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)
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...
icon
Related questions
Question
100%
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.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

Blurred answer
Similar questions
Recommended textbooks for you
Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
Delmar's Standard Textbook Of Electricity
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
Fundamentals of Electric Circuits
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:
9780078028229
Author:
Charles K Alexander, Matthew Sadiku
Publisher:
McGraw-Hill Education
Electric Circuits. (11th Edition)
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:
9780134746968
Author:
James W. Nilsson, Susan Riedel
Publisher:
PEARSON
Engineering Electromagnetics
Engineering Electromagnetics
Electrical Engineering
ISBN:
9780078028151
Author:
Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:
Mcgraw-hill Education,