Consider the systems whose input-output relations are described below. In each case, u indicates the input and y indicates the output, both of which can take any real value, unless indicated otherwise. Furthermore, t or k indicate the time variable, where t e T := {t € R | t > to}, for some to e R and k e K := {k € Z | k > ko}, for some ko e Z, where R and Z respectively denote the sets of real numbers and integers. Moreover, int(-) indicates the integer part of ·. For each case, determine whether the system is (i) deterministic or non-deterministic, (ii) static or dynamic, (iii) causal or non-causal, (iv) linear or non-linear, (v) tỉme-invariant or time-varying, (vi) continuous-time or discrete-time or hybrid, and (vii) analog or digital or hybrid. Explain your answer in each case. u(t), with probability a) y(t) : b) y(t) = (int (u(t))² -u(t), with probability rt+1 c) y(t) = / u(7)dr = [ | sin(7)u(7)dr d) y(t) e) j(t) + 3ÿ(t) +2y(t) = ủ(t) + 3u(t), y(to) = j(to) = u(to) = 0 f) y(k + 1) = ku(k)y(k), y(ko) = 1, u(k) e Z

Consider the systems whose input-output relations are described below. In each case, u indicates the input and y indicates the output, both of which can take any real value, unless indicated otherwise. Furthermore, t or k indicate the time variable, where t e T := {t € R | t > to}, for some to e R and k e K := {k € Z | k > ko}, for some ko e Z, where R and Z respectively denote the sets of real numbers and integers. Moreover, int(-) indicates the integer part of ·. For each case, determine whether the system is (i) deterministic or non-deterministic, (ii) static or dynamic, (iii) causal or non-causal, (iv) linear or non-linear, (v) tỉme-invariant or time-varying, (vi) continuous-time or discrete-time or hybrid, and (vii) analog or digital or hybrid. Explain your answer in each case. u(t), with probability a) y(t) : b) y(t) = (int (u(t))² -u(t), with probability rt+1 c) y(t) = / u(7)dr = [ | sin(7)u(7)dr d) y(t) e) j(t) + 3ÿ(t) +2y(t) = ủ(t) + 3u(t), y(to) = j(to) = u(to) = 0 f) y(k + 1) = ku(k)y(k), y(ko) = 1, u(k) e Z

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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