Using the M/T method at low speed, the sampling period of the speed controller is varied according to the motor speed. They are pro-vided this year as a complementary Hint: Z[t] = ( ) (1 1) 2 1 X z z Tz 27 Initial Value Theorem. Table of Laplace Transforms. Prove linearity property of Laplace transform. The first term in the brackets goes to zero if f(t) grows more slowly than an exponential (one of our requirements for existence of the Laplace Transform), and the second term goes to zero because the limits on the integral are equal.So the theorem is proven 6. = z f or z z has a zero at z=0 and a pole at z=1 6.2 Rational z-Transforms A physical interpretation of the concepts of poles and zeros can be given by plotting the log-magnitude 20log 10 |G(z)|as shown on next slide for 2 1 2 1 64 . 03 (b) Determine the inverse Z-transform of the following X(z) by the partial fraction expansion method. In other words, given a Laplace transform, what function did we originally have? Proofs of derivatives, integration and convolution properties. a) Find the Laplace transform of f(t) = f(t-T); {f(t)0 ST
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