DESIG.X OF REACTIVE EQUALIZERS 



741 



The solution in this case is particularly simple, and gives the well-known 

 Fourier coeilicients, 



= - / a(<p) dtp 



IT Jo 



2 r" 

 y = - / a(ip) COS j<p dip 



IT Jn 



U = 0), 



(i ^ 0). 



Hence, each coefficient oy is dependent only on the area under the correspond- 

 ing function a{<p) cos j<p. 



This result, even though it simplifies the procedure of calculating the aj 

 in eq. (28), has only limited usefulness in this problem. As mentioned above, 



TV 



the range of direct interest extends only to s = - . Thus, an approximation 



over the whole range requires that an f{x-) be arbitrarily specified in the 

 out-band region. Such a procedure, in this case, is an unnecessary restriction 

 on the form oif(x^) outside the useful frequency range. Thus, an approxima- 



tion over a hnite range to - is the procedure to be considered in detail. 



Starting as before, the system of equations in matrix notation which cor- 

 responds to eq. (28) is 



where the elements of [Pjk] up to and including Pss have been evaluated. 

 Hence, the problem is the solution of the first (n + 1) of these equations 

 for the coefficients Co • • • an . In practice, this solution may be simplitied 

 for a desired n by computing once and for all the elements of the inverse 

 matrk [Pik]"^. This matrix is formed by replacing each element of the 

 determinant || P,k \\ by its minor, dividmg each mmor by this determinant, 



