Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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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.
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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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