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ECE 2713 Homework 6 Spring 2019 Dr. Havlicek 1. Text problem P-7.3. (the problem is shown on page...
ECE 2713 Homework 6 Spring 2019 Dr. Havlicek 1. Text problem P-7.3. (the problem is shown on page 3) 2. Text problem P.7.8, parts (a), (b), and (d) only. (the problem is shown on page 3) 3. A discrete-time ITI system H has input rjnl and output vinl related by the linear constant coefficient difference equation (a) Find the transfer function H(z) a n find thefunctionalform of H(s) Note: yo but in this part you do not yet have enough...
Problem 3 (30 points) An LTI system has an impulse response hin], whose z-transform equals 1-1...
Problem 3 (30 points) An LTI system has an impulse response hin], whose z-transform equals 1-1 1. List all the poles and zeros of H(2). Sketch the pole-zero plot.. 2. If this system is causal, provide the ROC of H(2) and the expression of hin. case, is this system also stable? 3. If the ROC of H(z) does not exist, provide and the expression of hn.
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...
Question 3 (30 marks) Consider the digital filter structure shown in the below figure: x[n yIn] 3 (a) Transform the giv...
Question 3 (30 marks) Consider the digital filter structure shown in the below figure: x[n yIn] 3 (a) Transform the given block diagram to the transposed direct form II one. 2 (b) Determine the difference-equation representation of the system 4 (c) Find the transfer function for this causal filter and state the pole-zero pattern (d) Determine the impulse response of the system 2 (e) For what values of k is the system stable? (f) Determine yln if k 1 and...
1. A discrete-time LTI system has the system function H() given below: (a) Sketch the pole-zero...
1. A discrete-time LTI system has the system function H() given below: (a) Sketch the pole-zero plot for this system How many possible regions of convergence (ROCs) are there for H(). 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...
A discrete-time LTI system has the system function H(z) given below:
A discrete-time LTI system has the system function \(H(z)\) given below:$$ H(z)=\frac{z^{2}}{z^{2}-\frac{1}{4}} $$(a) Sketch the pole-zero plot for this system. How many possible regions of convergence (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 of...
4. 1 20 points). Consider a causal LTI system with a pole-zero plot for th the dfee equation H(2) as show below. The system is known to have a DC gain of 1. Find the difference equation for this...
4. 1 20 points). Consider a causal LTI system with a pole-zero plot for th the dfee equation H(2) as show below. The system is known to have a DC gain of 1. Find the difference equation for this system. Show all work. Z - plane 0.5 -0.5 0.5e
4. 1 20 points). Consider a causal LTI system with a pole-zero plot for th the dfee equation H(2) as show below. The system is known to have a DC gain...
For the following transfer function of an LTI system: Q.3) For the following transfer function of an ITI system: 8-5 (a...
For the following transfer function of an LTI system:
Q.3) For the following transfer function of an ITI system: 8-5 (a) Sketch the pole-zero plot. (b) If the system is stable, determine the large Why. st pssible ROC. Is the systeu causal? Explairn (c) If the system is causal, determine the lar gest possible ROC. Is the system stable? Explain
Q.3) For the following transfer function of an ITI system: 8-5 (a) Sketch the pole-zero plot. (b) If the system...
Consider a causal LTI system whose input xn] and output y[n] are related by the differenoe equati...
Consider a causal LTI system whose input xn] and output y[n] are related by the differenoe equation yn In--n] a. Find the impulse response of the system (without using any transform). (5 marks) b. Using convolution determine yin, 1f XIn = 1 un.(6 marks
Consider a causal LTI system whose input xn] and output y[n] are related by the differenoe equation yn In--n] a. Find the impulse response of the system (without using any transform). (5 marks) b. Using convolution...
5. The z transform is a very useful tool for studying difference equations. Often difference and ...
5. The z transform is a very useful tool for studying difference equations. Often difference and differential equations are used to describe causal systems and only the causal solution is of interest. This is the "initial condition" problem of a differential equations course. But both difference and differential equations describe more than just the causal system. For instance, "backwards" solutions and "two point boundary value" solutions. One way in which to think about the problem is the ROC of the...
ECE 2713 Homework 6 Spring 2019 Dr. Havlicek 1. Text problem P-7.3. (the problem is shown on page 3) 2. Text problem P.7.8, parts (a), (b), and (d) only. (the problem is shown on page 3) 3. A discrete-time ITI system H has input rjnl and output vinl related by the linear constant coefficient difference equation (a) Find the transfer function H(z) a n find thefunctionalform of H(s) Note: yo but in this part you do not yet have enough...
Problem 3 (30 points) An LTI system has an impulse response hin], whose z-transform equals 1-1 1. List all the poles and zeros of H(2). Sketch the pole-zero plot.. 2. If this system is causal, provide the ROC of H(2) and the expression of hin. case, is this system also stable? 3. If the ROC of H(z) does not exist, provide and the expression of hn.
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...
Question 3 (30 marks) Consider the digital filter structure shown in the below figure: x[n yIn] 3 (a) Transform the given block diagram to the transposed direct form II one. 2 (b) Determine the difference-equation representation of the system 4 (c) Find the transfer function for this causal filter and state the pole-zero pattern (d) Determine the impulse response of the system 2 (e) For what values of k is the system stable? (f) Determine yln if k 1 and...
1. A discrete-time LTI system has the system function H() given below: (a) Sketch the pole-zero plot for this system How many possible regions of convergence (ROCs) are there for H(). 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...
A discrete-time LTI system has the system function \(H(z)\) given below:$$ H(z)=\frac{z^{2}}{z^{2}-\frac{1}{4}} $$(a) Sketch the pole-zero plot for this system. How many possible regions of convergence (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 of...
4. 1 20 points). Consider a causal LTI system with a pole-zero plot for th the dfee equation H(2) as show below. The system is known to have a DC gain of 1. Find the difference equation for this system. Show all work. Z - plane 0.5 -0.5 0.5e
4. 1 20 points). Consider a causal LTI system with a pole-zero plot for th the dfee equation H(2) as show below. The system is known to have a DC gain...
For the following transfer function of an LTI system:
Q.3) For the following transfer function of an ITI system: 8-5 (a) Sketch the pole-zero plot. (b) If the system is stable, determine the large Why. st pssible ROC. Is the systeu causal? Explairn (c) If the system is causal, determine the lar gest possible ROC. Is the system stable? Explain
Q.3) For the following transfer function of an ITI system: 8-5 (a) Sketch the pole-zero plot. (b) If the system...
Consider a causal LTI system whose input xn] and output y[n] are related by the differenoe equation yn In--n] a. Find the impulse response of the system (without using any transform). (5 marks) b. Using convolution determine yin, 1f XIn = 1 un.(6 marks
Consider a causal LTI system whose input xn] and output y[n] are related by the differenoe equation yn In--n] a. Find the impulse response of the system (without using any transform). (5 marks) b. Using convolution...
5. The z transform is a very useful tool for studying difference equations. Often difference and differential equations are used to describe causal systems and only the causal solution is of interest. This is the "initial condition" problem of a differential equations course. But both difference and differential equations describe more than just the causal system. For instance, "backwards" solutions and "two point boundary value" solutions. One way in which to think about the problem is the ROC of the...
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Please help me with FLOWCHART and UML diagram for class,
thank you!
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