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2. In the following system, x(t) is the input and y(t) is the output. yt) fix(t)]...
2. (10 pts.) Consider a system with input c() and output y(t) = x(2t) - 2(t-2)....
2. (10 pts.) Consider a system with input c() and output y(t) = x(2t) - 2(t-2). Determine whether this system is time-invariant and/or linear. Justify your answers.
2.10. Window/modulator Consider the system where for an input x(t) the output is y(t) = x(oft)...
2.10. Window/modulator Consider the system where for an input x(t) the output is y(t) = x(oft) for some function f(t). (a) Letf(t)=u(t)-11(t-10). Determine whether the system with input x(t) and output y(t)is linear, time invariant, and causal, Suppose x(t) = 4 cos(T/2), and f(t)=cos(67t/7) periodic? What frequencies are present in the output? Is this system linear? Is it time invariant? Explain. (b) and both are periodic. Is the output y(t) also (c) Let f(t) = u(t)-u (t-2) and the input...
Problem 4. Given the input/output system represented by t-1 y(t) = 2 ( x(y - 3)...
Problem 4. Given the input/output system represented by t-1 y(t) = 2 ( x(y - 3) dy where x(t) is the input and y(t) is the output, a) Determine whether the system is linear or non-linear. b) Determine the impulse response h(t, to) of the system by setting x(t)= 8(t–to). c) Determine whether the system is time invariant or time variant. d) Determine whether the system is causal or non-causal.
In the following questions, r(t) represents the input of a system and y(t) represents the output...
In the following questions, r(t) represents the input of a system and y(t) represents the output (a) The system y(t) is linear, but not time-invariant. Is it causal? Explain your reasoning. (b) The system y(t)-VI tl) is linear, but not time-invariant. Is it causal? Explain your reasoning (c) For what value(s) of a, if any, is the system yt)exp(at)(t) time-invariant? (d) For what value(s) of a, if any, is the system y(t)- exp(at)z(t) linear?
1. Consider a continuous system whose input x(t) and output y(t) are related by dy(t) +...
1. Consider a continuous system whose input x(t) and output y(t) are related by dy(t) + ay(t) = x(t) dt where a is a constant. (a) Find y(t) with the condition y(0) = yo and x(t) = Ke-bu(t) (b) Express y(t) in terms of the zero-input and zero-state responses. 2. Consider the system in Problem 1. (a) Show that the system is not linear if y(0) = yo 70. (b) Show that the system is linear if y(0) = 0....
For a continuous time linear time-invariant system, the input-output relation is the following (x(t) the input, y(t) the...
For a continuous time linear time-invariant system, the
input-output relation is the following (x(t) the input, y(t)
the
output):
, where h(t) is the impulse response function of the
system.
Please explain why a signal like e/“* is always an eigenvector
of
this linear map for any w. Also, if ¥(w),X(w),and H(w) are
the
Fourier transforms of y(t),x(t),and h(t), respectively.
Please
derive in detail the relation between Y(w),X(w),and H(w),
which means to reproduce the proof of the basic convolution
property...
2. (Chapter 2). A linear, time-invariant, continuous-time (LTIC) system with input f(t) and output y(t) is specified by the differential equation D2(D +1)y(t) (D - 3)f(t) Find the characteristic poly...
2. (Chapter 2). A linear, time-invariant, continuous-time (LTIC) system with input f(t) and output y(t) is specified by the differential equation D2(D +1)y(t) (D - 3)f(t) Find the characteristic polynomial, characteristic equation, characteristic root(s), and characteristic mode(s) of this system. a. b. Is this system asymptotically stable, marginally stable, or unstable? Justify your answer.
2. (Chapter 2). A linear, time-invariant, continuous-time (LTIC) system with input f(t) and output y(t) is specified by the differential equation D2(D +1)y(t) (D - 3)f(t)...
A system with input x(t) and output y(t) is described by y(t) = 5 sin(x(t)). Identify...
A system with input x(t) and output y(t) is described by y(t) = 5 sin(x(t)). Identify the properties of the given system. Select one: a. Non-linear, time invariant, BIBO stable, memoryless, and causal b. Non-linear, time invariant, unstable, memoryless, and non-causal c. Linear, time varying, unstable, not memoryless, and non-causal d. Linear, time invariant, BIBO stable, not memoryless, and non-causal e. Linear, time invariant, BIBO stable, memoryless, and non-causal 0
For the system in problem below, find the output yt if the input xt=ut, and y0-=4,...
For the system in problem below, find the output yt if the input xt=ut, and y0-=4, y'0=0. y''t+10y't+16yt=3x(t)
Problem 2 - System Representation: Input/Output (20pts) (2 For the following set of coupled differential equations: or...
Problem 2 - System Representation: Input/Output (20pts) (2 For the following set of coupled differential equations: or the following set dx dt + F(t dt Find the input/output equation describing x, given the input force F(t).
Problem 2 - System Representation: Input/Output (20pts) (2 For the following set of coupled differential equations: or the following set dx dt + F(t dt Find the input/output equation describing x, given the input force F(t).
2. (10 pts.) Consider a system with input c() and output y(t) = x(2t) - 2(t-2). Determine whether this system is time-invariant and/or linear. Justify your answers.
2.10. Window/modulator Consider the system where for an input x(t) the output is y(t) = x(oft) for some function f(t). (a) Letf(t)=u(t)-11(t-10). Determine whether the system with input x(t) and output y(t)is linear, time invariant, and causal, Suppose x(t) = 4 cos(T/2), and f(t)=cos(67t/7) periodic? What frequencies are present in the output? Is this system linear? Is it time invariant? Explain. (b) and both are periodic. Is the output y(t) also (c) Let f(t) = u(t)-u (t-2) and the input...
Problem 4. Given the input/output system represented by t-1 y(t) = 2 ( x(y - 3) dy where x(t) is the input and y(t) is the output, a) Determine whether the system is linear or non-linear. b) Determine the impulse response h(t, to) of the system by setting x(t)= 8(t–to). c) Determine whether the system is time invariant or time variant. d) Determine whether the system is causal or non-causal.
In the following questions, r(t) represents the input of a system and y(t) represents the output (a) The system y(t) is linear, but not time-invariant. Is it causal? Explain your reasoning. (b) The system y(t)-VI tl) is linear, but not time-invariant. Is it causal? Explain your reasoning (c) For what value(s) of a, if any, is the system yt)exp(at)(t) time-invariant? (d) For what value(s) of a, if any, is the system y(t)- exp(at)z(t) linear?
1. Consider a continuous system whose input x(t) and output y(t) are related by dy(t) + ay(t) = x(t) dt where a is a constant. (a) Find y(t) with the condition y(0) = yo and x(t) = Ke-bu(t) (b) Express y(t) in terms of the zero-input and zero-state responses. 2. Consider the system in Problem 1. (a) Show that the system is not linear if y(0) = yo 70. (b) Show that the system is linear if y(0) = 0....
For a continuous time linear time-invariant system, the
input-output relation is the following (x(t) the input, y(t)
the
output):
, where h(t) is the impulse response function of the
system.
Please explain why a signal like e/“* is always an eigenvector
of
this linear map for any w. Also, if ¥(w),X(w),and H(w) are
the
Fourier transforms of y(t),x(t),and h(t), respectively.
Please
derive in detail the relation between Y(w),X(w),and H(w),
which means to reproduce the proof of the basic convolution
property...
2. (Chapter 2). A linear, time-invariant, continuous-time (LTIC) system with input f(t) and output y(t) is specified by the differential equation D2(D +1)y(t) (D - 3)f(t) Find the characteristic polynomial, characteristic equation, characteristic root(s), and characteristic mode(s) of this system. a. b. Is this system asymptotically stable, marginally stable, or unstable? Justify your answer.
2. (Chapter 2). A linear, time-invariant, continuous-time (LTIC) system with input f(t) and output y(t) is specified by the differential equation D2(D +1)y(t) (D - 3)f(t)...
A system with input x(t) and output y(t) is described by y(t) = 5 sin(x(t)). Identify the properties of the given system. Select one: a. Non-linear, time invariant, BIBO stable, memoryless, and causal b. Non-linear, time invariant, unstable, memoryless, and non-causal c. Linear, time varying, unstable, not memoryless, and non-causal d. Linear, time invariant, BIBO stable, not memoryless, and non-causal e. Linear, time invariant, BIBO stable, memoryless, and non-causal 0
Problem 2 - System Representation: Input/Output (20pts) (2 For the following set of coupled differential equations: or the following set dx dt + F(t dt Find the input/output equation describing x, given the input force F(t).
Problem 2 - System Representation: Input/Output (20pts) (2 For the following set of coupled differential equations: or the following set dx dt + F(t dt Find the input/output equation describing x, given the input force F(t).
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