HARMONIC ANALYSIS. 



The sinusoid a. sin pt is expressed by the analysis as 



93 



a.sin pt = C + a,.cosfcf + Oj.cos 2kt + ... (22) 



+ &i.sin kt + &2-sin 2kt + ... 



where 



■In 



(23) 



(24) 

 (25) 



l = ^sin';:?. (26) 



k 



_ gfcr cos {p + ik)t cos (p-ifc)M *" 

 "•~~2;rL p + ifc p — ifc Jo 



afcp , ^ P ^N 2afcp •, p (27) 



, afcrsin^pjJfclf_«WP:ZJ*)il'^ = _^^ (28) 



Putting p=yfc, we have, for o.sin jH, 



^_ g/Rsin'Try ^ (29) 



2a/.sin';ry (30) 



ai/.sin 2;r; (31) 



''^ n{f-i') ' 



__ 2aj.sin tt/i sin' rzj + t'.cos' ttj (32) 



