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Question 1 (25 points): Is the discrete-time system y (n) = 150 [n] 2 [n] +...
Consider the discrete-time system with input x[n] and output y[n] described by : y[n]=x[n]u[2-n] Which of the...
Consider the discrete-time system with input x[n] and output y[n] described by : y[n]=x[n]u[2-n] Which of the following properties does this system possess? Justify your answer in each case. Do not use Laplace transforms a) Memoryless b)Time-invariant c) Linear d)Casual e) Stable
1. (25 points) Consider the discrete-time LTI “at resť system described by In+ 2] + 5y[n+...
1. (25 points) Consider the discrete-time LTI “at resť system described by In+ 2] + 5y[n+ 1] + 6y[n] = x[n + 1] Use the iterative technique to solve for y[0], y[1], and y[2], i.e. the first three values of the system unit impulse response, and plot it.
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...
1. Consider a discrete-time system H with input x[n] and output y[n]Hn (a) Define the following...
1. Consider a discrete-time system H with input x[n] and output y[n]Hn (a) Define the following general properties of system H () memoryless;(ii BIBO stable; (ii) time-invariant. (b) Consider the DT system given by the input-output relation Indicate whether or not the above properties are satisfied by this system and justify your answer.
1) Determine if the discrete-time system,y[k] =x[k] +r·y[k−1]is linear / time-invariant / causal / memoryless. Show...
1) Determine if the discrete-time system,y[k] =x[k] +r·y[k−1]is linear / time-invariant / causal / memoryless. Show your work and explain each property. Start by assuming,x1[k]→y1[k], x2[k]→y2[k]. 2) Determine if the discrete-time system,y[k] =x[k] +rk·y[k−1]is linear / time-invariant / causal / memoryless. Show your work and explain each property. 3) For the system in part 1), if x[k] = 100·u[k−1] and y[k] = 0 for k<0, what is the range of values for r that makes this system BIBO stable? Show...
(2) Consider the causal discrete-time LTI system with an input r (n) and an output y(n)...
(2) Consider the causal discrete-time LTI system with an input r (n) and an output y(n) as shown in Figure 1, where K 6 (constant), system #1 is described by its impulse response: h(n) = -36(n) + 0.48(n- 1)+8.26(n-2), and system # 2 has the difference equation given by: y(n)+0.1y(n-1)+0.3y(n-2)- 2a(n). (a) Determine the corresponding difference equation of the system #1. Hence, write its fre- quency response. (b) Find the frequency response of system #2. 1 system #1 system #2...
Compute the unit-pulse response h[n] for the discrete-time system y[n + 2] - 2y[n + 1]...
Compute the unit-pulse response h[n] for the discrete-time system y[n + 2] - 2y[n + 1] + y[n] = x[n] (for n = 0, 1, 2, 3).
Discrete-Time Multiple Choice: Show your work for each question as much as you can (a) Which...
Discrete-Time Multiple Choice:
Show your work for each question as much as you can
(a) Which of the following systems is linear?) (B) y[n] 2 cos(x (n) (D) y[n] x(n) (b) Which of the following systems is time-invariant?() (C) yfn] n[n] (D) yIn] - x-2n] (B) y[n] - cos(nx(n)) (c) Which of the following systems is causal? () (A) yln]-2x[-n] (d) Which of the following systems is NOT stable? () (C) yln] vx(n) (B) yinl 50 sin(rIn)+ 10 cos(2x())D)h(n) (0.2)"u(r)...
Question 2 (a) Determine whether the discrete time system which has an output y[n] 2*x[n] over...
Question 2 (a) Determine whether the discrete time system which has an output y[n] 2*x[n] over the nterval 010 is linear or not by determining the response yi[n] to the input signalxj[n]- sin( (2*pi / 10 ) * n ) and the response y2[n] to the input signal x2[n] = cos( (2*pi/10 ) * n ). Determine the response y3[n] to the input signal x1n] = xi [n] + x2[n] and compare it with y4[n] = [n] + y2[n] ....
Name: 10. [8 points] Consider a discrete-time LTI system with input x[n] and out- put y[n]....
Name: 10. [8 points] Consider a discrete-time LTI system with input x[n] and out- put y[n]. When the input signal x[n] = (6)" is applied to the system, the output signal is y[n] = 0 for all n When the input signal xn] (3)" u[n] is applied to the system, the output signal is y[n] = A 8[n] + 2 (5)" u[n] for all n, where A is a constant number a) Find A. b) Find the impulse response of...
1. (25 points) Consider the discrete-time LTI “at resť system described by In+ 2] + 5y[n+ 1] + 6y[n] = x[n + 1] Use the iterative technique to solve for y[0], y[1], and y[2], i.e. the first three values of the system unit impulse response, and plot it.
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...
1. Consider a discrete-time system H with input x[n] and output y[n]Hn (a) Define the following general properties of system H () memoryless;(ii BIBO stable; (ii) time-invariant. (b) Consider the DT system given by the input-output relation Indicate whether or not the above properties are satisfied by this system and justify your answer.
(2) Consider the causal discrete-time LTI system with an input r (n) and an output y(n) as shown in Figure 1, where K 6 (constant), system #1 is described by its impulse response: h(n) = -36(n) + 0.48(n- 1)+8.26(n-2), and system # 2 has the difference equation given by: y(n)+0.1y(n-1)+0.3y(n-2)- 2a(n). (a) Determine the corresponding difference equation of the system #1. Hence, write its fre- quency response. (b) Find the frequency response of system #2. 1 system #1 system #2...
Discrete-Time Multiple Choice:
Show your work for each question as much as you can
(a) Which of the following systems is linear?) (B) y[n] 2 cos(x (n) (D) y[n] x(n) (b) Which of the following systems is time-invariant?() (C) yfn] n[n] (D) yIn] - x-2n] (B) y[n] - cos(nx(n)) (c) Which of the following systems is causal? () (A) yln]-2x[-n] (d) Which of the following systems is NOT stable? () (C) yln] vx(n) (B) yinl 50 sin(rIn)+ 10 cos(2x())D)h(n) (0.2)"u(r)...
Question 2 (a) Determine whether the discrete time system which has an output y[n] 2*x[n] over the nterval 010 is linear or not by determining the response yi[n] to the input signalxj[n]- sin( (2*pi / 10 ) * n ) and the response y2[n] to the input signal x2[n] = cos( (2*pi/10 ) * n ). Determine the response y3[n] to the input signal x1n] = xi [n] + x2[n] and compare it with y4[n] = [n] + y2[n] ....
Name: 10. [8 points] Consider a discrete-time LTI system with input x[n] and out- put y[n]. When the input signal x[n] = (6)" is applied to the system, the output signal is y[n] = 0 for all n When the input signal xn] (3)" u[n] is applied to the system, the output signal is y[n] = A 8[n] + 2 (5)" u[n] for all n, where A is a constant number a) Find A. b) Find the impulse response of...
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