PRACTICAL APPLICATION OF THE FOURIER INTEGRAL 677 



TABLE I (Continued) 



Part 7. Exponential and Trigonometric Functions of p. 



air 

 Vo. 



Coefficient F{f) for the 

 Cisoidal Oscillation 



Coefficient G{g) for the 

 Unit Impulse 



01. 



02. 

 03. 



04. 



05. 

 06. 

 07. 

 08. 

 09. 

 10. 



'11. 



'12. 

 JIS. 



714. 



715. 



716. 



CP', < \p\ 



Mf) - e-i^' = e--f\ _ 



x = /V4x in 703-711 



l(/) = - g-*^^(47r)^X 

 02(/) = 6-i-^(47r)(x2 - 1) 



Xf) = - e-'"^(47r)?(^' - 3x) 



0,(/) = e-'^^'(4Tyix' - 6x^ + 3) 



(^-(/) = - e-i-=(47r)i (x'' - lOx-3 + 15x) 



0g(/) = e-i-=(47r)3(x« - 15x^+45x2 - 15) 



)„(/) = - e-i-'(4Tr)i(x^ - 21x^ 



+ 105x3 _ losx) 



03(/) = e-l-=(47r)Hx^ - 28x« 



+ 210x^ - 420x- + 105) 



e—P{4:TP - 3)2 



-7r/3/2 



pe-^^'' 



1 



e-\gyp 



2V7rp 



</>o(g) = e--^' 

 i4>i{g) 



- 4>2(g) 



- i4>^{g) 



Mg) 



i4>.{g) 



- 4>e{g) 



- i<t>i{g) 



(g) 



g-T<72(47rg2 _ 3)2 



- D "g-'^e^/'' = ^=: — 



V^ " \^(V2/3)" 



X e-''^"'/^ 



KvW 



V^ 



g-irgilP 





-ffff2//3 



27r 



g-.e2/fi(27rg2 - /3) 



