Cody

# Problem 220. Signal filtering

Solution 134885

Submitted on 4 Sep 2012 by Aurelien Queffurust
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### Test Suite

Test Status Code Input and Output
1   Pass
%% y = sin(2*pi*(0:0.0001:0.9999)*100)' + randn(10000,1); z = filt(y); assert((sin(2*pi*(0:0.0001:0.9999)*100)*z/norm(sin(2*pi*(0:0.0001:0.9999)*100))/norm(z))>0.95)

tt = 0.5377 0.1003 0.3836 0.1220 0.6314 0.7478 1.0237 1.0306 0.9872 1.1296 1.2111 1.1693 1.2401 1.2875 1.2664 1.2542 1.2522 1.3183 1.2764 1.2591 1.2212 1.3009 1.3122 1.1713 1.1282 1.1174 1.0075 0.9691 0.9737 0.9480 0.9100 0.8948 0.8161 0.7644 0.7255 0.7100 0.6884 0.6303 0.4937 0.3976 0.3186 0.3013 0.2384 0.1925 0.1618 0.1185 0.0681 0.0529 0.0461 0.1313 0.0805 0.0178 -0.0619 -0.1886 -0.2193 -0.1871 -0.2513 -0.2865 -0.3525 -0.3389 -0.4093 -0.4950 -0.6066 -0.6660 -0.7464 -0.7568 -0.7411 -0.7170 -0.6965 -0.6631 -0.7622 -0.7268 -0.7227 -0.7319 -0.7681 -0.7724 -0.8114 -0.8218 -0.8263 -0.7785 -0.7892 -0.7129 -0.6685 -0.6738 -0.7422 -0.7523 -0.7157 -0.7036 -0.6923 -0.6438 -0.5419 -0.4685 -0.4216 -0.3414 -0.2256 -0.2300 -0.2614 -0.2440 -0.1982 -0.1532 -0.0896 -0.0597 0.0525 0.0313 0.1179 0.1681 0.3160 0.3696 0.3766 0.4100 0.4324 0.4689 0.6143 0.6584 0.7805 0.7142 0.7633 0.7591 0.7483 0.7770 0.8259 0.8253 0.7657 0.7541 0.7780 0.8431 0.8712 0.8103 0.7784 0.7235 0.6754 0.5736 0.5797 0.5434 0.4882 0.3906 0.3466 0.2624 0.2591 0.2069 0.2083 0.1208 0.0588 0.0327 0.0457 -0.0137 -0.0478 -0.0758 -0.1858 -0.1626 -0.1612 -0.1590 -0.2955 -0.3913 -0.4402 -0.4660 -0.5542 -0.6242 -0.7129 -0.7196 -0.7174 -0.7050 -0.7320 -0.6951 -0.7809 -0.8025 -0.8794 -0.8902 -0.9167 -0.9850 -0.9798 -0.9345 -1.0316 -0.9889 -0.9509 -0.9448 -0.9206 -0.8844 -0.9734 -1.0178 -1.0114 -0.9212 -0.8170 -0.7701 -0.7769 -0.6787 -0.5587 -0.5082 -0.4484 -0.4105 -0.3783 -0.3110 -0.2614 -0.2289 -0.2142 -0.1210 -0.1027 0.0377 0.0729 0.0914 0.0855 0.1380 0.1422 0.1638 0.2721 0.3225 0.3446 0.4604 0.5507 0.5879 0.5526 0.5276 0.5470 0.6023 0.6078 0.6502 0.7298 0.6817 0.6632 0.6546 0.6378 0.6329 0.6777 0.5873 0.5818 0.6447 0.5482 0.6054 0.6257 0.6373 0.6689 0.6031 0.5880 0.5658 0.5500 0.5575 0.4435 0.3639 0.3413 0.3670 0.3264 0.2786 0.2920 0.1745 0.1861 0.1330 0.1582 0.0804 0.0317 -0.0146 -0.0434 -0.1559 -0.0894 -0.1693 -0.2631 -0.2561 -0.3283 -0.3531 -0.3659 -0.4416 -0.4238 -0.4965 -0.6383 -0.6483 -0.6858 -0.6958 -0.6939 -0.7092 -0.7365 -0.7022 -0.6804 -0.7572 -0.7150 -0.8228 -0.7985 -0.8903 -0.8320 -0.8738 -0.8205 -0.7934 -0.7206 -0.7208 -0.7431 -0.7006 -0.7710 -0.8316 -0.8328 -0.8641 -0.7890 -0.7336 -0.6284 -0.5616 -0.5311 -0.4791 -0.3987 -0.3603 -0.2975 -0.2610 -0.2553 -0.1984 -0.2254 -0.1646 -0.1317 -0.1321 -0.0010 0.0806 0.1641 0.1627 0.1863 0.2231 0.2810 0.4236 0.4123 0.5204 0.5629 0.6330 0.6746 0.6467 0.6393 0.5821 0.6237 0.6041 0.6876 0.7069 0.6074 0.5934 0.5480 0.5392 0.5016 0.5887 0.5815 0.6612 0.6361 0.6003 0.5670 0.5743 0.5876 0.5579 0.5024 0.3889 0.3961 0.3623 0.3250 0.3694 0.2838 0.2231 0.1961 0.1474 0.1938 0.1106 0.1025 -0.0164 -0.1180 -0.1221 -0.2003 -0.2074 -0.3006 -0.3496 -0.4523 -0.4931 -0.5809 -0.6386 -0.7007 -0.7501 -0.8523 -0.8804 -0.8386 -0.8062 -0.7796 -0.8505 -0.8838 -0.8379 -0.8367 -0.8220 -0.8261 -0.8007 -0.8139 -0.8705 -0.8520 -0.9025 -0.9293 -0.9100 -0.9105 -0.8550 -0.8284 -0.7229 -0.6869 -0.6054 -0.6148 -0.6207 -0.5619 -0.5031 -0.4293 -0.3274 -0.2697 -0.2856 -0.2259 -0.1574 -0.1410 -0.1021 -0.1071 -0.0568 -0.0398 0.0256 0.0571 0.0909 0.1359 0.1993 0.2848 0.3609 0.4342 0.5397 0.6221 0.6755 0.7496 0.7488 0.7805 0.8505 0.9311 0.9886 0.9279 0.8584 0.8306 0.8095 0.8489 0.7989 0.8208 0.8571 0.8634 0.8599 0.7905 0.8344 0.8303 0.8726 0.8681 0.8748 0.8454 0.7381 0.6679 0.6271 0.5783 0.4321 0.3529 0.2507 0.1914 0.1556 0.0901 0.0786 -0.0329 -0.0049 -0.0661 -0.0958 -0.1844 -0.2751 -0.2845 -0.3545 -0.4374 -0.4230 -0.4577 -0.4746 -0.5522 -0.5799 -0.7113 -0.7089 -0.7880 -0.8400 -0.7948 -0.7993 -0.8497 -0.8489 -0.7927 -0.7932 -0.8023 -0.7848 -0.8157 -0.7801 -0.8621 -0.8102 -0.7878 -0.7203 -0.6205 -0.6026 -0.6202 -0.6883 -0.6395 -0.5661 -0.5636 -0.5241 -0.4834 -0.4522 -0.4195 -0.3252 -0.3010 -0.1336 -0.1030 -0.1218 -0.0982 -0.0782 -0.0598 -0.0475 0.0063 0.0681 0.1440 0.2158 0.3151 0.4309 0.4284 0.3774 0.4539 0.3779 0.4462 0.5159 0.6939 0.6987 0.6873 0.7316 0.7397 0.7635 0.7573 0.7329 0.7471 0.7125 0.5926 0.6873 0.7419 0.7781 0.8451 0.8446 0.8774 0.8611 0.8622 0.8520 0.7971 0.6812 0.5753 0.5796 0.6114 0.5302 0.5889 0.5355 0.5306 0.3904 0.3794 0.3304 0.2783 0.2520 0.1830 0.1357 0.1931 0.1607 0.1377 0.1412 0.0286 0.0136 0.0141 -0.1246 -0.1301 -0.1653 -0.2003 -0.2219 -0.2833 -0.3617 -0.4484 -0.4624 -0.4646 -0.4719 -0.4742 -0.5557 -0.5652 -0.6828 -0.7092 -0.7861 -0.7621 -0.7772 -0.8556 -0.8434 -0.8504 -0.9373 -0.9318 -0.9011 -0.8945 -0.8332 -0.8297 -0.8347 -0.7281 -0.6926 -0.6931 -0.6100 -0.6309 -0.5970 -0.4526 -0.3495 -0.2912 -0.2355 -0.1913 -0.1058 0.0020 0.0603 0.1438 0.2438 0.2789 0.3238 0.4064 0.5075 0.5913 0.7377 0.8439 0.8733 0.9400 0.9879 0.9571 0.9796 1.0437 1.0572 1.0730 1.0552 1.0394 1.0871 1.0665 1.0415 1.0712 1.0541 1.0330 0.9710 0.8543 0.7797 0.7338 0.7151 0.6275 0.6732 0.5946 0.5521 0.5502 0.4951 0.4003 0.3247 0.2310 0.1713 0.1512 0.2156 0.1721 0.0287 -0.0110 -0.0666 -0.0898 -0.1829 -0.1861 -0.2737 -0.3571 -0.4506 -0.4946 -0.5369 -0.5210 -0.5259 -0.5117 -0.5084 -0.4969 -0.5021 -0.5245 -0.4936 -0.4560 -0.4895 -0.4904 -0.5303 -0.5977 -0.5928 -0.6481 -0.7284 -0.7939 -0.8199 -0.8131 -0.8482 -0.8786 -0.8652 -0.8635 -0.9241 -0.8384 -0.7700 -0.7232 -0.6940 -0.7302 -0.7643 -0.7074 -0.7181 -0.6944 -0.7169 -0.6030 -0.5989 -0.5470 -0.6005 -0.5997 -0.5707 -0.5065 -0.4522 -0.4422 -0.4026 -0.3797 -0.3436 -0.2848 -0.2123 -0.1907 -0.1038 -0.0485 0.0351 0.1125 0.1320 0.1519 0.2213 0.2866 0.3487 0.4528 0.4674 0.4860 0.4656 0.5683 0.5067 0.5271 0.4771 0.4994 0.4152 0.3724 0.3192 0.3348 0.3888 0.4206 0.5381 0.5147 0.5151 0.4651 0.4837 0.3955 0.3629 0.3738 0.3278 0.3060 0.2049 0.2098 0.2324 0.2232 0.1369 0.1529 0.1183 0.0967 0.0429 -0.0257 -0.1385 -0.1346 -0.1637 -0.1028 -0.1025 -0.0704 -0.0565 -0.1230 -0.1376 -0.2519 -0.3019 -0.3857 -0.3593 -0.4036 -0.4028 -0.4762 -0.6022 -0.6511 -0.6676 -0.6061 -0.6622 -0.7272 -0.7849 -0.8078 -0.9145 -0.8953 -0.7982 -0.8155 -0.8029 -0.7117 -0.7669 -0.8281 -0.8015 -0.8369 -0.8515 -0.8212 -0.7693 -0.7436 -0.7802 -0.7122 -0.5667 -0.5369 -0.5418 -0.5119 -0.4609 -0.3512 -0.2978 -0.2348 -0.2401 -0.2384 -0.2438 -0.1362 -0.1146 -0.0242 0.0222 -0.0420 0.0038 0.0823 0.0749 0.1725 0.2647 0.2771 0.3294 0.3692 0.3040 0.3215 0.3137 0.3785 0.4168 0.3537 0.3871 0.5045 0.5339 0.5854 0.6159 0.6174 0.6372 0.6181 0.6856 0.6769 0.5862 0.6961 0.6959 0.6936 0.6917 0.6248 0.5029 0.5352 0.4950 0.4697 0.4672 0.4094 0.3460 0.4107 0.4042 0.3357 0.2461 0.1570 0.1411 0.1050 0.0233 -0.0623 -0.1145 -0.2308 -0.3154 -0.4111 -0.4644 -0.5663 -0.6170 -0.6170 -0.7330 -0.7962 -0.8791 -0.8726 -0.8633 -0.8003 -0.9156 -1.0026 -1.1021 -1.0623 -1.0132 -1.0098 -1.1107 -1.1956 -1.1542 -1.0427 -1.0966 -1.1314 -1.1753 -1.2523 -1.1863 -1.2095 -1.0980 -1.0698 -1.0213 -1.0031 -0.9968 -0.9844 -0.9363 -0.8477 -0.8235 -0.7576 -0.7815 -0.7605 -0.6804 -0.5826 -0.5173 -0.4322 -0.4793 -0.4694 -0.4569 -0.3647 -0.2283 -0.2021 -0.2088 -0.1719 -0.1286 -0.1195 -0.0103 0.0320 0.1511 0.1985 0.2579 0....

2   Pass
%% y = chirp(0:0.0001:0.9999,50,1,150)' + randn(10000,1); z = filt(y); assert((chirp(0:0.0001:0.9999,50,1,150)*z/norm(chirp(0:0.0001:0.9999,50,1,150))/norm(z))>0.95)

tt = -0.9184 0.0598 0.9269 1.0536 0.8198 1.0673 0.9684 1.0773 1.0451 0.9072 0.8608 0.8526 0.8588 0.8231 0.7670 0.8482 0.8451 0.8668 0.7439 0.7008 0.6900 0.6734 0.6125 0.6040 0.5463 0.5117 0.5116 0.5099 0.4280 0.4062 0.3917 0.3226 0.3501 0.3472 0.3644 0.3454 0.2697 0.2526 0.1647 0.1358 0.1024 0.1360 0.1563 0.1459 0.0384 0.0053 0.0052 -0.0737 -0.0646 -0.1998 -0.2562 -0.2274 -0.2651 -0.3045 -0.3269 -0.3186 -0.3450 -0.3867 -0.4125 -0.4588 -0.4974 -0.5152 -0.5308 -0.5583 -0.5927 -0.5813 -0.7055 -0.6441 -0.6897 -0.7436 -0.7726 -0.8325 -0.8998 -0.8516 -0.8866 -0.9874 -0.8786 -0.9254 -0.8868 -0.9418 -0.9847 -0.8895 -0.9104 -0.9683 -1.0230 -1.0239 -0.9677 -0.9954 -1.0340 -0.9691 -1.0290 -1.0186 -1.0731 -1.1048 -1.1748 -1.1194 -1.1674 -1.0966 -1.0350 -1.1199 -1.1121 -1.0765 -1.0966 -1.0769 -1.0276 -1.0970 -1.0882 -1.0781 -1.0467 -0.9940 -1.0790 -1.1019 -1.0952 -1.0530 -1.1063 -1.2038 -1.2282 -1.1647 -1.0836 -1.0464 -1.0293 -0.9214 -0.8375 -0.6919 -0.6578 -0.6082 -0.6346 -0.7000 -0.6321 -0.5823 -0.4929 -0.4351 -0.4070 -0.3520 -0.3239 -0.3326 -0.3037 -0.2919 -0.2608 -0.1940 -0.1926 -0.1287 -0.1496 -0.0922 0.0463 0.1732 0.1598 0.1044 0.1701 0.1767 0.1346 0.1590 0.0854 0.2247 0.2072 0.2599 0.3170 0.3241 0.3807 0.3481 0.3542 0.3784 0.3967 0.5022 0.5977 0.6719 0.7817 0.8046 0.7947 0.8511 0.8261 0.8985 0.9974 1.0246 1.0260 1.0396 1.0466 1.0569 1.0663 1.1309 1.1571 1.2127 1.1368 1.2004 1.2160 1.1940 1.2119 1.1566 1.1182 1.1117 1.1187 1.1485 1.1176 1.1385 1.0914 1.0615 1.0876 1.1045 1.1354 1.2330 1.1736 1.1203 1.0291 0.9745 0.9763 0.9759 0.9496 0.9148 0.8518 0.8113 0.8643 0.7993 0.7370 0.7158 0.7735 0.8165 0.8283 0.7944 0.8034 0.8087 0.7199 0.6620 0.5785 0.5748 0.5068 0.4660 0.4206 0.3578 0.3324 0.3540 0.2966 0.2846 0.2853 0.3100 0.3223 0.3627 0.3264 0.3111 0.1930 0.1184 0.1655 0.1462 0.0447 -0.0747 -0.0765 -0.1558 -0.0951 -0.1557 -0.2209 -0.2544 -0.2551 -0.2714 -0.3334 -0.3424 -0.4142 -0.4069 -0.4079 -0.4688 -0.5975 -0.6404 -0.6574 -0.6816 -0.7158 -0.7480 -0.8464 -0.7867 -0.8326 -0.8369 -0.8591 -0.8731 -0.8637 -0.8080 -0.7263 -0.8024 -0.7233 -0.7260 -0.7330 -0.7185 -0.6735 -0.6547 -0.6662 -0.5974 -0.5593 -0.5345 -0.4969 -0.5233 -0.5221 -0.4030 -0.3953 -0.4387 -0.4344 -0.4522 -0.4552 -0.4415 -0.5183 -0.4705 -0.3834 -0.3827 -0.4169 -0.4444 -0.4618 -0.5301 -0.5159 -0.5218 -0.5540 -0.5632 -0.5529 -0.5341 -0.5538 -0.5150 -0.5327 -0.5712 -0.5804 -0.5622 -0.5389 -0.5137 -0.5303 -0.4710 -0.4237 -0.4623 -0.5273 -0.4912 -0.4517 -0.3698 -0.3385 -0.4033 -0.3807 -0.2770 -0.2135 -0.1805 -0.1183 -0.1090 -0.1054 -0.0694 -0.0491 -0.0557 -0.0751 -0.0208 0.0295 0.0645 0.0731 0.1090 0.1292 0.1564 0.1188 0.1261 0.1641 0.2143 0.2994 0.4246 0.4554 0.5062 0.5256 0.5538 0.6560 0.6408 0.6332 0.6639 0.7064 0.7396 0.7573 0.7183 0.7362 0.8103 0.8807 0.9070 0.8725 0.9158 0.9825 1.1258 1.1015 1.0456 1.0723 1.1442 1.2067 1.1742 1.1801 1.1656 1.0952 1.0481 1.0236 0.9991 1.0131 1.0238 1.0754 1.0655 1.0998 1.0783 1.1758 1.2558 1.3486 1.2738 1.2264 1.1399 1.1421 1.1121 1.0264 1.0061 0.8681 0.8225 0.8257 0.7951 0.7881 0.7505 0.7363 0.7314 0.6820 0.7387 0.7804 0.7542 0.7854 0.7202 0.7094 0.6266 0.5800 0.5013 0.4459 0.2746 0.1610 0.0789 0.1635 0.1179 0.1684 0.1213 0.1049 0.0762 0.0668 0.0556 0.1391 0.1352 0.0941 0.0621 0.0294 0.0058 -0.0183 -0.0280 0.0021 -0.0625 -0.0660 -0.1037 -0.1559 -0.1715 -0.1220 -0.1798 -0.2186 -0.2436 -0.1793 -0.1884 -0.1761 -0.2482 -0.2310 -0.3101 -0.3424 -0.3522 -0.2803 -0.3471 -0.3288 -0.3835 -0.3244 -0.3110 -0.3316 -0.3747 -0.3893 -0.4577 -0.4374 -0.5474 -0.5167 -0.5226 -0.5707 -0.5606 -0.6674 -0.6796 -0.6306 -0.6503 -0.5504 -0.5754 -0.5557 -0.5870 -0.5622 -0.5956 -0.5793 -0.5940 -0.6252 -0.7662 -0.7343 -0.8155 -0.7439 -0.7899 -0.8671 -0.8802 -0.8150 -0.8235 -0.7446 -0.7825 -0.7385 -0.7144 -0.7157 -0.6503 -0.6143 -0.5682 -0.5568 -0.5607 -0.4592 -0.5346 -0.5256 -0.5699 -0.4872 -0.4628 -0.3596 -0.3358 -0.2561 -0.1385 -0.0545 -0.0586 -0.0054 -0.0649 -0.0631 0.0181 -0.0005 0.0118 0.0769 0.1041 0.2065 0.2062 0.1959 0.2212 0.2529 0.3155 0.3447 0.2971 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