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

MATH

 

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)

5_lap_laptransper_18pt__13.png


Answer


(b) Saw-tooth waveform:

5_lap_laptransper_18pt__22.png


Answer


(c) Full-wave rectification of sin t:

5_lap_laptransper_18pt__28.png


Answer




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