HARMONIC ANALYSIS 



395 



Then, resolving vertically, 

 1 



and resolving horizontally, 

 1 



The other coefficients can be obtained in a similar manner. 



194. Example 1. The following values are 12 equidistant 

 ordinates of a periodic function taken for a complete period. 

 Express the function as a Fourier's Series neglecting terms higher 

 than 30. 



5-41 6-42 5-40 8-58 



1-43 1-92 2-80 2-78 



3-40 

 1-60 



2-29 

 2-47 



Then 



B = (sum of the ordinates) 



lm 

 39-50 



To get A! and Bj (Fig. 131). 



Z-98 



1-80 



o-ia 



FIG. 131. 

 A i - ( 3 ' 98 sin 30 + 4-5 sin 60 +2-6 + 0-80 sin 60 - 0-18 sin 30 } 



-{2-60 + 3-80 sin 30 + 5-3 sin 60} 



A t =.l-51 



