11 Q-Consider the discrete tim system 1-1 x(k+1)= 1-5 1-2 0 1 0 11 3 x(k)...
Find the output y[n] using the discrete time domain method by hand: With: A-f ), B-M, c = [O 11, D = [1] and q(0)-A and x[n] = u[n] 2 01 Find the output y[n] using the discrete time domain method by hand: With: A-f ), B-M, c = [O 11, D = [1] and q(0)-A and x[n] = u[n] 2 01
5 11 Question 3 2 pts Consider a discrete-time linear system with frequency response H(12) = en The input to the system is the signal (0.2+ef) x[k] = 2 cos(1.2k).The output of the system is the signal y[k]. y[k]is a cosine with amplitude approximately equal to: 4.566 0.578 0.919 1.837
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...
4. Given the discrete time system y(k +1)-y(k) x(k + 1) find the system transfer function and its response for a sampled unit.
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...
Problem 3 A discrete random variable Y takes values {k= 0, 1, 2, ...,} such that PLY Z k} = ()* for k 20. 1. Derive P[Y = k) for any k > 0. 2. Evaluate expectation, E[Y] = 3. Given E[Y(Y - 1)] = 15 , find variance of Y, Var[Y] =
Question 7. (15 marks] Consider the discrete time system given by the state equation 07 x4 + 11-18 8/11 - 10/n VIK) = 10 11 **) 1. [3 marks) Determine if the system is (a) Lyapunov state, syptereally ) Bounded input Bounded Output (BIBO) stable. Provide brief explanations 2. (8 marks) Design a discrete-time state feedback control law of the form - Kxkl by finding the gain K to place the closed-loop eigenvalues at 0.5 3. [4 marks) Suppose the...
please asap 3. The table to the right shows the values of the joint probability distribution of the discrete random variables X and Y Find the cov(X, Y). ơxy- 11-u,' y. 0 0 1/12 1/6 1/24 7/24 1|¼ ¼ 1/40121/4。 2 Y 2 1/8 1/20 7/40 1/120 3 1/120 7/15 7/15 1/15! 3. The table to the right shows the values of the joint probability distribution of the discrete random variables X and Y Find the cov(X, Y). ơxy- 11-u,'...
Assume a =500 4. Consider the following system [ 1.2 1 0 1 x (k + 1) = 0.6 0 1 x (k) + | –0.8 0 0 y (k) = [ 5 +a 0 0 ]x (k) 0 1 | 0.8 u(k) where a is the last three digits of your student ID number. (a) Obtain the transfer function of the system. Is the origin a stable equilibrium point? (b) Is the system controllable? Provide your reasoning. If your...
Problem 1 Consider the matrix Problem 1 Consider the matriz a 2 5 3 11 08 a Find the cofactors C11,C2,C3 of A. b Find the determinant of 1, det(A) [ 2 4 61 Problem 2 Consider the matriz A=008 | 2 5 3 a Use the ero's to put A in upper triangular form 5 Pinul the determinant of A. (A) by keeping track of the row operations in part a and the properties of determinant Problem 3 Consider...