commit afe8c69338c1ce53b266462d03a31ae026de2898
parent 0ce746165bf1fafa8814719662b6699a96b0371c
Author: d.levin256@gmail.com <d.levin256@gmail.com>
Date: Tue, 26 Nov 2019 15:03:32 +0000
Chebyshev filters
Diffstat:
2 files changed, 363 insertions(+), 293 deletions(-)
diff --git a/examples/iir.cpp b/examples/iir.cpp
@@ -87,6 +87,22 @@ int main()
}
plot_save("butterworth_bandpass4", output, options + ", title='4th-order Butterworth filter, bandpass'");
+ {
+ zpk<fbase> filt = iir_lowpass(chebyshev1<fbase>(8, 2), 0.09);
+ std::vector<biquad_params<fbase>> bqs = to_sos(filt);
+ output = biquad<maxorder>(bqs, unitimpulse());
+ }
+ plot_save("chebyshev1_lowpass8", output,
+ options + ", title='8th-order Chebyshev type I filter, lowpass'");
+
+ {
+ zpk<fbase> filt = iir_lowpass(chebyshev2<fbase>(8, 80), 0.09);
+ std::vector<biquad_params<fbase>> bqs = to_sos(filt);
+ output = biquad<maxorder>(bqs, unitimpulse());
+ }
+ plot_save("chebyshev2_lowpass8", output,
+ options + ", title='8th-order Chebyshev type II filter, lowpass'");
+
println("SVG plots have been saved to svg directory");
return 0;
diff --git a/include/kfr/dsp/iir_design.hpp b/include/kfr/dsp/iir_design.hpp
@@ -27,6 +27,7 @@
#include "../base/filter.hpp"
#include "../base/pointer.hpp"
+#include "../math/hyperbolic.hpp"
#include "../simd/impl/function.hpp"
#include "../simd/operators.hpp"
#include "../simd/vec.hpp"
@@ -48,14 +49,67 @@ inline namespace CMT_ARCH_NAME
{
template <typename T>
+KFR_FUNCTION zpk<T> chebyshev1(int N, identity<T> rp)
+{
+ if (N <= 0)
+ {
+ return { {}, {}, 1 };
+ }
+
+ T eps = sqrt(exp10(0.1 * rp) - 1.0);
+ T mu = 1.0 / N * std::asinh(1 / eps);
+
+ univector<T> m = linspace(-N + 1, N + 1, N, false, true);
+
+ univector<T> theta = c_pi<T> * m / (2 * N);
+ univector<complex<T>> p = -csinh(make_complex(mu, theta));
+ T k = product(-p).re;
+ if (N % 2 == 0)
+ k = k / sqrt(1.0 + eps * eps);
+ return { {}, std::move(p), k };
+}
+
+template <typename T>
+KFR_FUNCTION zpk<T> chebyshev2(int N, identity<T> rs)
+{
+ if (N <= 0)
+ {
+ return { {}, {}, 1 };
+ }
+
+ T de = 1.0 / sqrt(exp10(0.1 * rs) - 1);
+ T mu = std::asinh(1.0 / de) / N;
+
+ univector<T> m;
+
+ if (N % 2)
+ {
+ m = concatenate(linspace(-N + 1, -2, N / 2, true, true), linspace(2, N - 1, N / 2, true, true));
+ }
+ else
+ {
+ m = linspace(-N + 1, N + 1, N, false, true);
+ }
+
+ univector<complex<T>> z = -cconj(complex<T>(0, 1) / sin(m * c_pi<T> / (2.0 * N)));
+
+ univector<complex<T>> p =
+ -cexp(complex<T>(0, 1) * c_pi<T> * linspace(-N + 1, N + 1, N, false, true) / (2 * N));
+ p = make_complex(sinh(mu) * real(p), cosh(mu) * imag(p));
+ p = 1.0 / p;
+
+ T k = (product(-p) / product(-z)).re;
+
+ return { std::move(z), std::move(p), k };
+}
+
+template <typename T>
KFR_FUNCTION zpk<T> butterworth(int N)
{
switch (N)
{
- case 0:
- return { {}, {}, 1 };
case 1:
- return { {}, { complex<T>(-1., -0.) }, 1 };
+ return { {}, { complex<T>(-1., +0.) }, 1 };
case 2:
return { {},
{ complex<T>(-0.7071067811865476, -0.7071067811865476),
@@ -63,356 +117,356 @@ KFR_FUNCTION zpk<T> butterworth(int N)
1 };
case 3:
return { {},
- { complex<T>(-1., -0.), complex<T>(-0.5000000000000001, -0.8660254037844386),
+ { complex<T>(-0.5000000000000001, -0.8660254037844386), complex<T>(-1., +0.),
complex<T>(-0.5000000000000001, +0.8660254037844386) },
1 };
case 4:
return { {},
- { complex<T>(-0.9238795325112867, -0.3826834323650898),
+ { complex<T>(-0.38268343236508984, -0.9238795325112867),
+ complex<T>(-0.9238795325112867, -0.3826834323650898),
complex<T>(-0.9238795325112867, +0.3826834323650898),
- complex<T>(-0.38268343236508984, -0.9238795325112867),
complex<T>(-0.38268343236508984, +0.9238795325112867) },
1 };
case 5:
return { {},
- { complex<T>(-1., -0.), complex<T>(-0.8090169943749475, -0.5877852522924731),
+ { complex<T>(-0.30901699437494745, -0.9510565162951535),
+ complex<T>(-0.8090169943749475, -0.5877852522924731), complex<T>(-1., +0.),
complex<T>(-0.8090169943749475, +0.5877852522924731),
- complex<T>(-0.30901699437494745, -0.9510565162951535),
complex<T>(-0.30901699437494745, +0.9510565162951535) },
1 };
case 6:
return { {},
- { complex<T>(-0.9659258262890683, -0.25881904510252074),
- complex<T>(-0.9659258262890683, +0.25881904510252074),
+ { complex<T>(-0.25881904510252096, -0.9659258262890682),
complex<T>(-0.7071067811865476, -0.7071067811865476),
+ complex<T>(-0.9659258262890683, -0.25881904510252074),
+ complex<T>(-0.9659258262890683, +0.25881904510252074),
complex<T>(-0.7071067811865476, +0.7071067811865476),
- complex<T>(-0.25881904510252096, -0.9659258262890682),
complex<T>(-0.25881904510252096, +0.9659258262890682) },
1 };
case 7:
return { {},
- { complex<T>(-1., -0.), complex<T>(-0.9009688679024191, -0.4338837391175581),
- complex<T>(-0.9009688679024191, +0.4338837391175581),
+ { complex<T>(-0.22252093395631445, -0.9749279121818236),
complex<T>(-0.6234898018587336, -0.7818314824680298),
+ complex<T>(-0.9009688679024191, -0.4338837391175581), complex<T>(-1., +0.),
+ complex<T>(-0.9009688679024191, +0.4338837391175581),
complex<T>(-0.6234898018587336, +0.7818314824680298),
- complex<T>(-0.22252093395631445, -0.9749279121818236),
complex<T>(-0.22252093395631445, +0.9749279121818236) },
1 };
case 8:
return { {},
- { complex<T>(-0.9807852804032304, -0.19509032201612825),
- complex<T>(-0.9807852804032304, +0.19509032201612825),
+ { complex<T>(-0.19509032201612833, -0.9807852804032304),
+ complex<T>(-0.5555702330196023, -0.8314696123025452),
complex<T>(-0.8314696123025452, -0.5555702330196022),
+ complex<T>(-0.9807852804032304, -0.19509032201612825),
+ complex<T>(-0.9807852804032304, +0.19509032201612825),
complex<T>(-0.8314696123025452, +0.5555702330196022),
- complex<T>(-0.5555702330196023, -0.8314696123025452),
complex<T>(-0.5555702330196023, +0.8314696123025452),
- complex<T>(-0.19509032201612833, -0.9807852804032304),
complex<T>(-0.19509032201612833, +0.9807852804032304) },
1 };
case 9:
return { {},
- { complex<T>(-1., -0.), complex<T>(-0.9396926207859084, -0.3420201433256687),
- complex<T>(-0.9396926207859084, +0.3420201433256687),
+ { complex<T>(-0.17364817766693041, -0.984807753012208),
+ complex<T>(-0.5000000000000001, -0.8660254037844386),
complex<T>(-0.766044443118978, -0.6427876096865393),
+ complex<T>(-0.9396926207859084, -0.3420201433256687), complex<T>(-1., +0.),
+ complex<T>(-0.9396926207859084, +0.3420201433256687),
complex<T>(-0.766044443118978, +0.6427876096865393),
- complex<T>(-0.5000000000000001, -0.8660254037844386),
complex<T>(-0.5000000000000001, +0.8660254037844386),
- complex<T>(-0.17364817766693041, -0.984807753012208),
complex<T>(-0.17364817766693041, +0.984807753012208) },
1 };
case 10:
return { {},
- { complex<T>(-0.9876883405951378, -0.15643446504023087),
- complex<T>(-0.9876883405951378, +0.15643446504023087),
+ { complex<T>(-0.15643446504023092, -0.9876883405951378),
+ complex<T>(-0.4539904997395468, -0.8910065241883678),
+ complex<T>(-0.7071067811865476, -0.7071067811865476),
complex<T>(-0.8910065241883679, -0.45399049973954675),
+ complex<T>(-0.9876883405951378, -0.15643446504023087),
+ complex<T>(-0.9876883405951378, +0.15643446504023087),
complex<T>(-0.8910065241883679, +0.45399049973954675),
- complex<T>(-0.7071067811865476, -0.7071067811865476),
complex<T>(-0.7071067811865476, +0.7071067811865476),
- complex<T>(-0.4539904997395468, -0.8910065241883678),
complex<T>(-0.4539904997395468, +0.8910065241883678),
- complex<T>(-0.15643446504023092, -0.9876883405951378),
complex<T>(-0.15643446504023092, +0.9876883405951378) },
1 };
case 11:
return { {},
- { complex<T>(-1., -0.), complex<T>(-0.9594929736144974, -0.28173255684142967),
- complex<T>(-0.9594929736144974, +0.28173255684142967),
+ { complex<T>(-0.14231483827328512, -0.9898214418809327),
+ complex<T>(-0.41541501300188644, -0.9096319953545183),
+ complex<T>(-0.654860733945285, -0.7557495743542583),
complex<T>(-0.8412535328311812, -0.5406408174555976),
+ complex<T>(-0.9594929736144974, -0.28173255684142967), complex<T>(-1., +0.),
+ complex<T>(-0.9594929736144974, +0.28173255684142967),
complex<T>(-0.8412535328311812, +0.5406408174555976),
- complex<T>(-0.654860733945285, -0.7557495743542583),
complex<T>(-0.654860733945285, +0.7557495743542583),
- complex<T>(-0.41541501300188644, -0.9096319953545183),
complex<T>(-0.41541501300188644, +0.9096319953545183),
- complex<T>(-0.14231483827328512, -0.9898214418809327),
complex<T>(-0.14231483827328512, +0.9898214418809327) },
1 };
case 12:
return { {},
- { complex<T>(-0.9914448613738104, -0.13052619222005157),
- complex<T>(-0.9914448613738104, +0.13052619222005157),
+ { complex<T>(-0.13052619222005193, -0.9914448613738104),
+ complex<T>(-0.38268343236508984, -0.9238795325112867),
+ complex<T>(-0.6087614290087207, -0.7933533402912352),
+ complex<T>(-0.7933533402912353, -0.6087614290087205),
complex<T>(-0.9238795325112867, -0.3826834323650898),
+ complex<T>(-0.9914448613738104, -0.13052619222005157),
+ complex<T>(-0.9914448613738104, +0.13052619222005157),
complex<T>(-0.9238795325112867, +0.3826834323650898),
- complex<T>(-0.7933533402912353, -0.6087614290087205),
complex<T>(-0.7933533402912353, +0.6087614290087205),
- complex<T>(-0.6087614290087207, -0.7933533402912352),
complex<T>(-0.6087614290087207, +0.7933533402912352),
- complex<T>(-0.38268343236508984, -0.9238795325112867),
complex<T>(-0.38268343236508984, +0.9238795325112867),
- complex<T>(-0.13052619222005193, -0.9914448613738104),
complex<T>(-0.13052619222005193, +0.9914448613738104) },
1 };
case 13:
return { {},
- { complex<T>(-1., -0.), complex<T>(-0.970941817426052, -0.23931566428755777),
- complex<T>(-0.970941817426052, +0.23931566428755777),
+ { complex<T>(-0.120536680255323, -0.992708874098054),
+ complex<T>(-0.35460488704253557, -0.9350162426854148),
+ complex<T>(-0.5680647467311558, -0.8229838658936565),
+ complex<T>(-0.7485107481711011, -0.6631226582407952),
complex<T>(-0.8854560256532099, -0.46472317204376856),
+ complex<T>(-0.970941817426052, -0.23931566428755777), complex<T>(-1., +0.),
+ complex<T>(-0.970941817426052, +0.23931566428755777),
complex<T>(-0.8854560256532099, +0.46472317204376856),
- complex<T>(-0.7485107481711011, -0.6631226582407952),
complex<T>(-0.7485107481711011, +0.6631226582407952),
- complex<T>(-0.5680647467311558, -0.8229838658936565),
complex<T>(-0.5680647467311558, +0.8229838658936565),
- complex<T>(-0.35460488704253557, -0.9350162426854148),
complex<T>(-0.35460488704253557, +0.9350162426854148),
- complex<T>(-0.120536680255323, -0.992708874098054),
complex<T>(-0.120536680255323, +0.992708874098054) },
1 };
case 14:
return { {},
- { complex<T>(-0.9937122098932426, -0.11196447610330786),
- complex<T>(-0.9937122098932426, +0.11196447610330786),
+ { complex<T>(-0.11196447610330791, -0.9937122098932426),
+ complex<T>(-0.3302790619551673, -0.9438833303083675),
+ complex<T>(-0.5320320765153366, -0.8467241992282841),
+ complex<T>(-0.7071067811865476, -0.7071067811865476),
+ complex<T>(-0.8467241992282842, -0.5320320765153366),
complex<T>(-0.9438833303083676, -0.3302790619551671),
+ complex<T>(-0.9937122098932426, -0.11196447610330786),
+ complex<T>(-0.9937122098932426, +0.11196447610330786),
complex<T>(-0.9438833303083676, +0.3302790619551671),
- complex<T>(-0.8467241992282842, -0.5320320765153366),
complex<T>(-0.8467241992282842, +0.5320320765153366),
- complex<T>(-0.7071067811865476, -0.7071067811865476),
complex<T>(-0.7071067811865476, +0.7071067811865476),
- complex<T>(-0.5320320765153366, -0.8467241992282841),
complex<T>(-0.5320320765153366, +0.8467241992282841),
- complex<T>(-0.3302790619551673, -0.9438833303083675),
complex<T>(-0.3302790619551673, +0.9438833303083675),
- complex<T>(-0.11196447610330791, -0.9937122098932426),
complex<T>(-0.11196447610330791, +0.9937122098932426) },
1 };
case 15:
return { {},
- { complex<T>(-1., -0.), complex<T>(-0.9781476007338057, -0.20791169081775931),
- complex<T>(-0.9781476007338057, +0.20791169081775931),
+ { complex<T>(-0.10452846326765346, -0.9945218953682733),
+ complex<T>(-0.30901699437494745, -0.9510565162951535),
+ complex<T>(-0.5000000000000001, -0.8660254037844386),
+ complex<T>(-0.6691306063588582, -0.7431448254773941),
+ complex<T>(-0.8090169943749475, -0.5877852522924731),
complex<T>(-0.9135454576426009, -0.40673664307580015),
+ complex<T>(-0.9781476007338057, -0.20791169081775931), complex<T>(-1., +0.),
+ complex<T>(-0.9781476007338057, +0.20791169081775931),
complex<T>(-0.9135454576426009, +0.40673664307580015),
- complex<T>(-0.8090169943749475, -0.5877852522924731),
complex<T>(-0.8090169943749475, +0.5877852522924731),
- complex<T>(-0.6691306063588582, -0.7431448254773941),
complex<T>(-0.6691306063588582, +0.7431448254773941),
- complex<T>(-0.5000000000000001, -0.8660254037844386),
complex<T>(-0.5000000000000001, +0.8660254037844386),
- complex<T>(-0.30901699437494745, -0.9510565162951535),
complex<T>(-0.30901699437494745, +0.9510565162951535),
- complex<T>(-0.10452846326765346, -0.9945218953682733),
complex<T>(-0.10452846326765346, +0.9945218953682733) },
1 };
case 16:
return { {},
- { complex<T>(-0.9951847266721969, -0.0980171403295606),
- complex<T>(-0.9951847266721969, +0.0980171403295606),
+ { complex<T>(-0.09801714032956077, -0.9951847266721968),
+ complex<T>(-0.29028467725446233, -0.9569403357322089),
+ complex<T>(-0.4713967368259978, -0.8819212643483549),
+ complex<T>(-0.6343932841636455, -0.7730104533627369),
+ complex<T>(-0.773010453362737, -0.6343932841636455),
+ complex<T>(-0.881921264348355, -0.47139673682599764),
complex<T>(-0.9569403357322088, -0.29028467725446233),
+ complex<T>(-0.9951847266721969, -0.0980171403295606),
+ complex<T>(-0.9951847266721969, +0.0980171403295606),
complex<T>(-0.9569403357322088, +0.29028467725446233),
- complex<T>(-0.881921264348355, -0.47139673682599764),
complex<T>(-0.881921264348355, +0.47139673682599764),
- complex<T>(-0.773010453362737, -0.6343932841636455),
complex<T>(-0.773010453362737, +0.6343932841636455),
- complex<T>(-0.6343932841636455, -0.7730104533627369),
complex<T>(-0.6343932841636455, +0.7730104533627369),
- complex<T>(-0.4713967368259978, -0.8819212643483549),
complex<T>(-0.4713967368259978, +0.8819212643483549),
- complex<T>(-0.29028467725446233, -0.9569403357322089),
complex<T>(-0.29028467725446233, +0.9569403357322089),
- complex<T>(-0.09801714032956077, -0.9951847266721968),
complex<T>(-0.09801714032956077, +0.9951847266721968) },
1 };
case 17:
return { {},
- { complex<T>(-1., -0.), complex<T>(-0.9829730996839018, -0.18374951781657034),
- complex<T>(-0.9829730996839018, +0.18374951781657034),
+ { complex<T>(-0.09226835946330202, -0.9957341762950345),
+ complex<T>(-0.273662990072083, -0.961825643172819),
+ complex<T>(-0.4457383557765383, -0.8951632913550623),
+ complex<T>(-0.6026346363792565, -0.7980172272802395),
+ complex<T>(-0.7390089172206591, -0.6736956436465572),
+ complex<T>(-0.8502171357296142, -0.5264321628773557),
complex<T>(-0.9324722294043558, -0.3612416661871529),
+ complex<T>(-0.9829730996839018, -0.18374951781657034), complex<T>(-1., +0.),
+ complex<T>(-0.9829730996839018, +0.18374951781657034),
complex<T>(-0.9324722294043558, +0.3612416661871529),
- complex<T>(-0.8502171357296142, -0.5264321628773557),
complex<T>(-0.8502171357296142, +0.5264321628773557),
- complex<T>(-0.7390089172206591, -0.6736956436465572),
complex<T>(-0.7390089172206591, +0.6736956436465572),
- complex<T>(-0.6026346363792565, -0.7980172272802395),
complex<T>(-0.6026346363792565, +0.7980172272802395),
- complex<T>(-0.4457383557765383, -0.8951632913550623),
complex<T>(-0.4457383557765383, +0.8951632913550623),
- complex<T>(-0.273662990072083, -0.961825643172819),
complex<T>(-0.273662990072083, +0.961825643172819),
- complex<T>(-0.09226835946330202, -0.9957341762950345),
complex<T>(-0.09226835946330202, +0.9957341762950345) },
1 };
case 18:
return { {},
- { complex<T>(-0.9961946980917455, -0.08715574274765817),
- complex<T>(-0.9961946980917455, +0.08715574274765817),
+ { complex<T>(-0.08715574274765814, -0.9961946980917455),
+ complex<T>(-0.25881904510252096, -0.9659258262890682),
+ complex<T>(-0.42261826174069944, -0.9063077870366499),
+ complex<T>(-0.5735764363510463, -0.8191520442889917),
+ complex<T>(-0.7071067811865476, -0.7071067811865476),
+ complex<T>(-0.8191520442889918, -0.573576436351046),
+ complex<T>(-0.9063077870366499, -0.4226182617406994),
complex<T>(-0.9659258262890683, -0.25881904510252074),
+ complex<T>(-0.9961946980917455, -0.08715574274765817),
+ complex<T>(-0.9961946980917455, +0.08715574274765817),
complex<T>(-0.9659258262890683, +0.25881904510252074),
- complex<T>(-0.9063077870366499, -0.4226182617406994),
complex<T>(-0.9063077870366499, +0.4226182617406994),
- complex<T>(-0.8191520442889918, -0.573576436351046),
complex<T>(-0.8191520442889918, +0.573576436351046),
- complex<T>(-0.7071067811865476, -0.7071067811865476),
complex<T>(-0.7071067811865476, +0.7071067811865476),
- complex<T>(-0.5735764363510463, -0.8191520442889917),
complex<T>(-0.5735764363510463, +0.8191520442889917),
- complex<T>(-0.42261826174069944, -0.9063077870366499),
complex<T>(-0.42261826174069944, +0.9063077870366499),
- complex<T>(-0.25881904510252096, -0.9659258262890682),
complex<T>(-0.25881904510252096, +0.9659258262890682),
- complex<T>(-0.08715574274765814, -0.9961946980917455),
complex<T>(-0.08715574274765814, +0.9961946980917455) },
1 };
case 19:
return { {},
- { complex<T>(-1., -0.), complex<T>(-0.9863613034027223, -0.1645945902807339),
- complex<T>(-0.9863613034027223, +0.1645945902807339),
+ { complex<T>(-0.0825793454723324, -0.9965844930066698),
+ complex<T>(-0.24548548714079924, -0.9694002659393304),
+ complex<T>(-0.40169542465296953, -0.9157733266550574),
+ complex<T>(-0.5469481581224269, -0.8371664782625285),
+ complex<T>(-0.6772815716257411, -0.7357239106731316),
+ complex<T>(-0.7891405093963936, -0.6142127126896678),
+ complex<T>(-0.8794737512064891, -0.4759473930370735),
complex<T>(-0.9458172417006346, -0.32469946920468346),
+ complex<T>(-0.9863613034027223, -0.1645945902807339), complex<T>(-1., +0.),
+ complex<T>(-0.9863613034027223, +0.1645945902807339),
complex<T>(-0.9458172417006346, +0.32469946920468346),
- complex<T>(-0.8794737512064891, -0.4759473930370735),
complex<T>(-0.8794737512064891, +0.4759473930370735),
- complex<T>(-0.7891405093963936, -0.6142127126896678),
complex<T>(-0.7891405093963936, +0.6142127126896678),
- complex<T>(-0.6772815716257411, -0.7357239106731316),
complex<T>(-0.6772815716257411, +0.7357239106731316),
- complex<T>(-0.5469481581224269, -0.8371664782625285),
complex<T>(-0.5469481581224269, +0.8371664782625285),
- complex<T>(-0.40169542465296953, -0.9157733266550574),
complex<T>(-0.40169542465296953, +0.9157733266550574),
- complex<T>(-0.24548548714079924, -0.9694002659393304),
complex<T>(-0.24548548714079924, +0.9694002659393304),
- complex<T>(-0.0825793454723324, -0.9965844930066698),
complex<T>(-0.0825793454723324, +0.9965844930066698) },
1 };
case 20:
return { {},
- { complex<T>(-0.996917333733128, -0.07845909572784494),
- complex<T>(-0.996917333733128, +0.07845909572784494),
+ { complex<T>(-0.078459095727845, -0.996917333733128),
+ complex<T>(-0.23344536385590525, -0.9723699203976767),
+ complex<T>(-0.38268343236508984, -0.9238795325112867),
+ complex<T>(-0.5224985647159487, -0.8526401643540923),
+ complex<T>(-0.6494480483301837, -0.7604059656000309),
+ complex<T>(-0.7604059656000309, -0.6494480483301837),
+ complex<T>(-0.8526401643540923, -0.5224985647159488),
+ complex<T>(-0.9238795325112867, -0.3826834323650898),
complex<T>(-0.9723699203976766, -0.2334453638559054),
+ complex<T>(-0.996917333733128, -0.07845909572784494),
+ complex<T>(-0.996917333733128, +0.07845909572784494),
complex<T>(-0.9723699203976766, +0.2334453638559054),
- complex<T>(-0.9238795325112867, -0.3826834323650898),
complex<T>(-0.9238795325112867, +0.3826834323650898),
- complex<T>(-0.8526401643540923, -0.5224985647159488),
complex<T>(-0.8526401643540923, +0.5224985647159488),
- complex<T>(-0.7604059656000309, -0.6494480483301837),
complex<T>(-0.7604059656000309, +0.6494480483301837),
- complex<T>(-0.6494480483301837, -0.7604059656000309),
complex<T>(-0.6494480483301837, +0.7604059656000309),
- complex<T>(-0.5224985647159487, -0.8526401643540923),
complex<T>(-0.5224985647159487, +0.8526401643540923),
- complex<T>(-0.38268343236508984, -0.9238795325112867),
complex<T>(-0.38268343236508984, +0.9238795325112867),
- complex<T>(-0.23344536385590525, -0.9723699203976767),
complex<T>(-0.23344536385590525, +0.9723699203976767),
- complex<T>(-0.078459095727845, -0.996917333733128),
complex<T>(-0.078459095727845, +0.996917333733128) },
1 };
case 21:
return { {},
- { complex<T>(-1., -0.),
+ { complex<T>(-0.07473009358642439, -0.9972037971811801),
+ complex<T>(-0.22252093395631445, -0.9749279121818236),
+ complex<T>(-0.3653410243663952, -0.9308737486442041),
+ complex<T>(-0.5000000000000001, -0.8660254037844386),
+ complex<T>(-0.6234898018587336, -0.7818314824680298),
+ complex<T>(-0.7330518718298263, -0.6801727377709194),
+ complex<T>(-0.8262387743159949, -0.563320058063622),
+ complex<T>(-0.9009688679024191, -0.4338837391175581),
+ complex<T>(-0.9555728057861408, -0.29475517441090415),
complex<T>(-0.9888308262251285, -0.14904226617617441),
+ complex<T>(-1., +0.),
complex<T>(-0.9888308262251285, +0.14904226617617441),
- complex<T>(-0.9555728057861408, -0.29475517441090415),
complex<T>(-0.9555728057861408, +0.29475517441090415),
- complex<T>(-0.9009688679024191, -0.4338837391175581),
complex<T>(-0.9009688679024191, +0.4338837391175581),
- complex<T>(-0.8262387743159949, -0.563320058063622),
complex<T>(-0.8262387743159949, +0.563320058063622),
- complex<T>(-0.7330518718298263, -0.6801727377709194),
complex<T>(-0.7330518718298263, +0.6801727377709194),
- complex<T>(-0.6234898018587336, -0.7818314824680298),
complex<T>(-0.6234898018587336, +0.7818314824680298),
- complex<T>(-0.5000000000000001, -0.8660254037844386),
complex<T>(-0.5000000000000001, +0.8660254037844386),
- complex<T>(-0.3653410243663952, -0.9308737486442041),
complex<T>(-0.3653410243663952, +0.9308737486442041),
- complex<T>(-0.22252093395631445, -0.9749279121818236),
complex<T>(-0.22252093395631445, +0.9749279121818236),
- complex<T>(-0.07473009358642439, -0.9972037971811801),
complex<T>(-0.07473009358642439, +0.9972037971811801) },
1 };
case 22:
return { {},
- { complex<T>(-0.9974521146102535, -0.07133918319923234),
- complex<T>(-0.9974521146102535, +0.07133918319923234),
+ { complex<T>(-0.07133918319923235, -0.9974521146102535),
+ complex<T>(-0.21256528955297682, -0.9771468659711595),
+ complex<T>(-0.3494641795990982, -0.9369497249997618),
+ complex<T>(-0.479248986720057, -0.8776789895672555),
+ complex<T>(-0.5992776665113468, -0.8005412409243605),
+ complex<T>(-0.7071067811865477, -0.7071067811865475),
+ complex<T>(-0.8005412409243604, -0.5992776665113468),
+ complex<T>(-0.8776789895672557, -0.4792489867200568),
+ complex<T>(-0.9369497249997617, -0.34946417959909837),
complex<T>(-0.9771468659711595, -0.21256528955297668),
+ complex<T>(-0.9974521146102535, -0.07133918319923234),
+ complex<T>(-0.9974521146102535, +0.07133918319923234),
complex<T>(-0.9771468659711595, +0.21256528955297668),
- complex<T>(-0.9369497249997617, -0.34946417959909837),
complex<T>(-0.9369497249997617, +0.34946417959909837),
- complex<T>(-0.8776789895672557, -0.4792489867200568),
complex<T>(-0.8776789895672557, +0.4792489867200568),
- complex<T>(-0.8005412409243604, -0.5992776665113468),
complex<T>(-0.8005412409243604, +0.5992776665113468),
- complex<T>(-0.7071067811865477, -0.7071067811865475),
complex<T>(-0.7071067811865477, +0.7071067811865475),
- complex<T>(-0.5992776665113468, -0.8005412409243605),
complex<T>(-0.5992776665113468, +0.8005412409243605),
- complex<T>(-0.479248986720057, -0.8776789895672555),
complex<T>(-0.479248986720057, +0.8776789895672555),
- complex<T>(-0.3494641795990982, -0.9369497249997618),
complex<T>(-0.3494641795990982, +0.9369497249997618),
- complex<T>(-0.21256528955297682, -0.9771468659711595),
complex<T>(-0.21256528955297682, +0.9771468659711595),
- complex<T>(-0.07133918319923235, -0.9974521146102535),
complex<T>(-0.07133918319923235, +0.9974521146102535) },
1 };
case 23:
return { {},
- { complex<T>(-1., -0.),
+ { complex<T>(-0.06824241336467123, -0.9976687691905392),
+ complex<T>(-0.20345601305263397, -0.9790840876823228),
+ complex<T>(-0.3348796121709863, -0.9422609221188204),
+ complex<T>(-0.4600650377311522, -0.8878852184023752),
+ complex<T>(-0.5766803221148672, -0.816969893010442),
+ complex<T>(-0.6825531432186541, -0.730835964278124),
+ complex<T>(-0.7757112907044199, -0.6310879443260528),
+ complex<T>(-0.8544194045464886, -0.5195839500354336),
+ complex<T>(-0.917211301505453, -0.39840108984624145),
+ complex<T>(-0.9629172873477994, -0.2697967711570243),
complex<T>(-0.9906859460363308, -0.1361666490962466),
+ complex<T>(-1., +0.),
complex<T>(-0.9906859460363308, +0.1361666490962466),
- complex<T>(-0.9629172873477994, -0.2697967711570243),
complex<T>(-0.9629172873477994, +0.2697967711570243),
- complex<T>(-0.917211301505453, -0.39840108984624145),
complex<T>(-0.917211301505453, +0.39840108984624145),
- complex<T>(-0.8544194045464886, -0.5195839500354336),
complex<T>(-0.8544194045464886, +0.5195839500354336),
- complex<T>(-0.7757112907044199, -0.6310879443260528),
complex<T>(-0.7757112907044199, +0.6310879443260528),
- complex<T>(-0.6825531432186541, -0.730835964278124),
complex<T>(-0.6825531432186541, +0.730835964278124),
- complex<T>(-0.5766803221148672, -0.816969893010442),
complex<T>(-0.5766803221148672, +0.816969893010442),
- complex<T>(-0.4600650377311522, -0.8878852184023752),
complex<T>(-0.4600650377311522, +0.8878852184023752),
- complex<T>(-0.3348796121709863, -0.9422609221188204),
complex<T>(-0.3348796121709863, +0.9422609221188204),
- complex<T>(-0.20345601305263397, -0.9790840876823228),
complex<T>(-0.20345601305263397, +0.9790840876823228),
- complex<T>(-0.06824241336467123, -0.9976687691905392),
complex<T>(-0.06824241336467123, +0.9976687691905392) },
1 };
case 24:
return { {},
- { complex<T>(-0.9978589232386035, -0.06540312923014306),
- complex<T>(-0.9978589232386035, +0.06540312923014306),
+ { complex<T>(-0.06540312923014327, -0.9978589232386035),
+ complex<T>(-0.19509032201612833, -0.9807852804032304),
+ complex<T>(-0.3214394653031617, -0.9469301294951056),
+ complex<T>(-0.44228869021900125, -0.8968727415326884),
+ complex<T>(-0.5555702330196024, -0.8314696123025451),
+ complex<T>(-0.6593458151000688, -0.7518398074789774),
+ complex<T>(-0.7518398074789775, -0.6593458151000687),
+ complex<T>(-0.8314696123025452, -0.5555702330196022),
+ complex<T>(-0.8968727415326884, -0.44228869021900125),
+ complex<T>(-0.9469301294951057, -0.32143946530316153),
complex<T>(-0.9807852804032304, -0.19509032201612825),
+ complex<T>(-0.9978589232386035, -0.06540312923014306),
+ complex<T>(-0.9978589232386035, +0.06540312923014306),
complex<T>(-0.9807852804032304, +0.19509032201612825),
- complex<T>(-0.9469301294951057, -0.32143946530316153),
complex<T>(-0.9469301294951057, +0.32143946530316153),
- complex<T>(-0.8968727415326884, -0.44228869021900125),
complex<T>(-0.8968727415326884, +0.44228869021900125),
- complex<T>(-0.8314696123025452, -0.5555702330196022),
complex<T>(-0.8314696123025452, +0.5555702330196022),
- complex<T>(-0.7518398074789775, -0.6593458151000687),
complex<T>(-0.7518398074789775, +0.6593458151000687),
- complex<T>(-0.6593458151000688, -0.7518398074789774),
complex<T>(-0.6593458151000688, +0.7518398074789774),
- complex<T>(-0.5555702330196024, -0.8314696123025451),
complex<T>(-0.5555702330196024, +0.8314696123025451),
- complex<T>(-0.44228869021900125, -0.8968727415326884),
complex<T>(-0.44228869021900125, +0.8968727415326884),
- complex<T>(-0.3214394653031617, -0.9469301294951056),
complex<T>(-0.3214394653031617, +0.9469301294951056),
- complex<T>(-0.19509032201612833, -0.9807852804032304),
complex<T>(-0.19509032201612833, +0.9807852804032304),
- complex<T>(-0.06540312923014327, -0.9978589232386035),
complex<T>(-0.06540312923014327, +0.9978589232386035) },
1 };
default:
@@ -428,7 +482,7 @@ KFR_FUNCTION zpk<T> bessel(int N)
case 0:
return { {}, {}, 1.0 };
case 1:
- return { {}, { complex<T>(-1., -0.) }, 1.0 };
+ return { {}, { complex<T>(-1., +0.) }, 1.0 };
case 2:
return { {},
{ complex<T>(-0.8660254037844385, -0.4999999999999999),
@@ -436,364 +490,363 @@ KFR_FUNCTION zpk<T> bessel(int N)
1.0 };
case 3:
return { {},
- { complex<T>(-0.9416000265332067, -0.), complex<T>(-0.7456403858480766, -0.7113666249728353),
+ { complex<T>(-0.7456403858480766, -0.7113666249728353), complex<T>(-0.9416000265332067, +0.),
complex<T>(-0.7456403858480766, +0.7113666249728353) },
1.0 };
case 4:
return { {},
- { complex<T>(-0.904758796788245, -0.27091873300387465),
+ { complex<T>(-0.6572111716718827, -0.830161435004873),
+ complex<T>(-0.904758796788245, -0.27091873300387465),
complex<T>(-0.904758796788245, +0.27091873300387465),
- complex<T>(-0.6572111716718827, -0.830161435004873),
complex<T>(-0.6572111716718827, +0.830161435004873) },
1.0 };
case 5:
return { {},
- { complex<T>(-0.92644207738776, -0.), complex<T>(-0.8515536193688396, -0.44271746394433276),
+ { complex<T>(-0.5905759446119192, -0.9072067564574549),
+ complex<T>(-0.8515536193688396, -0.44271746394433276), complex<T>(-0.92644207738776, +0.),
complex<T>(-0.8515536193688396, +0.44271746394433276),
- complex<T>(-0.5905759446119192, -0.9072067564574549),
complex<T>(-0.5905759446119192, +0.9072067564574549) },
1.0 };
case 6:
return { {},
- { complex<T>(-0.9093906830472273, -0.1856964396793047),
- complex<T>(-0.9093906830472273, +0.1856964396793047),
+ { complex<T>(-0.5385526816693108, -0.9616876881954276),
complex<T>(-0.7996541858328287, -0.5621717346937316),
+ complex<T>(-0.9093906830472273, -0.1856964396793047),
+ complex<T>(-0.9093906830472273, +0.1856964396793047),
complex<T>(-0.7996541858328287, +0.5621717346937316),
- complex<T>(-0.5385526816693108, -0.9616876881954276),
complex<T>(-0.5385526816693108, +0.9616876881954276) },
1.0 };
case 7:
return { {},
- { complex<T>(-0.919487155649029, -0.), complex<T>(-0.8800029341523379, -0.32166527623077407),
- complex<T>(-0.8800029341523379, +0.32166527623077407),
+ { complex<T>(-0.4966917256672317, -1.0025085084544205),
complex<T>(-0.7527355434093214, -0.6504696305522553),
+ complex<T>(-0.8800029341523379, -0.32166527623077407), complex<T>(-0.919487155649029, +0.),
+ complex<T>(-0.8800029341523379, +0.32166527623077407),
complex<T>(-0.7527355434093214, +0.6504696305522553),
- complex<T>(-0.4966917256672317, -1.0025085084544205),
complex<T>(-0.4966917256672317, +1.0025085084544205) },
1.0 };
case 8:
return { {},
- { complex<T>(-0.9096831546652911, -0.1412437976671423),
- complex<T>(-0.9096831546652911, +0.1412437976671423),
+ { complex<T>(-0.46217404125321254, -1.0343886811269012),
+ complex<T>(-0.7111381808485397, -0.71865173141084),
complex<T>(-0.8473250802359334, -0.42590175382729345),
+ complex<T>(-0.9096831546652911, -0.1412437976671423),
+ complex<T>(-0.9096831546652911, +0.1412437976671423),
complex<T>(-0.8473250802359334, +0.42590175382729345),
- complex<T>(-0.7111381808485397, -0.71865173141084),
complex<T>(-0.7111381808485397, +0.71865173141084),
- complex<T>(-0.46217404125321254, -1.0343886811269012),
complex<T>(-0.46217404125321254, +1.0343886811269012) },
1.0 };
case 9:
return { {},
- { complex<T>(-0.9154957797499037, -0.),
+ { complex<T>(-0.43314155615536226, -1.0600736701359301),
+ complex<T>(-0.6743622686854763, -0.7730546212691185),
+ complex<T>(-0.8148021112269014, -0.50858156896315),
complex<T>(-0.8911217017079759, -0.25265809345821644),
+ complex<T>(-0.9154957797499037, +0.),
complex<T>(-0.8911217017079759, +0.25265809345821644),
- complex<T>(-0.8148021112269014, -0.50858156896315),
complex<T>(-0.8148021112269014, +0.50858156896315),
- complex<T>(-0.6743622686854763, -0.7730546212691185),
complex<T>(-0.6743622686854763, +0.7730546212691185),
- complex<T>(-0.43314155615536226, -1.0600736701359301),
complex<T>(-0.43314155615536226, +1.0600736701359301) },
1.0 };
case 10:
return { {},
- { complex<T>(-0.9091347320900505, -0.11395831373355114),
- complex<T>(-0.9091347320900505, +0.11395831373355114),
+ { complex<T>(-0.4083220732868863, -1.0812748428191246),
+ complex<T>(-0.6417513866988322, -0.8175836167191022),
+ complex<T>(-0.7837694413101445, -0.5759147538499948),
complex<T>(-0.8688459641284763, -0.34300082337663096),
+ complex<T>(-0.9091347320900505, -0.11395831373355114),
+ complex<T>(-0.9091347320900505, +0.11395831373355114),
complex<T>(-0.8688459641284763, +0.34300082337663096),
- complex<T>(-0.7837694413101445, -0.5759147538499948),
complex<T>(-0.7837694413101445, +0.5759147538499948),
- complex<T>(-0.6417513866988322, -0.8175836167191022),
complex<T>(-0.6417513866988322, +0.8175836167191022),
- complex<T>(-0.4083220732868863, -1.0812748428191246),
complex<T>(-0.4083220732868863, +1.0812748428191246) },
1.0 };
case 11:
return { {},
- { complex<T>(-0.9129067244518985, -0.),
+ { complex<T>(-0.3868149510055096, -1.0991174667631216),
+ complex<T>(-0.6126871554915198, -0.8547813893314768),
+ complex<T>(-0.7546938934722305, -0.6319150050721849),
+ complex<T>(-0.8453044014712964, -0.4178696917801249),
complex<T>(-0.8963656705721169, -0.20804803750710327),
+ complex<T>(-0.9129067244518985, +0.),
complex<T>(-0.8963656705721169, +0.20804803750710327),
- complex<T>(-0.8453044014712964, -0.4178696917801249),
complex<T>(-0.8453044014712964, +0.4178696917801249),
- complex<T>(-0.7546938934722305, -0.6319150050721849),
complex<T>(-0.7546938934722305, +0.6319150050721849),
- complex<T>(-0.6126871554915198, -0.8547813893314768),
complex<T>(-0.6126871554915198, +0.8547813893314768),
- complex<T>(-0.3868149510055096, -1.0991174667631216),
complex<T>(-0.3868149510055096, +1.0991174667631216) },
1.0 };
case 12:
return { {},
- { complex<T>(-0.9084478234140686, -0.09550636521345042),
- complex<T>(-0.9084478234140686, +0.09550636521345042),
+ { complex<T>(-0.3679640085526314, -1.1143735756415463),
+ complex<T>(-0.5866369321861475, -0.8863772751320727),
+ complex<T>(-0.7276681615395161, -0.6792961178764695),
+ complex<T>(-0.8217296939939074, -0.48102121151006755),
complex<T>(-0.880253434201683, -0.2871779503524227),
+ complex<T>(-0.9084478234140686, -0.09550636521345042),
+ complex<T>(-0.9084478234140686, +0.09550636521345042),
complex<T>(-0.880253434201683, +0.2871779503524227),
- complex<T>(-0.8217296939939074, -0.48102121151006755),
complex<T>(-0.8217296939939074, +0.48102121151006755),
- complex<T>(-0.7276681615395161, -0.6792961178764695),
complex<T>(-0.7276681615395161, +0.6792961178764695),
- complex<T>(-0.5866369321861475, -0.8863772751320727),
complex<T>(-0.5866369321861475, +0.8863772751320727),
- complex<T>(-0.3679640085526314, -1.1143735756415463),
complex<T>(-0.3679640085526314, +1.1143735756415463) },
1.0 };
case 13:
return { {},
- { complex<T>(-0.9110914665984182, -0.),
+ { complex<T>(-0.35127923233898156, -1.1275915483177048),
+ complex<T>(-0.5631559842430193, -0.9135900338325103),
+ complex<T>(-0.7026234675721276, -0.7199611890171304),
+ complex<T>(-0.7987460692470972, -0.5350752120696802),
+ complex<T>(-0.8625094198260553, -0.35474137311729914),
complex<T>(-0.8991314665475196, -0.17683429561610436),
+ complex<T>(-0.9110914665984182, +0.),
complex<T>(-0.8991314665475196, +0.17683429561610436),
- complex<T>(-0.8625094198260553, -0.35474137311729914),
complex<T>(-0.8625094198260553, +0.35474137311729914),
- complex<T>(-0.7987460692470972, -0.5350752120696802),
complex<T>(-0.7987460692470972, +0.5350752120696802),
- complex<T>(-0.7026234675721276, -0.7199611890171304),
complex<T>(-0.7026234675721276, +0.7199611890171304),
- complex<T>(-0.5631559842430193, -0.9135900338325103),
complex<T>(-0.5631559842430193, +0.9135900338325103),
- complex<T>(-0.35127923233898156, -1.1275915483177048),
complex<T>(-0.35127923233898156, +1.1275915483177048) },
1.0 };
case 14:
return { {},
- { complex<T>(-0.9077932138396491, -0.08219639941940154),
- complex<T>(-0.9077932138396491, +0.08219639941940154),
+ { complex<T>(-0.3363868224902031, -1.1391722978398593),
+ complex<T>(-0.5418766775112306, -0.9373043683516926),
+ complex<T>(-0.6794256425119227, -0.7552857305042031),
+ complex<T>(-0.7766591387063624, -0.581917067737761),
+ complex<T>(-0.8441199160909851, -0.41316538251026935),
complex<T>(-0.8869506674916446, -0.24700791787653334),
+ complex<T>(-0.9077932138396491, -0.08219639941940154),
+ complex<T>(-0.9077932138396491, +0.08219639941940154),
complex<T>(-0.8869506674916446, +0.24700791787653334),
- complex<T>(-0.8441199160909851, -0.41316538251026935),
complex<T>(-0.8441199160909851, +0.41316538251026935),
- complex<T>(-0.7766591387063624, -0.581917067737761),
complex<T>(-0.7766591387063624, +0.581917067737761),
- complex<T>(-0.6794256425119227, -0.7552857305042031),
complex<T>(-0.6794256425119227, +0.7552857305042031),
- complex<T>(-0.5418766775112306, -0.9373043683516926),
complex<T>(-0.5418766775112306, +0.9373043683516926),
- complex<T>(-0.3363868224902031, -1.1391722978398593),
complex<T>(-0.3363868224902031, +1.1391722978398593) },
1.0 };
case 15:
return { {},
- { complex<T>(-0.9097482363849062, -0.), complex<T>(-0.9006981694176978, -0.1537681197278439),
- complex<T>(-0.9006981694176978, +0.1537681197278439),
+ { complex<T>(-0.3229963059766445, -1.14941615458363),
+ complex<T>(-0.5224954069658334, -0.9581787261092526),
+ complex<T>(-0.6579196593111002, -0.7862895503722519),
+ complex<T>(-0.7556027168970723, -0.6229396358758262),
+ complex<T>(-0.8256631452587148, -0.46423487527343266),
complex<T>(-0.8731264620834984, -0.30823524705642674),
+ complex<T>(-0.9006981694176978, -0.1537681197278439), complex<T>(-0.9097482363849062, +0.),
+ complex<T>(-0.9006981694176978, +0.1537681197278439),
complex<T>(-0.8731264620834984, +0.30823524705642674),
- complex<T>(-0.8256631452587148, -0.46423487527343266),
complex<T>(-0.8256631452587148, +0.46423487527343266),
- complex<T>(-0.7556027168970723, -0.6229396358758262),
complex<T>(-0.7556027168970723, +0.6229396358758262),
- complex<T>(-0.6579196593111002, -0.7862895503722519),
complex<T>(-0.6579196593111002, +0.7862895503722519),
- complex<T>(-0.5224954069658334, -0.9581787261092526),
complex<T>(-0.5224954069658334, +0.9581787261092526),
- complex<T>(-0.3229963059766445, -1.14941615458363),
complex<T>(-0.3229963059766445, +1.14941615458363) },
1.0 };
case 16:
return { {},
- { complex<T>(-0.9072099595087003, -0.07214211304111734),
- complex<T>(-0.9072099595087003, +0.07214211304111734),
+ { complex<T>(-0.31087827556453856, -1.1585528411993304),
+ complex<T>(-0.504760644442476, -0.9767137477799086),
+ complex<T>(-0.6379502514039066, -0.8137453537108762),
+ complex<T>(-0.7356166304713119, -0.6591950877860395),
+ complex<T>(-0.8074790293236005, -0.5092933751171799),
+ complex<T>(-0.8584264231521322, -0.3621697271802063),
complex<T>(-0.8911723070323642, -0.2167089659900575),
+ complex<T>(-0.9072099595087003, -0.07214211304111734),
+ complex<T>(-0.9072099595087003, +0.07214211304111734),
complex<T>(-0.8911723070323642, +0.2167089659900575),
- complex<T>(-0.8584264231521322, -0.3621697271802063),
complex<T>(-0.8584264231521322, +0.3621697271802063),
- complex<T>(-0.8074790293236005, -0.5092933751171799),
complex<T>(-0.8074790293236005, +0.5092933751171799),
- complex<T>(-0.7356166304713119, -0.6591950877860395),
complex<T>(-0.7356166304713119, +0.6591950877860395),
- complex<T>(-0.6379502514039066, -0.8137453537108762),
complex<T>(-0.6379502514039066, +0.8137453537108762),
- complex<T>(-0.504760644442476, -0.9767137477799086),
complex<T>(-0.504760644442476, +0.9767137477799086),
- complex<T>(-0.31087827556453856, -1.1585528411993304),
complex<T>(-0.31087827556453856, +1.1585528411993304) },
1.0 };
case 17:
return { {},
- { complex<T>(-0.9087141161336388, -0.),
+ { complex<T>(-0.29984894599900724, -1.1667612729256673),
+ complex<T>(-0.48846293376727057, -0.9932971956316782),
+ complex<T>(-0.6193710717342136, -0.8382497252826987),
+ complex<T>(-0.7166893842372348, -0.6914936286393606),
+ complex<T>(-0.7897644147799701, -0.5493724405281085),
+ complex<T>(-0.8433414495836128, -0.41007592829100215),
+ complex<T>(-0.8801100704438625, -0.2725347156478803),
complex<T>(-0.9016273850787279, -0.13602679951730237),
+ complex<T>(-0.9087141161336388, +0.),
complex<T>(-0.9016273850787279, +0.13602679951730237),
- complex<T>(-0.8801100704438625, -0.2725347156478803),
complex<T>(-0.8801100704438625, +0.2725347156478803),
- complex<T>(-0.8433414495836128, -0.41007592829100215),
complex<T>(-0.8433414495836128, +0.41007592829100215),
- complex<T>(-0.7897644147799701, -0.5493724405281085),
complex<T>(-0.7897644147799701, +0.5493724405281085),
- complex<T>(-0.7166893842372348, -0.6914936286393606),
complex<T>(-0.7166893842372348, +0.6914936286393606),
- complex<T>(-0.6193710717342136, -0.8382497252826987),
complex<T>(-0.6193710717342136, +0.8382497252826987),
- complex<T>(-0.48846293376727057, -0.9932971956316782),
complex<T>(-0.48846293376727057, +0.9932971956316782),
- complex<T>(-0.29984894599900724, -1.1667612729256673),
complex<T>(-0.29984894599900724, +1.1667612729256673) },
1.0 };
case 18:
return { {},
- { complex<T>(-0.9067004324162776, -0.06427924106393067),
- complex<T>(-0.9067004324162776, +0.06427924106393067),
+ { complex<T>(-0.28975920298804847, -1.1741830106000584),
+ complex<T>(-0.4734268069916154, -1.0082343003148009),
+ complex<T>(-0.6020482668090646, -0.8602708961893666),
+ complex<T>(-0.698782144500527, -0.7204696509726628),
+ complex<T>(-0.7726285030739557, -0.5852778162086639),
+ complex<T>(-0.8281885016242831, -0.45293856978159136),
+ complex<T>(-0.8681095503628832, -0.32242049251632576),
complex<T>(-0.8939764278132456, -0.19303746408947586),
+ complex<T>(-0.9067004324162776, -0.06427924106393067),
+ complex<T>(-0.9067004324162776, +0.06427924106393067),
complex<T>(-0.8939764278132456, +0.19303746408947586),
- complex<T>(-0.8681095503628832, -0.32242049251632576),
complex<T>(-0.8681095503628832, +0.32242049251632576),
- complex<T>(-0.8281885016242831, -0.45293856978159136),
complex<T>(-0.8281885016242831, +0.45293856978159136),
- complex<T>(-0.7726285030739557, -0.5852778162086639),
complex<T>(-0.7726285030739557, +0.5852778162086639),
- complex<T>(-0.698782144500527, -0.7204696509726628),
complex<T>(-0.698782144500527, +0.7204696509726628),
- complex<T>(-0.6020482668090646, -0.8602708961893666),
complex<T>(-0.6020482668090646, +0.8602708961893666),
- complex<T>(-0.4734268069916154, -1.0082343003148009),
complex<T>(-0.4734268069916154, +1.0082343003148009),
- complex<T>(-0.28975920298804847, -1.1741830106000584),
complex<T>(-0.28975920298804847, +1.1741830106000584) },
1.0 };
case 19:
return { {},
- { complex<T>(-0.9078934217899399, -0.),
+ { complex<T>(-0.2804866851439361, -1.1809316284532905),
+ complex<T>(-0.4595043449730983, -1.0217687769126707),
+ complex<T>(-0.5858613321217832, -0.8801817131014564),
+ complex<T>(-0.6818424412912442, -0.7466272357947761),
+ complex<T>(-0.7561260971541627, -0.6176483917970176),
+ complex<T>(-0.8131725551578203, -0.491536503556246),
+ complex<T>(-0.8555768765618422, -0.3672925896399872),
+ complex<T>(-0.8849290585034385, -0.24425907575498182),
complex<T>(-0.9021937639390656, -0.12195683818720263),
+ complex<T>(-0.9078934217899399, +0.),
complex<T>(-0.9021937639390656, +0.12195683818720263),
- complex<T>(-0.8849290585034385, -0.24425907575498182),
complex<T>(-0.8849290585034385, +0.24425907575498182),
- complex<T>(-0.8555768765618422, -0.3672925896399872),
complex<T>(-0.8555768765618422, +0.3672925896399872),
- complex<T>(-0.8131725551578203, -0.491536503556246),
complex<T>(-0.8131725551578203, +0.491536503556246),
- complex<T>(-0.7561260971541627, -0.6176483917970176),
complex<T>(-0.7561260971541627, +0.6176483917970176),
- complex<T>(-0.6818424412912442, -0.7466272357947761),
complex<T>(-0.6818424412912442, +0.7466272357947761),
- complex<T>(-0.5858613321217832, -0.8801817131014564),
complex<T>(-0.5858613321217832, +0.8801817131014564),
- complex<T>(-0.4595043449730983, -1.0217687769126707),
complex<T>(-0.4595043449730983, +1.0217687769126707),
- complex<T>(-0.2804866851439361, -1.1809316284532905),
complex<T>(-0.2804866851439361, +1.1809316284532905) },
1.0 };
case 20:
return { {},
- { complex<T>(-0.9062570115576768, -0.0579617802778495),
- complex<T>(-0.9062570115576768, +0.0579617802778495),
+ { complex<T>(-0.27192995802516506, -1.187099379810886),
+ complex<T>(-0.44657006982051484, -1.0340977025608422),
+ complex<T>(-0.5707026806915716, -0.8982829066468254),
+ complex<T>(-0.6658120544829932, -0.7703721701100759),
+ complex<T>(-0.7402780309646764, -0.6469975237605227),
+ complex<T>(-0.7984251191290602, -0.526494238881713),
+ complex<T>(-0.8427907479956664, -0.4078917326291931),
+ complex<T>(-0.8749560316673335, -0.2905559296567909),
complex<T>(-0.8959150941925766, -0.17403171759187044),
+ complex<T>(-0.9062570115576768, -0.0579617802778495),
+ complex<T>(-0.9062570115576768, +0.0579617802778495),
complex<T>(-0.8959150941925766, +0.17403171759187044),
- complex<T>(-0.8749560316673335, -0.2905559296567909),
complex<T>(-0.8749560316673335, +0.2905559296567909),
- complex<T>(-0.8427907479956664, -0.4078917326291931),
complex<T>(-0.8427907479956664, +0.4078917326291931),
- complex<T>(-0.7984251191290602, -0.526494238881713),
complex<T>(-0.7984251191290602, +0.526494238881713),
- complex<T>(-0.7402780309646764, -0.6469975237605227),
complex<T>(-0.7402780309646764, +0.6469975237605227),
- complex<T>(-0.6658120544829932, -0.7703721701100759),
complex<T>(-0.6658120544829932, +0.7703721701100759),
- complex<T>(-0.5707026806915716, -0.8982829066468254),
complex<T>(-0.5707026806915716, +0.8982829066468254),
- complex<T>(-0.44657006982051484, -1.0340977025608422),
complex<T>(-0.44657006982051484, +1.0340977025608422),
- complex<T>(-0.27192995802516506, -1.187099379810886),
complex<T>(-0.27192995802516506, +1.187099379810886) },
1.0 };
case 21:
return { {},
- { complex<T>(-0.9072262653142963, -0.),
+ { complex<T>(-0.2640041595834027, -1.192762031948052),
+ complex<T>(-0.4345168906815268, -1.045382255856986),
+ complex<T>(-0.5564766488918566, -0.9148198405846728),
+ complex<T>(-0.6506315378609466, -0.7920349342629495),
+ complex<T>(-0.7250839687106612, -0.6737426063024383),
+ complex<T>(-0.7840287980408347, -0.5583186348022857),
+ complex<T>(-0.8299435470674444, -0.44481777394079575),
+ complex<T>(-0.8643915813643203, -0.33262585125221866),
+ complex<T>(-0.8883808106664449, -0.221306921508435),
complex<T>(-0.9025428073192694, -0.11052525727898564),
+ complex<T>(-0.9072262653142963, +0.),
complex<T>(-0.9025428073192694, +0.11052525727898564),
- complex<T>(-0.8883808106664449, -0.221306921508435),
complex<T>(-0.8883808106664449, +0.221306921508435),
- complex<T>(-0.8643915813643203, -0.33262585125221866),
complex<T>(-0.8643915813643203, +0.33262585125221866),
- complex<T>(-0.8299435470674444, -0.44481777394079575),
complex<T>(-0.8299435470674444, +0.44481777394079575),
- complex<T>(-0.7840287980408347, -0.5583186348022857),
complex<T>(-0.7840287980408347, +0.5583186348022857),
- complex<T>(-0.7250839687106612, -0.6737426063024383),
complex<T>(-0.7250839687106612, +0.6737426063024383),
- complex<T>(-0.6506315378609466, -0.7920349342629495),
complex<T>(-0.6506315378609466, +0.7920349342629495),
- complex<T>(-0.5564766488918566, -0.9148198405846728),
complex<T>(-0.5564766488918566, +0.9148198405846728),
- complex<T>(-0.4345168906815268, -1.045382255856986),
complex<T>(-0.4345168906815268, +1.045382255856986),
- complex<T>(-0.2640041595834027, -1.192762031948052),
complex<T>(-0.2640041595834027, +1.192762031948052) },
1.0 };
case 22:
return { {},
- { complex<T>(-0.9058702269930871, -0.05277490828999903),
- complex<T>(-0.9058702269930871, +0.05277490828999903),
+ { complex<T>(-0.2566376987939318, -1.1979824335552132),
+ complex<T>(-0.4232528745642629, -1.055755605227546),
+ complex<T>(-0.5430983056306306, -0.9299947824439877),
+ complex<T>(-0.6362427683267828, -0.811887504024635),
+ complex<T>(-0.7105305456418792, -0.6982266265924527),
+ complex<T>(-0.7700332930556816, -0.5874255426351151),
+ complex<T>(-0.8171682088462721, -0.47856194922027806),
+ complex<T>(-0.8534754036851689, -0.37103893194823206),
+ complex<T>(-0.8799661455640174, -0.26443630392015344),
complex<T>(-0.8972983138153532, -0.15843519122898653),
+ complex<T>(-0.9058702269930871, -0.05277490828999903),
+ complex<T>(-0.9058702269930871, +0.05277490828999903),
complex<T>(-0.8972983138153532, +0.15843519122898653),
- complex<T>(-0.8799661455640174, -0.26443630392015344),
complex<T>(-0.8799661455640174, +0.26443630392015344),
- complex<T>(-0.8534754036851689, -0.37103893194823206),
complex<T>(-0.8534754036851689, +0.37103893194823206),
- complex<T>(-0.8171682088462721, -0.47856194922027806),
complex<T>(-0.8171682088462721, +0.47856194922027806),
- complex<T>(-0.7700332930556816, -0.5874255426351151),
complex<T>(-0.7700332930556816, +0.5874255426351151),
- complex<T>(-0.7105305456418792, -0.6982266265924527),
complex<T>(-0.7105305456418792, +0.6982266265924527),
- complex<T>(-0.6362427683267828, -0.811887504024635),
complex<T>(-0.6362427683267828, +0.811887504024635),
- complex<T>(-0.5430983056306306, -0.9299947824439877),
complex<T>(-0.5430983056306306, +0.9299947824439877),
- complex<T>(-0.4232528745642629, -1.055755605227546),
complex<T>(-0.4232528745642629, +1.055755605227546),
- complex<T>(-0.2566376987939318, -1.1979824335552132),
complex<T>(-0.2566376987939318, +1.1979824335552132) },
1.0 };
case 23:
return { {},
- { complex<T>(-0.9066732476324991, -0.),
+ { complex<T>(-0.24976972022089572, -1.2028131878706978),
+ complex<T>(-0.4126986617510148, -1.0653287944755134),
+ complex<T>(-0.5304922463810198, -0.9439760364018306),
+ complex<T>(-0.6225903228771341, -0.830155830281298),
+ complex<T>(-0.6965966033912708, -0.720734137475305),
+ complex<T>(-0.7564660146829886, -0.6141594859476034),
+ complex<T>(-0.8045561642053178, -0.5095305912227259),
+ complex<T>(-0.8423805948021129, -0.4062657948237603),
+ complex<T>(-0.8709469395587415, -0.3039581993950041),
+ complex<T>(-0.8909283242471254, -0.20230246993812237),
complex<T>(-0.9027564979912508, -0.10105343353140452),
+ complex<T>(-0.9066732476324991, +0.),
complex<T>(-0.9027564979912508, +0.10105343353140452),
- complex<T>(-0.8909283242471254, -0.20230246993812237),
complex<T>(-0.8909283242471254, +0.20230246993812237),
- complex<T>(-0.8709469395587415, -0.3039581993950041),
complex<T>(-0.8709469395587415, +0.3039581993950041),
- complex<T>(-0.8423805948021129, -0.4062657948237603),
complex<T>(-0.8423805948021129, +0.4062657948237603),
- complex<T>(-0.8045561642053178, -0.5095305912227259),
complex<T>(-0.8045561642053178, +0.5095305912227259),
- complex<T>(-0.7564660146829886, -0.6141594859476034),
complex<T>(-0.7564660146829886, +0.6141594859476034),
- complex<T>(-0.6965966033912708, -0.720734137475305),
complex<T>(-0.6965966033912708, +0.720734137475305),
- complex<T>(-0.6225903228771341, -0.830155830281298),
complex<T>(-0.6225903228771341, +0.830155830281298),
- complex<T>(-0.5304922463810198, -0.9439760364018306),
complex<T>(-0.5304922463810198, +0.9439760364018306),
- complex<T>(-0.4126986617510148, -1.0653287944755134),
complex<T>(-0.4126986617510148, +1.0653287944755134),
- complex<T>(-0.24976972022089572, -1.2028131878706978),
complex<T>(-0.24976972022089572, +1.2028131878706978) },
1.0 };
case 24:
return { {},
- { complex<T>(-0.9055312363372773, -0.0484400665404787),
- complex<T>(-0.9055312363372773, +0.0484400665404787),
+ { complex<T>(-0.24334813375248746, -1.2072986837319728),
+ complex<T>(-0.4027853855197519, -1.0741951965186751),
+ complex<T>(-0.518591457482032, -0.9569048385259057),
+ complex<T>(-0.6096221567378332, -0.8470292433077199),
+ complex<T>(-0.6832565803536519, -0.7415032695091649),
+ complex<T>(-0.7433392285088533, -0.6388084216222569),
+ complex<T>(-0.7921695462343489, -0.5380628490968016),
+ complex<T>(-0.8312326466813242, -0.4386985933597306),
+ complex<T>(-0.8615278304016355, -0.34032021126186246),
+ complex<T>(-0.8837358034555707, -0.24263352344013836),
complex<T>(-0.8983105104397872, -0.14540561338736102),
+ complex<T>(-0.9055312363372773, -0.0484400665404787),
+ complex<T>(-0.9055312363372773, +0.0484400665404787),
complex<T>(-0.8983105104397872, +0.14540561338736102),
- complex<T>(-0.8837358034555707, -0.24263352344013836),
complex<T>(-0.8837358034555707, +0.24263352344013836),
- complex<T>(-0.8615278304016355, -0.34032021126186246),
complex<T>(-0.8615278304016355, +0.34032021126186246),
- complex<T>(-0.8312326466813242, -0.4386985933597306),
complex<T>(-0.8312326466813242, +0.4386985933597306),
- complex<T>(-0.7921695462343489, -0.5380628490968016),
complex<T>(-0.7921695462343489, +0.5380628490968016),
- complex<T>(-0.7433392285088533, -0.6388084216222569),
complex<T>(-0.7433392285088533, +0.6388084216222569),
- complex<T>(-0.6832565803536519, -0.7415032695091649),
complex<T>(-0.6832565803536519, +0.7415032695091649),
- complex<T>(-0.6096221567378332, -0.8470292433077199),
complex<T>(-0.6096221567378332, +0.8470292433077199),
- complex<T>(-0.518591457482032, -0.9569048385259057),
complex<T>(-0.518591457482032, +0.9569048385259057),
- complex<T>(-0.4027853855197519, -1.0741951965186751),
complex<T>(-0.4027853855197519, +1.0741951965186751),
- complex<T>(-0.24334813375248746, -1.2072986837319728),
complex<T>(-0.24334813375248746, +1.2072986837319728) },
1.0 };
-
default:
return { {}, {}, 1.f };
}
@@ -841,9 +894,10 @@ KFR_FUNCTION biquad_params<T> zpk2tf(const zero_pole_pairs<T>& pairs, identity<T
}
template <typename T>
-KFR_FUNCTION univector<complex<T>> cplxreal(const univector<complex<T>>& x)
+KFR_FUNCTION univector<complex<T>> cplxreal(const univector<complex<T>>& list)
{
- // conjugate pairs must be adjacent
+ univector<complex<T>> x = list;
+ std::sort(x.begin(), x.end(), [](const complex<T>& a, const complex<T>& b) { return a.re < b.re; });
T tol = std::numeric_limits<T>::epsilon() * 100;
univector<complex<T>> result = x;
for (size_t i = result.size(); i > 1; i--)
