3.7. The input to a causal linear time-invariant system is x[n] = u[−n − 1] + (})" u[n]. The z-transform of the output of this system is Y(z) = (1 − −¹)(1 + z−¹)* (a) Determine H(z), the z-transform of the system impulse response. Be sure to specify the region of convergence. (b) What is the region of convergence for Y(z)? (c) Determine y[n].

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3.7. The input to a causal linear time-invariant system is
x[n] = u[−n − 1] + (})" u[n].
The z-transform of the output of this system is
Y(z) =
(1 − −¹)(1 + z−¹)*
(a) Determine H(z), the z-transform of the system impulse response. Be sure to specify
the region of convergence.
(b) What is the region of convergence for Y(z)?
(c) Determine y[n].
Transcribed Image Text:3.7. The input to a causal linear time-invariant system is x[n] = u[−n − 1] + (})" u[n]. The z-transform of the output of this system is Y(z) = (1 − −¹)(1 + z−¹)* (a) Determine H(z), the z-transform of the system impulse response. Be sure to specify the region of convergence. (b) What is the region of convergence for Y(z)? (c) Determine y[n].
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