Given the difference equation x(k+ 3) - 2.2x(k+ 2) +1.57x(k+1) 0.36x(k) = e(k) where e(k) = 1

Given the difference equation

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x(k+ 3) - 2.2x(k+ 2) +1.57x(k+1) 0.36x(k) = e(k) where e(k) = 1 for all k 0, and x(0) = x(1) = x(2) = 0 . (a) Write a digital computer program that will calculate x(k). Run this program solving for x(3), x(4).... x(25). (b) Using the sequential technique, check the values of x(k), 0k <5. (c) Use the z-transform and the power-series method to verify the values x(k), 0k5.