1 X(z) = \frac{1}{(z - 1)^2 z^2} Find the inverse z transform by using a) Long division b) The partial-fraction method c) Calculations in Matlab using lsim d) Simulation in Simulink Hint (c+d): Remember that the Z-transform of the impulse function is 1
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Long division: To find the inverse transform using long division, we divide the numerator by the denominator. In this case, we have: X(z) = (z - 1)^2 / z^2 Dividing (z - 1)^2 by z^2, we get: X(z) = (z^2 - 2z + 1) / z^2 So, the long division gives us: X(z) = 1 Show more…
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Problem 2: Expand the following function F(s) into partial fractions using MATLAB. Determine the inverse Laplace transform of F(s). F(s) = 1 / (s^4 + 5s^3 + 7s^2) The MATLAB program for determining the partial-fraction expansion is given below: Problem 3: For the following function F(s): F(s) = (s^4 + 3s^3 + 5s^2 + 7s + 25) / (s^4 + 5s^3 + 20s^2 + 40s + 45) Using MATLAB, find the partial-fraction expansion of F(s). Also, find the inverse Laplace transformation of F(s). Problem 4: Find the Laplace transform of the following function using MATLAB. f(t) = 7t^3 cos (5t + 60°) f(t) = -7te^-5t f(t) = -3 cos 5t Problem 5: Determine the inverse Laplace transform of the following functions using MATLAB. F(s) = s / (s(s + 2)(s + 6)) F(s) = (3s + 1) / (s^2 + 2s + 9)
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