void autotest_iirdes_cplxpair_n6()
{
float tol = 1e-8f;
//
float complex r[6] = {
0.980066577841242 + 0.198669330795061 * _Complex_I,
5.000000000000000 + 0.000000000000000 * _Complex_I,
-0.416146836547142 + 0.909297426825682 * _Complex_I,
0.980066577841242 - 0.198669330795061 * _Complex_I,
0.300000000000000 + 0.000000000000000 * _Complex_I,
-0.416146836547142 - 0.909297426825682 * _Complex_I
};
float complex p[6];
float complex ptest[6] = {
-0.416146836547142 - 0.909297426825682 * _Complex_I,
-0.416146836547142 + 0.909297426825682 * _Complex_I,
0.980066577841242 - 0.198669330795061 * _Complex_I,
0.980066577841242 + 0.198669330795061 * _Complex_I,
0.300000000000000 + 0.000000000000000 * _Complex_I,
5.000000000000000 + 0.000000000000000 * _Complex_I
};
// compute complex pairs
liquid_cplxpair(r,6,1e-6f,p);
unsigned int i;
if (liquid_autotest_verbose) {
printf("complex set:\n");
for (i=0; i<6; i++)
printf(" r[%3u] : %12.8f + j*%12.8f\n", i, crealf(r[i]), cimagf(r[i]));
printf("complex pairs:\n");
for (i=0; i<6; i++)
printf(" p[%3u] : %12.8f + j*%12.8f\n", i, crealf(p[i]), cimagf(p[i]));
}
// run test
for (i=0; i<6; i++) {
CONTEND_DELTA( crealf(p[i]), crealf(ptest[i]), tol );
CONTEND_DELTA( cimagf(p[i]), cimagf(ptest[i]), tol );
}
}
// converts discrete-time zero/pole/gain (zpk) recursive (iir)
// filter representation to second-order sections (sos) form
//
// _zd : discrete zeros array (size _n)
// _pd : discrete poles array (size _n)
// _n : number of poles, zeros
// _kd : gain
//
// _B : output numerator matrix (size (L+r) x 3)
// _A : output denominator matrix (size (L+r) x 3)
//
// L is the number of sections in the cascade:
// r = _n % 2
// L = (_n - r) / 2;
void iirdes_dzpk2sosf(float complex * _zd,
float complex * _pd,
unsigned int _n,
float complex _kd,
float * _B,
float * _A)
{
int i;
float tol=1e-6f; // tolerance for conjuate pair computation
// find/group complex conjugate pairs (poles)
float complex zp[_n];
liquid_cplxpair(_zd,_n,tol,zp);
// find/group complex conjugate pairs (zeros)
float complex pp[_n];
liquid_cplxpair(_pd,_n,tol,pp);
// TODO : group pole pairs with zero pairs
// _n = 2*L + r
unsigned int r = _n % 2; // odd/even order
unsigned int L = (_n - r)/2; // filter semi-length
#if LIQUID_IIRDES_DEBUG_PRINT
printf(" n=%u, r=%u, L=%u\n", _n, r, L);
printf("poles :\n");
for (i=0; i<_n; i++)
printf(" p[%3u] = %12.8f + j*%12.8f\n", i, crealf(_pd[i]), cimagf(_pd[i]));
printf("zeros :\n");
for (i=0; i<_n; i++)
printf(" z[%3u] = %12.8f + j*%12.8f\n", i, crealf(_zd[i]), cimagf(_zd[i]));
printf("poles (conjugate pairs):\n");
for (i=0; i<_n; i++)
printf(" p[%3u] = %12.8f + j*%12.8f\n", i, crealf(pp[i]), cimagf(pp[i]));
printf("zeros (conjugate pairs):\n");
for (i=0; i<_n; i++)
printf(" z[%3u] = %12.8f + j*%12.8f\n", i, crealf(zp[i]), cimagf(zp[i]));
#endif
float complex z0, z1;
float complex p0, p1;
for (i=0; i<L; i++) {
p0 = -pp[2*i+0];
p1 = -pp[2*i+1];
z0 = -zp[2*i+0];
z1 = -zp[2*i+1];
// expand complex pole pairs
_A[3*i+0] = 1.0;
_A[3*i+1] = crealf(p0+p1);
_A[3*i+2] = crealf(p0*p1);
// expand complex zero pairs
_B[3*i+0] = 1.0;
_B[3*i+1] = crealf(z0+z1);
_B[3*i+2] = crealf(z0*z1);
}
// add remaining zero/pole pair if order is odd
if (r) {
p0 = -pp[_n-1];
z0 = -zp[_n-1];
_A[3*i+0] = 1.0;
_A[3*i+1] = -pp[_n-1];
_A[3*i+2] = 0.0;
_B[3*i+0] = 1.0;
_B[3*i+1] = -zp[_n-1];
_B[3*i+2] = 0.0;
}
// distribute gain equally amongst all feed-forward
// coefficients
float k = powf( crealf(_kd), 1.0f/(float)(L+r) );
// adjust gain of first element
for (i=0; i<L+r; i++) {
_B[3*i+0] *= k;
_B[3*i+1] *= k;
_B[3*i+2] *= k;
}
}
void autotest_iirdes_cplxpair_n20()
{
float tol = 1e-8f;
//
float complex r[20] = {
-0.340396183901119 + 1.109902927794652 * _Complex_I,
1.148964416793990 + 0.000000000000000 * _Complex_I,
0.190037889511651 + 0.597517076404221 * _Complex_I,
-0.340396183901119 - 1.109902927794652 * _Complex_I,
0.890883293686046 + 0.000000000000000 * _Complex_I,
-0.248338528396292 - 0.199390430636670 * _Complex_I,
0.190037889511651 - 0.597517076404221 * _Complex_I,
0.003180396218998 + 0.000000000000000 * _Complex_I,
0.261949046540733 - 0.739400953405199 * _Complex_I,
0.261949046540733 + 0.739400953405199 * _Complex_I,
0.309342570837113 + 0.000000000000000 * _Complex_I,
0.035516103001236 + 0.000000000000000 * _Complex_I,
-0.184159864176452 - 0.240335024546875 * _Complex_I,
-0.485244526317243 + 0.452251520655749 * _Complex_I,
-0.485244526317243 - 0.452251520655749 * _Complex_I,
-0.581633365450190 + 0.000000000000000 * _Complex_I,
-0.248338528396292 + 0.199390430636670 * _Complex_I,
-0.184159864176452 + 0.240335024546875 * _Complex_I,
1.013685316242435 + 0.000000000000000 * _Complex_I,
-0.089598596934739 + 0.000000000000000 * _Complex_I
};
float complex p[20];
float complex ptest[20] = {
-0.485244526317243 - 0.452251520655749 * _Complex_I,
-0.485244526317243 + 0.452251520655749 * _Complex_I,
-0.340396183901119 - 1.109902927794652 * _Complex_I,
-0.340396183901119 + 1.109902927794652 * _Complex_I,
-0.248338528396292 - 0.199390430636670 * _Complex_I,
-0.248338528396292 + 0.199390430636670 * _Complex_I,
-0.184159864176452 - 0.240335024546875 * _Complex_I,
-0.184159864176452 + 0.240335024546875 * _Complex_I,
0.190037889511651 - 0.597517076404221 * _Complex_I,
0.190037889511651 + 0.597517076404221 * _Complex_I,
0.261949046540733 - 0.739400953405199 * _Complex_I,
0.261949046540733 + 0.739400953405199 * _Complex_I,
-0.581633365450190 + 0.000000000000000 * _Complex_I,
-0.089598596934739 + 0.000000000000000 * _Complex_I,
0.003180396218998 + 0.000000000000000 * _Complex_I,
0.035516103001236 + 0.000000000000000 * _Complex_I,
0.309342570837113 + 0.000000000000000 * _Complex_I,
0.890883293686046 + 0.000000000000000 * _Complex_I,
1.013685316242435 + 0.000000000000000 * _Complex_I,
1.148964416793990 + 0.000000000000000 * _Complex_I
};
// compute complex pairs
liquid_cplxpair(r,20,1e-6f,p);
unsigned int i;
if (liquid_autotest_verbose) {
printf("complex set:\n");
for (i=0; i<20; i++)
printf(" r[%3u] : %12.8f + j*%12.8f\n", i, crealf(r[i]), cimagf(r[i]));
printf("complex pairs:\n");
for (i=0; i<20; i++)
printf(" p[%3u] : %12.8f + j*%12.8f\n", i, crealf(p[i]), cimagf(p[i]));
}
// run test
for (i=0; i<20; i++) {
CONTEND_DELTA( crealf(p[i]), crealf(ptest[i]), tol );
CONTEND_DELTA( cimagf(p[i]), cimagf(ptest[i]), tol );
}
}
