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In the following questions, r(t) represents the input of a system and y(t) represents the output...
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 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...
2.10. 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.
4. Let S be a linear, time-invariant, and causal system whose input x(t) and corresponding output...
4. Let S be a linear, time-invariant, and causal system whose input x(t) and corresponding output y(t) are shown below: r(t) Page 1 of 2 Please go to next page... y(t) ? (a) Find the impulse response function h(t) of ? (b) Find the output of S when its input is e*, t<0, t2, t20
2. (a) For each sample of a discrete time signal x[n] as input, a system S...
2. (a) For each sample of a discrete time signal x[n] as input, a system S outputs the value y[n- . Determine whether the system S is i. linear ii. time-invariant 1ll. causal iv. stable Each of your answers should be supported by justification. In other words, show your reasoning (b) Consider a stable linear time-invariant (LTI) system with transfer function H(z). It is required to design a LTI compensator system G(z) that is in cascade with H(z) such that...
2. Let y(t)(e')u(t) represent the output of a causal, linear and time-invariant continuous-time system with unit...
2. Let y(t)(e')u(t) represent the output of a causal, linear and time-invariant continuous-time system with unit impulse response h[nu(t) for some input signal z(t). Find r(t) Hint: Use the Laplace transform of y(t) and h(t) to first find the Laplace transform of r(t), and then find r(t) using inverse Laplace transform. 25 points
A system is BIBO (bounded-input, bounded-output) stable if every bounded input X(t) yields a bounded output...
A system is BIBO (bounded-input, bounded-output) stable if every bounded input X(t) yields a bounded output y(t). A system is NOT BIBO stable if there exists any bounded input that results in an unbounded output. By "bounded", we mean that the magnitude of the signal is always less than some finite number. (The signal x(t)=sin(t) would be considered a bounded signal, but X(t)t would not be a bounded signal.) Signals that are infinite in time, but with a magnitude that...
Question 1.. Detemine if the following systems are linear or not (a) (5 points) y(t) =...
Question 1.. Detemine if the following systems are linear or not (a) (5 points) y(t) = tx(t (b) (5 points) y(t) = 2(t (c) (5 points) y(t) = 2.r(t) +3 15 points Question 2 Determine if the following systems are time-invariant or not 10 points (a) (5 points) y(t) = x(2t) (b) (5 points) y(t) =r(t)u(t) 5 points Question 3 Determine if the following systems are causal or not (a) (5 points) y(t) = r(-t) 20 points Question 4 Consider...
Memory less ? Causal ? Bounded input bounded output stable ? Is the system invertible ?...
Memory less ?
Causal ?
Bounded input bounded output stable ?
Is the system invertible ?
Linear ?
Time invariant?
Question (1) ls the system S, given by (6 Marka y(t) = 3x(t-1)-2 a) Memoryless?
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 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...
2.10. 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.
4. Let S be a linear, time-invariant, and causal system whose input x(t) and corresponding output y(t) are shown below: r(t) Page 1 of 2 Please go to next page... y(t) ? (a) Find the impulse response function h(t) of ? (b) Find the output of S when its input is e*, t<0, t2, t20
2. (a) For each sample of a discrete time signal x[n] as input, a system S outputs the value y[n- . Determine whether the system S is i. linear ii. time-invariant 1ll. causal iv. stable Each of your answers should be supported by justification. In other words, show your reasoning (b) Consider a stable linear time-invariant (LTI) system with transfer function H(z). It is required to design a LTI compensator system G(z) that is in cascade with H(z) such that...
2. Let y(t)(e')u(t) represent the output of a causal, linear and time-invariant continuous-time system with unit impulse response h[nu(t) for some input signal z(t). Find r(t) Hint: Use the Laplace transform of y(t) and h(t) to first find the Laplace transform of r(t), and then find r(t) using inverse Laplace transform. 25 points
A system is BIBO (bounded-input, bounded-output) stable if every bounded input X(t) yields a bounded output y(t). A system is NOT BIBO stable if there exists any bounded input that results in an unbounded output. By "bounded", we mean that the magnitude of the signal is always less than some finite number. (The signal x(t)=sin(t) would be considered a bounded signal, but X(t)t would not be a bounded signal.) Signals that are infinite in time, but with a magnitude that...
Question 1.. Detemine if the following systems are linear or not (a) (5 points) y(t) = tx(t (b) (5 points) y(t) = 2(t (c) (5 points) y(t) = 2.r(t) +3 15 points Question 2 Determine if the following systems are time-invariant or not 10 points (a) (5 points) y(t) = x(2t) (b) (5 points) y(t) =r(t)u(t) 5 points Question 3 Determine if the following systems are causal or not (a) (5 points) y(t) = r(-t) 20 points Question 4 Consider...
Memory less ?
Causal ?
Bounded input bounded output stable ?
Is the system invertible ?
Linear ?
Time invariant?
Question (1) ls the system S, given by (6 Marka y(t) = 3x(t-1)-2 a) Memoryless?
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