Question

Consider a causal LTI system. When the input to the system is $x[n] = \frac{-1}{3} \left(\frac{1}{2}\right)^n u[n] - \frac{4}{3} (2)^n u[-n - 1]$, the z transform of the output is $Y(z) = \frac{1 - z^{-2}}{(1 - \frac{1}{2}z^{-1})(1 - 2z^{-1})}$ a) Find the z transform of the input signal. b) What are the possible choices for the ROC of $Y(z)$? c) What are the possible choices for the linear constant coefficient difference equation used to describe the system? d) What are the possible choices of the impulse response for the system?

          Consider a causal LTI system. When the input to the system is
$x[n] = \frac{-1}{3} \left(\frac{1}{2}\right)^n u[n] - \frac{4}{3} (2)^n u[-n - 1]$,
the z transform of the output is
$Y(z) = \frac{1 - z^{-2}}{(1 - \frac{1}{2}z^{-1})(1 - 2z^{-1})}$
a) Find the z transform of the input signal.
b) What are the possible choices for the ROC of $Y(z)$?
c) What are the possible choices for the linear constant coefficient difference equation used
to describe the system?
d) What are the possible choices of the impulse response for the system?

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Consider a causal LTI system. When the input to the system is
x[n] = (-1)/(3)((1)/(2))^n u[n] - (4)/(3) (2)^n u[-n - 1],
the z transform of the output is
Y(z) = (1 - z^-2)/((1 - (1)/(2)z^-1)(1 - 2z^-1))
a) Find the z transform of the input signal.
b) What are the possible choices for the ROC of Y(z)?
c) What are the possible choices for the linear constant coefficient difference equation used
to describe the system?
d) What are the possible choices of the impulse response for the system?

Added by Christine M.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Hubert Agamasu

Step 1

The z-transform of the unit step function u[n] is given by: U(z) = 1 / (1 - z^-1) The z-transform of the delayed unit step function u[-n-1] can be found by substituting n with -n-1 in the z-transform of u[n]: U(-z^-1) = 1 / (1 - (-z^-1)) = 1 / (1 + z^-1) Now, Show more…

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Consider a causal LTI system. When the input to the system is x[n] = u[n] - 2u[-n-1], the z-transform of the output is Y(z) = 1 / (1 - 2z^-1). a) Find the z-transform of the input signal. b) What are the possible choices for the ROC of Y(z)? c) What are the possible choices for the linear constant coefficient difference equation used to describe the system? d) What are the possible choices of the impulse response for the system?

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