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Problem. Find the Fourier series representation for the periodic function of period T defined by


ole.gif

ole1.gif


2)      f(t + T) = f(t)


shown in Fig. 1.                                               


Solution. The Fourier series representation is given by


ole2.gif


where


             ole3.gif


             ole4.gif



Evaluation of an



ole5.gif


             ole6.gif



             ole7.gif


             ole8.gif

 

            = 0      for n ≠ 0



For n = 0,


             ole9.gif


since the average value of f(t) over a period is zero.


____________________________________________________________________


Evaluation of bn



ole10.gif


             ole11.gif



             ole12.gif




             ole13.gif


             ole14.gif



Since cos nπ = (-1)n


             ole15.gif

____________________________________________________________________



Thus


             ole16.gif



             ole17.gif



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