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Signals and Systems
2. The pole-zero diagram below has 2 zeros at the origin and 2...
A) Given: H(S) = 32 - 48 +3 52 +8s +12 1. Construct the pole-zero diagram...
A) Given: H(S) = 32 - 48 +3 52 +8s +12 1. Construct the pole-zero diagram and clearly indicate all poles and zeros II . Write the equivalent differential equation for the system III. Find h(t) IV . Is the system Causal? Stable? Justify your answers mathematically
1. Pole-zero placement. We wish to design a stable and causal second-order discrete-time (DT) fil...
1. Pole-zero placement. We wish to design a stable and causal second-order discrete-time (DT) filter (i.e., having two poles and two zeros, including those at 0 and oo) using pole-zero placement. (a) [5 pts] Where might you place the poles and zeros to achieve the following magnitude frequency response? Sketch the pole-zero plot in the complex z-plane. -Π -Tt/2 0 (b) [3 pts] Give an expression for the transfer function H(z). Justify your answer. (c) [2 pts] Write an expression...
Question 3 The block diagram of a digital control system is given in Fig. 2. R(Z)...
Question 3 The block diagram of a digital control system is given in Fig. 2. R(Z) + VT CZ 0.52 0.24(2 +0.5) (2-0.4) (z-1) Fig. 2 (a) Write an expression for the closed-loop z-transfer function of the system, C(z)/R(z). Given that one of the poles is located at z=0.235, complete a pole-zero diagram for the system. [8 marks] (b) Using a sampling interval, T = 0.5 s, map the poles and zeros onto the primary strip in the s-plane. [8...
(20 pts) Pole-zero cancellation: common poles and zeros will bring us some issues in the system d...
(20 pts) Pole-zero cancellation: common poles and zeros will bring us some issues in the system design and analysis. In this problem, we will analyze how to properly handle common poles and zeros. 2.1 Consider the following two systems System 1: G(s)~5+2 System 2: G(s) S+2 (s+1.99) (s+20) Using inverse Laplace transform, determine the step response and discuss whether you can use a first-order system to approximate the step response. 2.2 Now consider the following system G(s) = (s -1.99)...
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.
Question 2: Poles and zeros, and how they affect the transient response modes This question tests...
Question 2: Poles and zeros, and how they affect the transient response modes This question tests your understanding of the effects of nearby poles and ze- ros to the response mode of a specified pole (or conjugate pair). You should also understand what a pole-zero-gain plot is and how it is specified by, and specifies a transfer function A unit impulse function is applied to the system described by the transfer function G(8) = K (8+) (s + 1)(8 +2)...
5. The diagram function Ha) oco.s on the let shows the pole-zero plot of the transfer...
5. The diagram function Ha) oco.s on the let shows the pole-zero plot of the transfer a DT LTI systen Assume that the pole is at a dista the from theorigin and that the zero not at the origin is a origin. a) Write a mathematical expressio n for the tr the impulse response of the sy from t , inction of the system. b) Obtain assuming that it is UNSTABLE (15 pts.)
Answer the following questions for a causal digital filter with the following system function H(z) 23-2+0.64z-0.64 1-1. (0.5 point) Locate the poles and zeros of H(z) on the z-plane. (sol) 1-2. (...
Answer the following questions for a causal digital filter with the following system function H(z) 23-2+0.64z-0.64 1-1. (0.5 point) Locate the poles and zeros of H(z) on the z-plane. (sol) 1-2. (1.5 point) Sketch the magnitude spectrum, H(e i), of the filter. Find the exact values of lH(eml. IH(efr/2)I, and IH(e") , (sol) 1-3. (1 point) Relocate only one pole so that 9 s Hle)s 10 (sol) 1-4 (1 point) Take the inverse Z-transform on H(z) to find the impulse...
Signals & Systems Course Question 2. The response of a system is for t 20 and...
Signals & Systems Course Question
2. The response of a system is for t 20 and zero otherwise. (a) Find the system's impulse response h(t). (b) When (t)-u(t), the corresponding output of the system is called unit-step response s(t). Find s(t) and calculate ds(t)/dt, what does this correspond to the result from (a).
Signals and System: MATLAB code provided? Begin with the MATLAB script named lab4.m as follows. You...
Signals and System: MATLAB code provided?
Begin with the MATLAB script named lab4.m as follows. You will modify this example code to cover each of the parts of this lab. You must always carefully document and include appropriate comments in any MATLAB code. & starting point for Lab#4 % LAPLACE TRANSFORM %---------- clear all; close all; -------------------- s = tf('s'); sys = 1/(5+1); & define H(s) for a dynamic system named sys ---------------- figure(1); bode (sys); % plot magnitude and...
A) Given: H(S) = 32 - 48 +3 52 +8s +12 1. Construct the pole-zero diagram and clearly indicate all poles and zeros II . Write the equivalent differential equation for the system III. Find h(t) IV . Is the system Causal? Stable? Justify your answers mathematically
1. Pole-zero placement. We wish to design a stable and causal second-order discrete-time (DT) filter (i.e., having two poles and two zeros, including those at 0 and oo) using pole-zero placement. (a) [5 pts] Where might you place the poles and zeros to achieve the following magnitude frequency response? Sketch the pole-zero plot in the complex z-plane. -Π -Tt/2 0 (b) [3 pts] Give an expression for the transfer function H(z). Justify your answer. (c) [2 pts] Write an expression...
Question 3 The block diagram of a digital control system is given in Fig. 2. R(Z) + VT CZ 0.52 0.24(2 +0.5) (2-0.4) (z-1) Fig. 2 (a) Write an expression for the closed-loop z-transfer function of the system, C(z)/R(z). Given that one of the poles is located at z=0.235, complete a pole-zero diagram for the system. [8 marks] (b) Using a sampling interval, T = 0.5 s, map the poles and zeros onto the primary strip in the s-plane. [8...
(20 pts) Pole-zero cancellation: common poles and zeros will bring us some issues in the system design and analysis. In this problem, we will analyze how to properly handle common poles and zeros. 2.1 Consider the following two systems System 1: G(s)~5+2 System 2: G(s) S+2 (s+1.99) (s+20) Using inverse Laplace transform, determine the step response and discuss whether you can use a first-order system to approximate the step response. 2.2 Now consider the following system G(s) = (s -1.99)...
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.
Question 2: Poles and zeros, and how they affect the transient response modes This question tests your understanding of the effects of nearby poles and ze- ros to the response mode of a specified pole (or conjugate pair). You should also understand what a pole-zero-gain plot is and how it is specified by, and specifies a transfer function A unit impulse function is applied to the system described by the transfer function G(8) = K (8+) (s + 1)(8 +2)...
5. The diagram function Ha) oco.s on the let shows the pole-zero plot of the transfer a DT LTI systen Assume that the pole is at a dista the from theorigin and that the zero not at the origin is a origin. a) Write a mathematical expressio n for the tr the impulse response of the sy from t , inction of the system. b) Obtain assuming that it is UNSTABLE (15 pts.)
Answer the following questions for a causal digital filter with the following system function H(z) 23-2+0.64z-0.64 1-1. (0.5 point) Locate the poles and zeros of H(z) on the z-plane. (sol) 1-2. (1.5 point) Sketch the magnitude spectrum, H(e i), of the filter. Find the exact values of lH(eml. IH(efr/2)I, and IH(e") , (sol) 1-3. (1 point) Relocate only one pole so that 9 s Hle)s 10 (sol) 1-4 (1 point) Take the inverse Z-transform on H(z) to find the impulse...
Signals & Systems Course Question
2. The response of a system is for t 20 and zero otherwise. (a) Find the system's impulse response h(t). (b) When (t)-u(t), the corresponding output of the system is called unit-step response s(t). Find s(t) and calculate ds(t)/dt, what does this correspond to the result from (a).
Signals and System: MATLAB code provided?
Begin with the MATLAB script named lab4.m as follows. You will modify this example code to cover each of the parts of this lab. You must always carefully document and include appropriate comments in any MATLAB code. & starting point for Lab#4 % LAPLACE TRANSFORM %---------- clear all; close all; -------------------- s = tf('s'); sys = 1/(5+1); & define H(s) for a dynamic system named sys ---------------- figure(1); bode (sys); % plot magnitude and...
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