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,
then
`ccL{f(t)}=(ccL{f_1(t)})/(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))`.
Examples
Find the Laplace transforms of the periodic functions shown below:
(a)

(b) Saw-tooth waveform:

(c) Full-wave rectification of sin t:

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