5. Laplace Transform of a Periodic Function f(t)

If function f(t) is:

Periodic with period p > 0, so that f(t + p) = f(t), and

f1(t) is one period (i.e. one cycle) of the function, written using Unit Step functions,


`{f(t)}= ` `{f_1(t)}xx 1/(1-e^(-sp))`

NOTE: In English, the formula says:

The Laplace Transform of the periodic function f(t) with period p, equals the Laplace Transform of one cycle of the function, divided by `(1-e^(-sp))`.


Find the Laplace transforms of the periodic functions shown below:


(b) Saw-tooth waveform:

(c) Full-wave rectification of sin t:


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