PLEASE HELP WITH APRT B) Find the z-transform of the following sampled signals:

Question

PLEASE HELP WITH APRT B)

Find the z-transform of the following sampled signals: a) x (k) = {1 when k = 0 0 when k notequalto 0 b) x (k) = {1 when k = 1 0 when k notequalto 1 c) x (k) = {1 for k greaterthanorequalto 0 0 for k > 0 d) {x (0) = x (1) = x (2) = 0 x (3) = 1/3 x (4) = 2/3 x (k) = 1, k = 5, 6, or equivalently, A continuous-time controller was designed to achieve a closed-loop system with a phase margin (PM) of 45 degree at the corresponding gain crossover frequency of 10 Hz. The controller is implemented with an embedded processor in discrete-time. Assume the implementation is perfect and no additional delay is present except for the DAC that acts as a zero-order-hold (ZOH). Determine the minimal sample frequency to ensure the computer controller system is stable.

Explanation / Answer

Two times the gain cross over frequency.At the gain cross over frequency the system is marginally stable

20 hertzs are the minimal sample frequency so that system is stable.

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