systems below, i.e. see what properties they have or do not us-00 JT=- have. The properties you should be investigate for are (i) homogeneity, (ii) superposition property, (iii) linearity, (iv) time-invariance, (v) causality, (vi) memoryless property and (vii) Bounded- Input/Bounded-Output (BIBO) stability. Assume that their inputs z is an arbitrary, complex- valued signal. T {x(t)} = |x(t)| T2 {r(t)} = Re {x(t))} (la) (1b) T3 {r(t)} = x*(t) TA {r(t)} = x²(t) x² (t-1) (lc) (ld) when r(t) + 0 T3 {x(t)} = r(t) (le) otherwise T6 {r(t)} = x(t) cos (wt), w> 0 T7 {r(t)} = x(t)u(t) (1f) (1g) 1 Ts {r(t)} = T I(T)dr, T> 0 (1h) dr(t) T9 {r(t)} = 2. dt2 t rtoo | v(T)x(t' –T)dr, where v is a given signal (li) Comments: T; is not BIBO stable, but it is quite hard to show. So, if you don't manage to tackle it, don't worry; just review its solution, when it is posted.
Transcribed Image Text:Problem 1. (B01) Characterize the systems below, i.e. see what properties they have or do not us-00 JT=- have. The properties you should be investigate for are (i) homogeneity, (ii) superposition property, (iii) linearity, (iv) time-invariance, (v) causality, (vi) memoryless property and (vii) Bounded- Input/Bounded-Output (BIBO) stability. Assume that their inputs z is an arbitrary, complex- valued signal. T {x(t)} = |x(t)| T2 {r(t)} = Re {x(t))} (la) (1b) T3 {r(t)} = x*(t) TA {r(t)} = x²(t) x² (t-1) (lc) (ld) when r(t) + 0 T3 {x(t)} = r(t) (le) otherwise T6 {r(t)} = x(t) cos (wt), w> 0 T7 {r(t)} = x(t)u(t) (1f) (1g) 1 Ts {r(t)} = T I(T)dr, T> 0 (1h) dr(t) T9 {r(t)} = 2. dt2 t rtoo | v(T)x(t' –T)dr, where v is a given signal (li) Comments: T; is not BIBO stable, but it is quite hard to show. So, if you don't manage to tackle it, don't worry; just review its solution, when it is posted.
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