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.