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Test of filter design routines
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Stabilisation of real filters
Polynomial, p = [0.7 3 -0.4]
p2 = polystab(p) = [0.7 0.067948 -0.0205197]
Polynomial, p = [-0.283885 1.36446 0.906001 1.24942 1.55783 0.56497 -0.596145]
p2 = polystab(p) = [-0.283885 -0.1827 -0.132481 -0.12513 -0.0297861 0.0793631 -0.012405]
Polynomial, p = [1 -2 1.13 -0.154]
p2 = polystab(p) = [1 -1.80909 0.958182 -0.127273]
Stabilisation of complex filters
Polynomial, p = [0.7+0i 3+0i -0.4+0i]
p2 = polystab(p) = [0.7+0i 0.067948+0i -0.0205197+0i]
Polynomial, p = [-0.846632-0.896303i -0.212404-0.759858i 1.67214+1.67236i 0.868358+0.165559i -0.517613-1.48884i -0.652983-1.33804i -0.469741-0.614789i]
p2 = polystab(p) = [-0.846632-0.896303i -0.507607-0.353231i 0.2481+0.781307i 0.0734606+0.5071i -0.117401-0.086041i -0.202569-0.25927i -0.101812-0.13325i]
Polynomial, p = [1+0i -2+0i 1.13+0i -0.154+0i]
p2 = polystab(p) = [1+0i -1.80909+0i 0.958182+0i -0.127273+0i]
a = [-0.0356921+0.565461i 0.72725-0.636742i -0.160972-1.29916i 0.0361926+1.01917i]
b = [-1.04693+0.760191i -0.280465+0.361084i 0.780099+0.643584i 0.794379+1.03288i -0.190616-0.710921i 1.32367+0.349763i]
freqz(b,a,32) = [-0.165674+4.19633i 0.470012+3.08506i 0.702477+1.92199i 0.682517+0.880545i 0.550411+0.0388362i 0.397606-0.574834i 0.267659-0.958963i 0.172126-1.13158i 0.108526-1.12555i 0.0728061-0.981531i 0.0642769-0.74076i 0.0853369-0.440152i 0.139327-0.110415i 0.228562+0.223937i 0.353196+0.543771i 0.510842+0.834431i 0.696683+1.085i 0.903834+1.2878i 1.12382+1.43804i 1.34706+1.53356i 1.56333+1.57461i 1.76209+1.56362i 1.93276+1.5048i 2.06476+1.40351i 2.14745+1.26512i 2.17028+1.09255i 2.1252+0.881888i 2.01672+0.618081i 1.88261+0.287479i 1.7856-0.0739272i 1.73342-0.379213i 1.66954-0.587277i]
Yulewalk filter design
f = [0 0.5 0.6 1]
m = [1 1 0 0]
filter_design_autocorrelation(32, f, m, R):
R = [0.532559 0.315821 -0.031951 -0.098821 0.030194 0.052117 -0.027468 -0.030472 0.024049 0.017893 -0.020260 -0.010026 0.016429 0.005118 -0.012847 -0.002225 0.009732 0.000713 -0.007211 -0.000100 0.005318 0.000009 -0.004008 -0.000158 0.003178 0.000354 -0.002694 -0.000487 0.002425 0.000517 -0.002257 -0.000453 0.002112 0.000332 -0.001947 -0.000198 0.001752 0.000087 -0.001541 -0.000020 0.001334 0.000000 -0.001154 -0.000016 0.001015 0.000050 -0.000918 -0.000083 0.000856 0.000102 -0.000817 -0.000102 0.000786 0.000084 -0.000751 -0.000057 0.000707 0.000029 -0.000654 -0.000009 0.000596 0.000000 -0.000542 -0.000003 0.000495 0.000013 -0.000460 -0.000026 0.000436 0.000035 -0.000420 -0.000037 0.000409 0.000033 -0.000396 -0.000024 0.000381 0.000014 -0.000361 -0.000005 0.000338 0.000001 -0.000315 -0.000001 0.000294 0.000005 -0.000277 -0.000010 0.000265 0.000015 -0.000257 -0.000017 0.000251 0.000017 -0.000246 -0.000013 0.000239 0.000008 -0.000230 -0.000003 0.000219 0.000001 -0.000207 -0.000000 0.000196 0.000002 -0.000186 -0.000005 0.000179 0.000008 -0.000174 -0.000009 0.000171 0.000009 -0.000168 -0.000008 0.000165 0.000005 -0.000160 -0.000003 0.000154 0.000001 -0.000147 -0.000000 0.000140 0.000001 -0.000135 -0.000002 0.000130 0.000004 -0.000127 -0.000005 0.000125 0.000006 -0.000123 -0.000005 0.000121 0.000004 -0.000118 -0.000002 0.000115 0.000001 -0.000111 -0.000000 0.000106 0.000000 -0.000103 -0.000001 0.000099 0.000002 -0.000097 -0.000003 0.000096 0.000004 -0.000095 -0.000003 0.000093 0.000003 -0.000092 -0.000002 0.000089 0.000001 -0.000087 -0.000000 0.000084 0.000000 -0.000081 -0.000001 0.000079 0.000001 -0.000077 -0.000002 0.000076 0.000003 -0.000075 -0.000002 0.000075 0.000002 -0.000074 -0.000001 0.000072 0.000001 -0.000070 -0.000000 0.000068 0.000000 -0.000066 -0.000000 0.000065 0.000001 -0.000063 -0.000001 0.000063 0.000002 -0.000062 -0.000002 0.000061 0.000002 -0.000061 -0.000001 0.000060 0.000000 -0.000059 -0.000000 0.000057 0.000000 -0.000056 -0.000000 0.000054 0.000001 -0.000053 -0.000001 0.000053 0.000001 -0.000052 -0.000001 0.000052 0.000001 -0.000051 -0.000001 0.000051 0.000000 -0.000050 -0.000000 0.000049 0.000000 -0.000048 -0.000000 0.000047 0.000000 -0.000046 -0.000001 0.000045 0.000001 -0.000045 -0.000001 0.000045 0.000001 -0.000044 -0.000001 0.000044 0.000000 -0.000043 -0.000000 0.000042 0.000000 -0.000042 -0.000000 0.000041 0.000000 -0.000040 -0.000000 0.000040 0.000001 -0.000039 -0.000001]
arma_estimator(8, 8, R, b, a):
a = [1.000000 0.674659 1.903750 0.910429 1.202849 0.356944 0.264436 0.033088 0.009850]
b = [0.098191 0.427406 0.944264 1.365558 1.419767 1.112417 0.654916 0.271520 0.062529]
R = [1.000000 0.903713 0.642512 0.290564 -0.054960 -0.304242 -0.401986 -0.342615 -0.168862 0.045176 0.220277 0.298483 0.260759 0.130387 -0.038298 -0.181211 -0.247891 -0.218682 -0.109979 0.033729 0.157507 0.216539 0.192023 0.096868 -0.030454 -0.141182 -0.194690 -0.173208 -0.087544 0.027970 0.129064 0.178348 0.159020 0.080477 -0.026004 -0.119609 -0.165531 -0.147829 -0.074884 0.024400 0.111968 0.155131 0.138710 0.070314 -0.023059 -0.105625 -0.146473 -0.131094 -0.066490 0.021917 0.100251 0.139119 0.124608 0.063229 -0.020929 -0.095621 -0.132772 -0.118998 -0.060405 0.020063 0.091579 0.127221 0.114084 0.057928 -0.019296 -0.088009 -0.122313 -0.109732 -0.055733 0.018611 0.084827 0.117932 0.105843 0.053770 -0.017994 -0.081967 -0.113991 -0.102340 -0.052000 0.017434 0.079377 0.110420 0.099163 0.050395 -0.016923 -0.077019 -0.107165 -0.096265 -0.048929 0.016455 0.074859 0.104181 0.093607 0.047585 -0.016024 -0.072871 -0.101434 -0.091157 -0.046345 0.015625 0.071033 0.098893 0.088890 0.045197 -0.015254 -0.069328 -0.096534 -0.086785 -0.044131 0.014908 0.067740 0.094336 0.084822 0.043137 -0.014585 -0.066256 -0.092282 -0.082987 -0.042207 0.014282 0.064866 0.090356 0.081266 0.041335 -0.013997 -0.063560 -0.088546 -0.079647 -0.040514 0.013729 0.062330 0.086841 0.078122 0.039741 -0.013475 -0.061168 -0.085231 -0.076681 -0.039010 0.013235 0.060069 0.083707 0.075317 0.038319 -0.013007 -0.059027 -0.082261 -0.074023 -0.037662 0.012791 0.058038 0.080889 0.072794 0.037039 -0.012585 -0.057096 -0.079582 -0.071624 -0.036445 0.012389 0.056199 0.078337 0.070509 0.035879 -0.012202 -0.055343 -0.077149 -0.069444 -0.035338 0.012023 0.054525 0.076013 0.068426 0.034822 -0.011851 -0.053743 -0.074926 -0.067451 -0.034327 0.011687 0.052993 0.073884 0.066517 0.033853 -0.011529 -0.052273 -0.072885 -0.065621 -0.033398 0.011378 0.051582 0.071925 0.064760 0.032961 -0.011232 -0.050918 -0.071002 -0.063932 -0.032540 0.011092 0.050279 0.070114 0.063135 0.032135 -0.010957 -0.049663 -0.069258 -0.062367 -0.031745 0.010827 0.049070 0.068432 0.061627 0.031369 -0.010701 -0.048497 -0.067636 -0.060912 -0.031006 0.010579 0.047943 0.066867 0.060221 0.030655 -0.010462 -0.047409 -0.066123 -0.059554 -0.030316 0.010348 0.046891 0.065404 0.058908 0.029988 -0.010238 -0.046391 -0.064708 -0.058283 -0.029670 0.010132 0.045906 0.064033 0.057677 0.029362 -0.010029 -0.045436 -0.063379 -0.057090 -0.029064 0.009929 0.044980 0.062745 0.056520 0.028774 -0.009831 -0.044537 -0.062129]
arma_estimator(8, 8, R, b, a):
a = [1.000000 -5.639923 14.887872 -23.713094 24.788487 -17.355262 7.935089 -2.164767 0.269989]
b = [0.117196 -0.457317 0.947020 -1.258532 1.157363 -0.723747 0.290453 -0.062104 0.004607]
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