Determine the zero-input response of the system | Holooly The zero-input response of the system can be obtained from the homogenous solution by evaluating the constants in (2 4 22), given the initial conditions y (-1) and y (-2) From the difference equation in (2 4 21) we have y (0) = 3y (-1) + 4y (-2) y (1) = 3y (0) +4y (-1) = 3 [3y (-1) + 4y (-2)] + 4y (-1) = 13y (-1) + 12y (-2)
Discrete Time Systems Difference Equations Questions and Answers . . . What is the zero-input response of the system described by the homogenous second order equation y(n)-3y(n-1)-4y(n-2)=0 if the initial conditions are y(-1)=5 and y(-2)=0? a) (-1) n-1 + (4) n-2 b) (-1) n+1 + (4) n+2
Solved 1. Determine the zero-input response of the system - Chegg 1 Determine the zero-input response of the system described by the second-order difference equation [n]–3y{n-1]-4y{n-2]=0 2 Determine the particular solution of the difference equation y[n] - 3 y[n - 1] - 4 y[n - 2) = x[n] + 2x[n - 1] to the input x[n] = 4"u[n] Assume that y,[n] = K n4"u[n] 3 Determine the total response of the system
Question 15: Determine the zero-input response of the system described . . . The zero-input response of the above second-order difference equation is given by the initial conditions when x(n) = 0 That means no input is present at the input port To find the zero-input response we have to use the characteristic equation which is given by: ar² + br + c = 0
Zero-input response basics - Imperial College London In order to determine the N arbitrary constants, we need to have N constraints (i e initial or boundary or auxiliary conditions) when the initial conditions are y 0(0) = −5 The characteristic roots are therefore λ1 = -1 and λ2 = -2 The zero-input response is
Which one of the following is the zero-input response of the system described by the homogeneous second-order difference equation if y [-2] = 0 and y [-1] = 5 ? Option 3 : y zi (n) = (-1) n+1 + (4) n+2, n ≥ 0 Concept: Zero input solution: The zero input solution is the response of the system to the initial conditions, with the input set to zero The zero state solution:
ELC 4351: Digital Signal Processing - Baylor University homogeneous difference equation is y h(n) = C 1λn1 + C 2λn2 + ···+ C N λn N where C 1,C 2, ,C N are weighting coefficients These coefficients are determined from the initial conditions of the system y h(n) is the zero-input response of the system
Difference Equations - Natural Response (Zero Input Response), Complete . . . Determine the response y(n), n ≥ 0 of the system (by finding the homogeneous and particular solutions) described by the second order difference equation y(n) – 3 y(n-1) – 4 y(n-2) = x(n) + 2 x(n-1) when the input sequencer is x(n) = 4 n u(n)
Which one of the following is the zero-input response of the system y[n . . . Correct Answer - Option 3 : y zi (n) = (-1) n+1 + (4) n+2, n ≥ 0 Concept: Zero input solution: The zero input solution is the response of the system to the initial conditions, with the input set to zero The zero state solution: The zero state solution is the response of the system to the input, with initial conditions set to zero
determine the impulse response of given second order difference equation The impulse response of a system is its zero-state response to an impulse at the input If the system is linear and time-invariant (LTI), then the system's response to any input signal can be described in terms of the impulse response The impulse response only depends on the structure of the system, and it cannot depend on any