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8. Can the anticausal system described by h(t) = e2tu(-t) be stable? Justify by using an...
A system is given by: yt=5xt+1-3 Is the system BIBO stable? Justify Is the system memoryless?...
A system is given by: yt=5xt+1-3 Is the system BIBO stable? Justify Is the system memoryless? Explain Is the system causal? Explain Is the system time invariant? Justify Is the system linear? Justify What is the impulse response h(t) of the system? Is the system internally stable? If you could not figure out h(t) from part f, use the h(t) from the problem below. ht=5e-tut-u(t-4)
A continuous-time LTI system has unit impulse response h(t). The Laplace transform of h(t), also called...
A continuous-time LTI system has unit impulse response h(t). The
Laplace transform of h(t), also called the “transfer function” of
the LTI system, is
.
For each of the following cases, determine the region of
convergence (ROC) for H(s) and the corresponding h(t), and
determine whether the Fourier transform of h(t) exists.
(a) The LTI system is causal but not stable.
(b) The LTI system is stable but not causal.
(c) The LTI system is neither stable nor causal
8...
Question 1: (25marks) Determine whether each of the following represents a BIBO (Binary Input/Binary Output) stable...
Question 1: (25marks) Determine whether each of the following represents a BIBO (Binary Input/Binary Output) stable system: H(z) (z-7)(z2+1/9), causal b. H(z) (z-7)(z2+1/9), anticausal H(z) z/[(z-0.7) (2+z+1)], mixed d. H(z)-(z+1)(2-1), causal a. C. For each case in which the system is determined the ROC.
Question 1: (25marks) Determine whether each of the following represents a BIBO (Binary Input/Binary Output) stable system: H(z) (z-7)(z2+1/9), causal b. H(z) (z-7)(z2+1/9), anticausal H(z) z/[(z-0.7) (2+z+1)], mixed d. H(z)-(z+1)(2-1), causal a. C. For each case...
3. (l’+2° +1²=4') Topic: Laplace transform, CT system described by differential equations, LTI system properties. Consider...
3. (l’+2° +1²=4') Topic: Laplace transform, CT system described by differential equations, LTI system properties. Consider a differential equation system for which the input x(t) and output y(t) are related by the differential equation d’y(t) dy(t) -6y(t) = 5x(t). dt dt Assume that the system is initially at rest. a) Determine the transfer function. b) Specify the ROC of H(s) and justify it. c) Determine the system impulse response h(t).
2.6.1 Consider a causal continuous-time LTI system described by the differential equation u"(t) +...
2.6.1-2.6.62.6.1 Consider a causal contimuous-time LTI system described by the differential equation$$ y^{\prime \prime}(t)+y(t)=x(t) $$(a) Find the transfer function \(H(s)\), its \(R O C\), and its poles.(b) Find the impulse response \(h(t)\).(c) Classify the system as stable/unstable.(d) Find the step response of the system.2.6.2 Given the impulse response of a continuous-time LTI system, find the transfer function \(H(s),\) the \(\mathrm{ROC}\) of \(H(s)\), and the poles of the system. Also find the differential equation describing each system.(a) \(h(t)=\sin (3 t) u(t)\)(b)...
Problem 3 Assume a system function of an LTI system is H(-) =(257-6 The input to...
Problem 3 Assume a system function of an LTI system is H(-) =(257-6 The input to the system x(n) = 3"u(n). Assuming y(n) and Y(z) are the Z-transform pair, and y(n) is the output of the above system: a) determine Y(z) assuming ROC of H(z) is z/>3 b) Determine y(n) by inverting Y(z) using the method of residuals (assuming ROC of H(z) is [z/>3) c) What is the ROC of a stable system given by H(z) ? d) What is...
2. The transfer function of a CT LTI system is given by H(s) (s2 +6s +10) (s2 -4s +8) a) Draw the...
2. The transfer function of a CT LTI system is given by H(s) (s2 +6s +10) (s2 -4s +8) a) Draw the pole-zero plot of the transfer function. b) Show all possible ROC's associated with this transfer function. c) Obtain the impulse response h(t) associated with each ROC of the transfer function. d) Which one (if any) of the impulse responses of part c) is stable?
2. The transfer function of a CT LTI system is given by H(s) (s2...
1. Prove that h(t) * (t) = (t) *h(t) 2. A system has an impulse function...
1. Prove that h(t) * (t) = (t) *h(t) 2. A system has an impulse function h(t) = sinº (3t)u(t). Find the unit step (NOTE: an integral table is posted on D2L.) 3. Consider a system with input (t) and output y(t). Let r(t) y(t) = 1 + x(t-1) Is this system linear? Is it causal? Is it BIBO stable? Justify your answer
A discrete-time LTI system has the system function H(z) given below: 2 H(z (a) Sketch the...
A discrete-time LTI system has the system function H(z) given below: 2 H(z (a) Sketch the pole-zero plot for this system. How many possible (ROCs) are there for H(z). List the possible ROCs and indicate what type of sequence (left-sided, right-sided, two-sided, finite-length) they correspond to (b) Which ROC (or ROCs) correspond to a stable system? Why? (c) Which ROC (or ROCs) correspond to a causal system? Why? (d) Write a difference equation that relates the input to the output...
Suppose that the system function of an LTI system is 1+z H(z)=7 (1-12 '\1-22-X1 - 3z-")...
Suppose that the system function of an LTI system is 1+z H(z)=7 (1-12 '\1-22-X1 - 3z-") (a) Determine the ROC of H(z) if it is known that the system is stable. (b) Determine the ROC of H(z) if it is known that the system is causal. (c) Is it possible for the system to be both stable and causal?
A continuous-time LTI system has unit impulse response h(t). The
Laplace transform of h(t), also called the “transfer function” of
the LTI system, is
.
For each of the following cases, determine the region of
convergence (ROC) for H(s) and the corresponding h(t), and
determine whether the Fourier transform of h(t) exists.
(a) The LTI system is causal but not stable.
(b) The LTI system is stable but not causal.
(c) The LTI system is neither stable nor causal
8...
Question 1: (25marks) Determine whether each of the following represents a BIBO (Binary Input/Binary Output) stable system: H(z) (z-7)(z2+1/9), causal b. H(z) (z-7)(z2+1/9), anticausal H(z) z/[(z-0.7) (2+z+1)], mixed d. H(z)-(z+1)(2-1), causal a. C. For each case in which the system is determined the ROC.
Question 1: (25marks) Determine whether each of the following represents a BIBO (Binary Input/Binary Output) stable system: H(z) (z-7)(z2+1/9), causal b. H(z) (z-7)(z2+1/9), anticausal H(z) z/[(z-0.7) (2+z+1)], mixed d. H(z)-(z+1)(2-1), causal a. C. For each case...
3. (l’+2° +1²=4') Topic: Laplace transform, CT system described by differential equations, LTI system properties. Consider a differential equation system for which the input x(t) and output y(t) are related by the differential equation d’y(t) dy(t) -6y(t) = 5x(t). dt dt Assume that the system is initially at rest. a) Determine the transfer function. b) Specify the ROC of H(s) and justify it. c) Determine the system impulse response h(t).
2.6.1-2.6.62.6.1 Consider a causal contimuous-time LTI system described by the differential equation$$ y^{\prime \prime}(t)+y(t)=x(t) $$(a) Find the transfer function \(H(s)\), its \(R O C\), and its poles.(b) Find the impulse response \(h(t)\).(c) Classify the system as stable/unstable.(d) Find the step response of the system.2.6.2 Given the impulse response of a continuous-time LTI system, find the transfer function \(H(s),\) the \(\mathrm{ROC}\) of \(H(s)\), and the poles of the system. Also find the differential equation describing each system.(a) \(h(t)=\sin (3 t) u(t)\)(b)...
Problem 3 Assume a system function of an LTI system is H(-) =(257-6 The input to the system x(n) = 3"u(n). Assuming y(n) and Y(z) are the Z-transform pair, and y(n) is the output of the above system: a) determine Y(z) assuming ROC of H(z) is z/>3 b) Determine y(n) by inverting Y(z) using the method of residuals (assuming ROC of H(z) is [z/>3) c) What is the ROC of a stable system given by H(z) ? d) What is...
2. The transfer function of a CT LTI system is given by H(s) (s2 +6s +10) (s2 -4s +8) a) Draw the pole-zero plot of the transfer function. b) Show all possible ROC's associated with this transfer function. c) Obtain the impulse response h(t) associated with each ROC of the transfer function. d) Which one (if any) of the impulse responses of part c) is stable?
2. The transfer function of a CT LTI system is given by H(s) (s2...
1. Prove that h(t) * (t) = (t) *h(t) 2. A system has an impulse function h(t) = sinº (3t)u(t). Find the unit step (NOTE: an integral table is posted on D2L.) 3. Consider a system with input (t) and output y(t). Let r(t) y(t) = 1 + x(t-1) Is this system linear? Is it causal? Is it BIBO stable? Justify your answer
A discrete-time LTI system has the system function H(z) given below: 2 H(z (a) Sketch the pole-zero plot for this system. How many possible (ROCs) are there for H(z). List the possible ROCs and indicate what type of sequence (left-sided, right-sided, two-sided, finite-length) they correspond to (b) Which ROC (or ROCs) correspond to a stable system? Why? (c) Which ROC (or ROCs) correspond to a causal system? Why? (d) Write a difference equation that relates the input to the output...
Suppose that the system function of an LTI system is 1+z H(z)=7 (1-12 '\1-22-X1 - 3z-") (a) Determine the ROC of H(z) if it is known that the system is stable. (b) Determine the ROC of H(z) if it is known that the system is causal. (c) Is it possible for the system to be both stable and causal?
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