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1. A discrete-time system has seven poles at z 0 and seven zeros at Find the...
A discrete-time system has seven poles at z - 0 and seven zeros at Find the...
A discrete-time system has seven poles at z - 0 and seven zeros at Find the transfer function H(z) and find the constant term bo such that the gain of the filter at zero angle (9-0) is 1, that is a. Note that H (θ) = H(z)IFeje and H(θ)le=0- 1 is equivalent to H(z)1-1 -1
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...
For a causal LTI discrete-time system described by the difference equation:
For a causal LTI discrete-time system described by the difference equation: y[n] + y[n – 1] = x[n] a) Find the transfer function H(z).b) Find poles and zeros and then mark them on the z-plane (pole-zero plot). Is this system BIBO? c) Find its impulse response h[n]. d) Draw the z-domain block diagram (using the unit delay block z-1) of the discrete-time system. e) Find the output y[n] for input x[n] = 10 u[n] if all initial conditions are 0.
Problem #1. Topics: Z Transform Find the Z transform of: x[n]=-(0.9 )n-2u-n+5] X(Z) Problem #2. T...
Problem #1. Topics: Z Transform Find the Z transform of: x[n]=-(0.9 )n-2u-n+5] X(Z) Problem #2. Topics: Filter Design, Effective Time Constant Design a causal 2nd order, normalized, stable Peak Filter centered at fo 1000Hz. Use only two conjugate poles and two zeros at the origin. The system is to be sampled at Fs- 8000Hz. The duration of the transient should be as close as possible to teft 7.5 ms. The transient is assumed to end when the largest pole elevated...
A filter has two poles at -0.6±0.8j and a zero at -1 on the z-plane. The...
A filter has two poles at -0.6±0.8j and a zero at -1 on the z-plane. The DC gain is 1. What is the transfer function H(z)? Draw the pole-zero plot.
A causal discrete-time LTI system is described by the equation
A causal discrete-time LTI system is described by the equationwhere z is the input signal, and y the output signal y(n) = 1/3x(n) + 1/3x(n -1) + 1/3x(n - 2) (a) Sketch the impulse response of the system. (b) What is the dc gain of the system? (Find Hf(0).) (c) Sketch the output of the system when the input x(n) is the constant unity signal, x(n) = 1. (d) Sketch the output of the system when the input x(n) is the unit step signal, x(n)...
Poles and Zeros For the transfer function given: 0.85 8-44.64 G(s) = 긁+0.83 12.00 Part A-Poles Find the system pole 8 Submit Part B-Poles Find the system pole s2 Submit Part C-Zeros Find the system...
Poles and Zeros For the transfer function given: 0.85 8-44.64 G(s) = 긁+0.83 12.00 Part A-Poles Find the system pole 8 Submit Part B-Poles Find the system pole s2 Submit Part C-Zeros Find the system zero Submit Part D-Type of Response Based on the locations af the poles and zeros, what will be the response to a unit step inpue? O Harmonic Oscillations (Marginally stable) Oscillatory motion with exponential decay tending to zero (stable O Critically damped exponential decay (stable)...
QUESTION 1 Consider a system of impulse response h[n] of transfer function H(z) with distinct poles...
QUESTION 1 Consider a system of impulse response h[n] of transfer function H(z) with distinct poles and zeros. We are interested in a system whose transfer function G(z) has the same poles and zeros as H(z) but doubled (meaning that each pole of H(z) is a double pole of G(z), and same for the zeros). How should we choose g[n]? g[n]=h[n]+h[n] (addition) g[n]=h[n].h[n] (multiplication) g[n]=h[n]th[n] (convolution) None of the above
alpha = 5.0 beta = 7.1 zeta = 6.9 PROBLEM 1 (20 points). Given the filter with transfer function +28-1+-2 11(2) = 1-(α/10)2-4 (a2/100):-2 Use MATLAB to Find the zeros and poles of H() Plot the pole...
alpha = 5.0
beta = 7.1
zeta = 6.9
PROBLEM 1 (20 points). Given the filter with transfer function +28-1+-2 11(2) = 1-(α/10)2-4 (a2/100):-2 Use MATLAB to Find the zeros and poles of H() Plot the poles and zeros on the -plane. The pot should include the uit circle. Plot the magnitude response (in dB) Plot the phase response. Deliverables: Your MATLAB code used to solve Problem 1 and all the generated plots.
PROBLEM 1 (20 points). Given the filter...
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)...
A discrete-time system has seven poles at z - 0 and seven zeros at Find the transfer function H(z) and find the constant term bo such that the gain of the filter at zero angle (9-0) is 1, that is a. Note that H (θ) = H(z)IFeje and H(θ)le=0- 1 is equivalent to H(z)1-1 -1
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...
Problem #1. Topics: Z Transform Find the Z transform of: x[n]=-(0.9 )n-2u-n+5] X(Z) Problem #2. Topics: Filter Design, Effective Time Constant Design a causal 2nd order, normalized, stable Peak Filter centered at fo 1000Hz. Use only two conjugate poles and two zeros at the origin. The system is to be sampled at Fs- 8000Hz. The duration of the transient should be as close as possible to teft 7.5 ms. The transient is assumed to end when the largest pole elevated...
Poles and Zeros For the transfer function given: 0.85 8-44.64 G(s) = 긁+0.83 12.00 Part A-Poles Find the system pole 8 Submit Part B-Poles Find the system pole s2 Submit Part C-Zeros Find the system zero Submit Part D-Type of Response Based on the locations af the poles and zeros, what will be the response to a unit step inpue? O Harmonic Oscillations (Marginally stable) Oscillatory motion with exponential decay tending to zero (stable O Critically damped exponential decay (stable)...
QUESTION 1 Consider a system of impulse response h[n] of transfer function H(z) with distinct poles and zeros. We are interested in a system whose transfer function G(z) has the same poles and zeros as H(z) but doubled (meaning that each pole of H(z) is a double pole of G(z), and same for the zeros). How should we choose g[n]? g[n]=h[n]+h[n] (addition) g[n]=h[n].h[n] (multiplication) g[n]=h[n]th[n] (convolution) None of the above
alpha = 5.0
beta = 7.1
zeta = 6.9
PROBLEM 1 (20 points). Given the filter with transfer function +28-1+-2 11(2) = 1-(α/10)2-4 (a2/100):-2 Use MATLAB to Find the zeros and poles of H() Plot the poles and zeros on the -plane. The pot should include the uit circle. Plot the magnitude response (in dB) Plot the phase response. Deliverables: Your MATLAB code used to solve Problem 1 and all the generated plots.
PROBLEM 1 (20 points). Given the filter...
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)...
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