![Let d be a positive real number. Consider the system given by y[n] = vſn – d. What is the transfer function of this system? H](http://img.homeworklib.com/questions/d13c3830-052a-11eb-82fd-23e8f8df486d.png?x-oss-process=image/resize,w_560)
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![Y[n] = [-] By using Laplace transform. ac [m] = X(6) YCS) = v(s) eds x (m-no) = x(s) é YG éds VCS -sno = e By using 7 transfo](http://img.homeworklib.com/questions/3e86f250-052b-11eb-85e9-913022c2ee0b.png?x-oss-process=image/resize,w_560)
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Let d be a positive real number. Consider the system given by y[n] = vſn –...
Let a be a positive real number. Consider a discrete-time echo system (called system 1) given...
Let a be a positive real number. Consider a discrete-time echo system (called system 1) given by the difference equation y[n] = v[n] + av[n – 4). Here v is the input signal and y is the output signal. A. (1 mark) Determine the systems' transfer function H1 (2). B. (1 mark) What are the pole(s) of this system? Plot the pole(s) in the complex plane. C. (2 marks) Is this system stable? Explain your answer. D. (2 marks) Determine...
2. Let a be a positive real number, let r be a real number satisfying r...
2. Let a be a positive real number, let r be a real number satisfying r >1, let N be an integer greater than one, and let tR -R be the integrable simple function defined such that tr,N(r) = 0 whenver x < a or z > ar*, tr,N(a) = a-2 and tr,N(z) = (ar)-2 whenever arj-ıく < ar] for some integer j satisfying 1 < j < N. Determine the value of JR trN(x) dz.
Part 15A and 15B (15) Let n E Z+,and let d be a positive divisor of...
Part 15A and 15B
(15) Let n E Z+,and let d be a positive divisor of n. Theorem 23.7 tells us that Zn contains exactly one subgroup of order d, but not how many elements Z has of order d. We will determine that number in this exercise. (a) Determine the number of elements in Z12 of each order d. Fill in the table below to compare your answers to the number of integers between 1 and d that are...
4. (25 points) Consider a sampled data system shown in the following figure, wherein the transfer function of the y (t)...
4. (25 points) Consider a sampled data system shown in the following figure, wherein the transfer function of the y (t) r*(t ZOH Process zero-order hold, and the process are given by 2s +1 Go(s) =--s G(s) = There parameter a is some real number, and T is the sampling time. (a) (15 points) Determine the discrete-time transfer function G(z).
4. (25 points) Consider a sampled data system shown in the following figure, wherein the transfer function of the y...
Consider a discrete-time system described by the following difference equation. y(n) = y(n−1)−.24y(n−2) + 2x(n−1)−1.6x(n−2) Find...
Consider a discrete-time system described by the following difference equation. y(n) = y(n−1)−.24y(n−2) + 2x(n−1)−1.6x(n−2) Find the transfer function H(z). Find the zero-state response to the causal exponential input x(k) = .8nµ(n). This means that given H(z), we can calculate Y(z) and subsequently the output, y(n) with all initial conditions presumed to be zero. Hence the term, zero-state.
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...
Let k 21 be a positive integer, and let r R be a non-zero real number. For any real number e, we ...
Let k 21 be a positive integer, and let r R be a non-zero real number. For any real number e, we would like to show that for all 0 SjSk-, the function satisfies the advancement operator equation (A -r)f0 (a) Show that this is true whenever J-0. You can use the fact that f(n) = crn satisfies (A-r)f = 0. (b) Suppose fm n) satisfies the equation when m s k-2 for every choice of c. Show that )...
A discrete-time system has a difference equation given by y(n) = y(n-1) - 2y(n-2) + x(n) + 2x(n-1) + x(n-2)
A discrete-time system has a difference equation given by y(n) = y(n-1) - 2y(n-2) + x(n) + 2x(n-1) + x(n-2). (a) Find h(n) using iteration. (b) Find the system's z-transfer function H(z). (c) Assume x(n) = δ(n) - 2δ(n-1) + 3δ(n-2). Find y(3) using any method you like. (d) Is this system a FIR or IRR system? How can you tell?
Real analysis. Please solve all questions thank you 1. Let h be a positive real number,...
Real analysis. Please solve all questions
thank you
1. Let h be a positive real number, a <c< d < b and let Sh c< x <d, J() = 1 0 r < c, x > d (a) Using the definition only, find ſº f(x)dx. In fact, given e > 0, you should find an explicit d > 0) which works in the definition. (b) For a given partition P of [a, b], find a good upper bound on S(P)...
Problem 5. (20 pts) Let ER be a positive real number and consider the damped system...
Problem 5. (20 pts) Let ER be a positive real number and consider the damped system modeled by the following second-order differential equation: y"(t) + yy' (t) + 25y(t) = 0, (a) Show that the long-term behaviour of all solutions is independent of y. (b) For which values of ye R+ does the above differential equation have oscillating solutions ? (i.e. solutions with infinitely many zeroes.) (c) Classify the above damped system into underdamped, critically damped and overdamped in terms...
Let a be a positive real number. Consider a discrete-time echo system (called system 1) given by the difference equation y[n] = v[n] + av[n – 4). Here v is the input signal and y is the output signal. A. (1 mark) Determine the systems' transfer function H1 (2). B. (1 mark) What are the pole(s) of this system? Plot the pole(s) in the complex plane. C. (2 marks) Is this system stable? Explain your answer. D. (2 marks) Determine...
2. Let a be a positive real number, let r be a real number satisfying r >1, let N be an integer greater than one, and let tR -R be the integrable simple function defined such that tr,N(r) = 0 whenver x < a or z > ar*, tr,N(a) = a-2 and tr,N(z) = (ar)-2 whenever arj-ıく < ar] for some integer j satisfying 1 < j < N. Determine the value of JR trN(x) dz.
Part 15A and 15B
(15) Let n E Z+,and let d be a positive divisor of n. Theorem 23.7 tells us that Zn contains exactly one subgroup of order d, but not how many elements Z has of order d. We will determine that number in this exercise. (a) Determine the number of elements in Z12 of each order d. Fill in the table below to compare your answers to the number of integers between 1 and d that are...
4. (25 points) Consider a sampled data system shown in the following figure, wherein the transfer function of the y (t) r*(t ZOH Process zero-order hold, and the process are given by 2s +1 Go(s) =--s G(s) = There parameter a is some real number, and T is the sampling time. (a) (15 points) Determine the discrete-time transfer function G(z).
4. (25 points) Consider a sampled data system shown in the following figure, wherein the transfer function of the y...
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...
Let k 21 be a positive integer, and let r R be a non-zero real number. For any real number e, we would like to show that for all 0 SjSk-, the function satisfies the advancement operator equation (A -r)f0 (a) Show that this is true whenever J-0. You can use the fact that f(n) = crn satisfies (A-r)f = 0. (b) Suppose fm n) satisfies the equation when m s k-2 for every choice of c. Show that )...
Real analysis. Please solve all questions
thank you
1. Let h be a positive real number, a <c< d < b and let Sh c< x <d, J() = 1 0 r < c, x > d (a) Using the definition only, find ſº f(x)dx. In fact, given e > 0, you should find an explicit d > 0) which works in the definition. (b) For a given partition P of [a, b], find a good upper bound on S(P)...
Problem 5. (20 pts) Let ER be a positive real number and consider the damped system modeled by the following second-order differential equation: y"(t) + yy' (t) + 25y(t) = 0, (a) Show that the long-term behaviour of all solutions is independent of y. (b) For which values of ye R+ does the above differential equation have oscillating solutions ? (i.e. solutions with infinitely many zeroes.) (c) Classify the above damped system into underdamped, critically damped and overdamped in terms...
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