II. An LTI discrete-time system is described by the following difference equation 0.1y[n] -0.09y(n-1)=0.5x[n] where x(t) is the input and y(t) is the output of the system. Assume zero initials to solve the following questions: 1) Determine the transfer function H(z) of the system 2) Determine the impulse response h[n]

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II. An LTI discrete-time system is described by the following difference equation
0.1y[n] -0.09y[n 1] = 0.5x[n]
where x(t) is the input and y(t) is the output of the system. Assume zero initials to
solve the following questions:
1) Determine the transfer function H(z) of the system
2) Determine the impulse response h[n]
3) Determine the output in the discrete-time domain y[n] and the Z-domain Y (2) for
an input signal
x[n] = n(0.9)"u[n] + 8[n]
Transcribed Image Text:II. An LTI discrete-time system is described by the following difference equation 0.1y[n] -0.09y[n 1] = 0.5x[n] where x(t) is the input and y(t) is the output of the system. Assume zero initials to solve the following questions: 1) Determine the transfer function H(z) of the system 2) Determine the impulse response h[n] 3) Determine the output in the discrete-time domain y[n] and the Z-domain Y (2) for an input signal x[n] = n(0.9)"u[n] + 8[n]
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