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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 (1) deterministic or non-deterministic, (ii) static or dynamic, (iii) causal or non-causal, (iv) linear or non-linear, (v) time-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 c) y(t) = u(T)dr d) y(t) = [ sin(7)u(7)dr e) ü(t)+3ÿ(t) +2y(t) = ủ(t) + 3u(t), y(to)= ý(to) = u(to) = 0 %3D f) y(k+1) = ku(k)y(k), y(ko) =1, u(k) E Z Find the impulse-response function (the two-variable one) of each system described in Question 1, which is deterministic, linear, continuous-time, and analog.

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 (1) deterministic or non-deterministic, (ii) static or dynamic, (iii) causal or non-causal, (iv) linear or non-linear, (v) time-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 c) y(t) = u(T)dr d) y(t) = [ sin(7)u(7)dr e) ü(t)+3ÿ(t) +2y(t) = ủ(t) + 3u(t), y(to)= ý(to) = u(to) = 0 %3D f) y(k+1) = ku(k)y(k), y(ko) =1, u(k) E Z Find the impulse-response function (the two-variable one) of each system described in Question 1, which is deterministic, linear, continuous-time, and analog.

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
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3. Find the single-variable impulse-response function of each system described in Question 1, which is deterministic, linear, time-invariant, continuous-time, and analog. 4. Assuming to = 0, find the transfer function of each system described in Question 1, which is deterministic, causal, linear, time-invariant, continuous-time, and analog.
Transcribed Image Text:3. Find the single-variable impulse-response function of each system described in Question 1, which is deterministic, linear, time-invariant, continuous-time, and analog. 4. Assuming to = 0, find the transfer function of each system described in Question 1, which is deterministic, causal, linear, time-invariant, continuous-time, and analog.
1. 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) time-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 а) у() b) y(t) = (int (u(t)))? -u(t), with probability rt+1 c) y(t) = |, u(T)dr d) y(t) = i sin(т)u(т)dт e) ÿ(t)+3ÿ(t) +2y(t) = ủ(t) + 3u(t), y(to) = ý(to) = u(to) = 0 f) y(k +1) = ku(k)y(k), y(ko) =1, u(k) € Z 2. Find the impulse-response function (the two-variable one) of each system described in Question 1, which is deterministic, linear, continuous-time, and analog.
Transcribed Image Text:1. 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) time-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 а) у() b) y(t) = (int (u(t)))? -u(t), with probability rt+1 c) y(t) = |, u(T)dr d) y(t) = i sin(т)u(т)dт e) ÿ(t)+3ÿ(t) +2y(t) = ủ(t) + 3u(t), y(to) = ý(to) = u(to) = 0 f) y(k +1) = ku(k)y(k), y(ko) =1, u(k) € Z 2. Find the impulse-response function (the two-variable one) of each system described in Question 1, which is deterministic, linear, continuous-time, and analog.
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