Let a DT system described by the following difference equation:
y[n]-5/6y[n-1]-1/6y[n-2]=1/6x[n-1]
Find the zero input and zero state responses of this system for n≥0 assuming that the input s x[n]=2^nu[n] and the initial conditions y[-1]=1 and y[-2]=2.
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Let a DT system described by the following difference equation: y[n]-5/6y[n-1]-1/6y[n-2]=1/6x[n-1] Find the zero input and...
Solve y[n+2]−5 6y[n+1]+1 6y[n]=5x[n+1]−x[n] if the initial conditions are y[−1]=2, y[−2]=0, and the input x[n]=u[n]. Separate the response into zero-input and zero-state responses.
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] +...
Question 2. Consider the DT system described by the difference equation y[n] - 0.2y[n-1]xIn-1] Determine directly yl-1]-1. in the time domain its zero-input response for the initial value of Question 2. Consider the DT system described by the difference equation y[n] - 0.2y[n-1]xIn-1] Determine directly yl-1]-1. in the time domain its zero-input response for the initial value of
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If the input to the system described by the difference equation y(n+1) (1/2)x(n+) -x(n) is a) Does it matter what are the initial conditions for nc0 in order to find y(n) for n20? Explain your b) x(n) -u(n) answer. (3 points). Determine the transfer function H(z) and the Frequency Response (H(est) (10 points). Find the amplitude lH(epT)I and the phase He*') as a function of co. Evaluate both for normalized frequency ω T=z/4. ( 10 points) c) Find the steady...
Question 3. Consider the DT system described by the difference equation y[n+1]+ 0.3 y[n] 0.4x[n] Using the Z-transform, determine the system's zero-input response for the initial value of y[0] 1/3. The solution directly in the time domain is not accepted
5. A DT system having input x[n] and output yIn] is described by the difference equation J?nJ 0.8 IJln 2] x[n]-0.75x(n-l]. Assuming that x[n]-n(0.75)" u[n], use transfomn methods to determine the output y[n]. The property of DTFTs glnl Lm?G(e'?) then > / G(er) should help in obtaining the DTFT of the input. (20 pts.) ds2
Consider a discrete-time system described by the following difference equation. y(n) = y(n−1)−.24y(n−2) + 2x(n−1)−1.6x(n−2) Find the transfer function H(z). Find the zero-state response to the causal exponential input x(k) = .8nµ(n). This means that given H(z), we can calculate Y(z) and subsequently the output, y(n) with all initial conditions presumed to be zero. Hence the term, zero-state.
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