A LTI system has the following difference equation: y(n)−0.2 y(n−1)+0.8 y(n−2)=2.2333 x(n)+ 2.5 x(n−1)+2.3333 x(n−2).
As far as the stability is concerned, choose the right answer from the following list to identify system stability.
A LTI system has the following difference equation: y(n)−0.2 y(n−1)+0.8 y(n−2)=2.2333 x(n)+ 2.5 x(n−1)+2.3333 x(n−2). As...
Consider an LTI system whose input x[n] and output y[n] are related by the difference equation y[n – 1] + 3 y[n] + $y[n + 1] = x[n]. Determine the three possible choices for the impulse response that makes this system 1) causal, 2) two-sided and 3) anti-causal. Then for each case, determine if the system is stable or not. Causality Impulse Response Stability Causal Unstable v two-sided Unstable anti-Causal Unstable y In your answers, enter z(n) for a discrete-time...
2) An LTI DT system is defined by the difference equation: y[n] = -0.4yIn - 1] + x[n]. a) Derive the impulse response of the system. (2 pt) b) Determine if the system is BIBO stable. (1 pt) c) Assuming initial conditions yl-1) = 1, derive the complete system response to an input x[n] = u[n] - u[n-2), for n > 0.(2 pt) d) Derive the zero-state system response to an input z[n] = u[n] - 2u[n - 2] +...
Problem 2 Given is the LCC difference equation that represents some LTI system: y(n)y(n 2) = x(n) +;x(n- 1) 2 Draw a Direct- I and Direct Il block diagram representations of the system Find the impulse response of the system a) b)
a causal discrete time LTI system is implemented using the difference equation y(n)-0.5y(n-1)=x(n)+x(n-1) where x(n) is the input signal and y(n) the output signal. Find and sketch the impulse response of the system
1. Determine y(n) of the given LTI Difference equation y(n)=1.2 y(n-1) -0.32 y(n-2)+10x(n) +6x(n-1) a. x(n) = 0.4"u(n) b. x(n)= 8(n) (Impulse response) c. Draw the network structure in direct form I and II of the given LTI Difference equation
Consider an LTI system with input sequence x[n] and output sequence y[n] that satisfy the difference equation 3y[n] – 7y[n – 1] + 2y[n – 2] = 3x[n] – 3x[n – 1] (2.1) The fact that sequences x[ ] and y[ ] are in input-output relation and satisfy (2.1) does not yet determine which LTI system. a) We assume each possible input sequence to this system has its Z-transform and that the impulse response of this system also has its Z-transform. Express the...
2. A discrete time LTI system is described by the difference equation (assume initial conditions are zero) y[n] + y[n – 1] = x[n] + 1/4x[n – 1] – 1/8x[n – 2] a) Find the transfer function of the system H(z). b) If you take the inverse of the transfer function (1/H(z)), is the system stable? Prove yes or no.
A causal LTI system is described by the following difference equation: y(n) – Ay(n-1) - 2A2y(n − 2) = x(n) – 2x(n-1) + x(n–2), where A is a real constant. Determine the z-domain transfer function, H(z), of the system in terms of A.
A causal and stable LTI system has the property that: 〖(4/5)〗^n u(n) →n 〖(4/5)〗^n u(n) Determine the frequency response H(e^jω) for the system. Determine a difference equation relating any input x(n) and the corresponding output y(n). Question 3:[4 Marks] A causal and stable LTI system has the property that: 4 4 a) Determine the frequency response H(e/ø) for the system. b) Determine a difference equation relating any input x(n) and the corresponding output y(n)
Determine the impulse response h[n] of the LTI system described by the difference equationy[n] - 0.35y[n-1] = x[n]