(a) The Laplace transform of α piece wise continuous function f(t) with period p is Prove this...
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Prove this theorem. Write «0 = «p0 + «2pp + . . ..
Set t = (n - 1)p in the nth integral. Take out e-(n-1)p from under the integral sign. Use the sum formula for the geometric series.
(b) Using (11), show that the half-wave rectification of sin Ït in Fig. 137 has the Laplace transform
(A half-wave rectifier clips the negative portions of the curve. A full-wave rectifier converts them to positive; see Fig. 138.)
(c) Show that the Laplace transform of the full-wave rectification of sin Ït is
(d) Find the Laplace transform of the saw-tooth wave in Fig. 139.
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