Which terms will be present in the fourier series

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Find, without calculation, which terms will be present in the Fourier series for the periodic functions f ( t ), of period T , that are given in the range - T / 2 to T / 2 by:

(a) f ( t ) = 2 for 0 ≤ | t | T / 4 , f = 1 for T / 4 ≤ | t | T / 2;

(b) f ( t ) = exp[-( t - T / 4) 2 ];

(c) f ( t ) = -1 for - T / 2 ≤ t -3 T / 8 and 3 T / 8 ≤ t T / 2 ,f ( t ) = 1 for

- T / 8 ≤ t T / 8; the graph of f is completed by two straight lines in the remaining ranges so as to form a continuous function.

Reference no: EM13887390

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