Page 282 - Analog and Digital Filter Design

Phase-Shift Networks (All-Pass Filters) 2 79

of modulus k', where K = cos 6, which can be found using the same program.
The modular angle, 6, can be found from the upper to lower passband frequency
ratio, oh/w,,:

(31
Hence k = sin 6 = sin cos-' -

The rejection of the unwanted sideband can be found from the equation:

tan( 6/2)
[ - : ' I
where 6 = 4q' and q = exp ~

These values are also calculated in the computer program HILBERT.CPP,
given in Listing 9.2

',' Hiibert.cpp-to find poles and zeroes for quadrature networks
II using Jacobian functions sn and cn. based on program given in
.I/ "mmerical P.ecipes in C", by Press. et a1 (Cambridge).
#include (rnath.h)
#include (iostrearn.h)
#define TOL 0.0i)OOl
#defme PI 3.1415926
#define AF.FAY 2 0
void jacobian(doub1e. double) ;
double integrate2(d~ublsi:
int rnain(voidi ;
,' (global variables
double sn. cn;
int main(v-oid)
excern double sn. cn;
doubie ratio;
double k, kk, angle. q;
double kay, kaydash.del;
double u, rejeccion,rnc, ur,:<i;
double pole:
int i, j, n;
cout <c "Enter filter order" c< endl;
cin >> n;