(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.0' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 2768266, 52359]*) (*NotebookOutlinePosition[ 2783062, 52900]*) (* CellTagsIndexPosition[ 2783018, 52896]*) (*WindowFrame->Normal*) Notebook[{ Cell["Power spectral analysis", "Title"], Cell[TextData[{ "This notebook has been written in ", StyleBox["Mathematica ", FontSlant->"Italic"], "by \n\n", StyleBox["Mark J. McCready\nProfessor and Chair of Chemical and \ Biomolecular Engineering\nUniversity of Notre Dame\nNotre Dame IN 46556\nUSA", FontSize->14], "\n\n", ButtonBox["Mark.J.McCready.1@nd.edu", ButtonData:>{ URL[ "mailto:mccready.1@nd.edu"], None}, ButtonStyle->"Hyperlink"], "\n", ButtonBox["http://www.nd.edu/~mjm/", ButtonData:>{ URL[ "http://www.nd.edu/~mjm/"], None}, ButtonStyle->"Hyperlink"], "\n\n\nIt is copyrighted to the extent allowed by whatever laws pertain to \ the World Wide Web and the Internet.\n\nI would hope that as a professional \ courtesy that this notice remain visible to other users. \nThere is no charge \ for copying and dissemination \n\nVersion: 02/02/04\n " }], "Text"], Cell["\<\ This notebook is intended as a first primer for engineers to learn \ about power spectral analysis of time series. 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Is there \ anything there?\n\nThe first thing that you would do is, ", StyleBox["Spectral Analysis", FontSlant->"Italic"], ". Let's do it and then see if we can understand what we did. \n\nLet's \ do the standard FFT thing" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(z1fft = Fourier[zz]\)], "Input", CellLabel->"In[9]:="], Cell[BoxData[ \({\(\(7.845658203988351`\)\(\[InvisibleSpace]\)\) + 0.`\ \[ImaginaryI], \(\(0.5341728575287651`\)\(\[InvisibleSpace]\)\) \ - 0.24817351508469598`\ \[ImaginaryI], \(-0.06893668855756775`\) + 0.02503026385169841`\ \[ImaginaryI], \(-0.08154686666179178`\) - 0.09903462561362872`\ \[ImaginaryI], \(-0.3107007858099069`\) + 0.5411707335096274`\ \[ImaginaryI], \(\(0.3214652269992608`\)\(\ \[InvisibleSpace]\)\) + 0.006576762297443445`\ \[ImaginaryI], \(-0.02901775885445984`\) - 0.08288088347376996`\ \[ImaginaryI], \(-0.199718192460788`\) + 0.15576400467266954`\ \[ImaginaryI], \(-0.4315937030228543`\) - 0.1151992513230208`\ \[ImaginaryI], \(-0.251097479267634`\) + 0.008353496409846575`\ \[ImaginaryI], \(\(0.1306821727837257`\)\(\ \[InvisibleSpace]\)\) + 0.0006676045453620078`\ 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ooooo`00003oooooo`Wooooo000Eooooo`03o`000?oooooo00000?oooooo2Oooool001Gooooo00?o 0000ooooool00000ooooool9ooooo`00\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-21.1446, -0.0643454, \ 0.987964, 0.0051087}}] }, Open ]], Cell["\<\ From this we can't see anything. Let's calculate a power spectum. We need more data to make this \ better.\ \>", "Text"], Cell[CellGroupData[{ Cell["zz=Table[.06*Cos[N[2 Pi i/100]] + Random[ ],{i,1,10240}];", "Input", CellLabel->"In[16]:=", CellGroupingRules->"OutputGrouping", AspectRatioFixed->True], Cell["\<\ We will break the data into segments that are 256 points long\ \>", \ "Text"], Cell["windsize=256;", "Input", CellLabel->"In[17]:=", CellGroupingRules->"OutputGrouping", AspectRatioFixed->True], Cell["The spacing between data points is 1", "Text"], Cell[BoxData[ \(\(\(timeinterval = 1\ ;\)\(\ \ \)\)\)], "Input", CellLabel->"In[18]:="], Cell["\<\ This will make the spacing between our \"estimates\" in spectral \ space\ \>", "Text"], Cell[CellGroupData[{ Cell["dfreq=1./timeinterval/windsize", "Input", CellLabel->"In[19]:=", AspectRatioFixed->True], Cell[BoxData[ \(0.00390625`\)], "Output", CellLabel->"Out[19]="] }, Open ]], Cell["We can make a scale for our plot", "Text"], Cell["freqscale=Table[i *dfreq,{i,0,windsize/2}];", "Input", CellLabel->"In[20]:=", AspectRatioFixed->True], Cell["\<\ Now take the average of the data set. We want to center it on 0.\ \ \>", "Text"], Cell[CellGroupData[{ Cell["ave=Sum[zz[[i]],{i,1,Length[zz]}]/Length[zz]", "Input", CellLabel->"In[21]:=", AspectRatioFixed->True], Cell[BoxData[ \(0.4953011404082311`\)], "Output", CellLabel->"Out[21]="] }, Open ]], Cell[CellGroupData[{ Cell["lengthzz=Length[zz]", "Input", CellLabel->"In[22]:=", AspectRatioFixed->True], Cell[BoxData[ \(10240\)], "Output", CellLabel->"Out[22]="] }, Open ]], Cell["0 the data set.", "Text"], Cell["zza=zz-ave;", "Input", CellLabel->"In[23]:=", AspectRatioFixed->True], Cell["\<\ Calculate the variance. This will be the \"power\" and will be \ useful later\ \>", "Text"], Cell[CellGroupData[{ Cell["var=Sum[zza[[i]]^2,{i,1,lengthzz}]/lengthzz", "Input", CellLabel->"In[24]:=", AspectRatioFixed->True], Cell[BoxData[ \(0.08403770947432808`\)], "Output", CellLabel->"Out[24]="] }, Open ]], Cell["How many data segments will there be?", "Text"], Cell[CellGroupData[{ Cell["k=lengthzz/windsize", "Input", CellLabel->"In[25]:=", CellGroupingRules->"OutputGrouping", AspectRatioFixed->True], Cell[BoxData[ \(40\)], "Output", CellLabel->"Out[25]="] }, Open ]], Cell["\<\ Since we break up the data set, it will have ends. As you get \ closer to an end, it is more difficult for the FFT algorithm to \"figure \ out\" what the freqency of the signal is. 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.22158 L .29866 .21436 L .29899 .2092 L .29931 .25701 L .29964 .38652 L .29996 .45448 L .30029 .5133 L Mistroke .30061 .56284 L .30094 .59598 L .30126 .59976 L .30159 .58428 L .30191 .58944 L .30224 .60332 L .30256 .57752 L .30289 .54254 L .30321 .49931 L .30354 .439 L .30386 .37925 L .30419 .35185 L .30451 .31951 L .30484 .30128 L .30517 .27137 L .30549 .24876 L .30582 .22988 L .30614 .22416 L .30647 .21335 L .30679 .21385 L .30712 .26317 L .30744 .35671 L .30777 .44209 L .30809 .50115 L .30842 .55324 L .30874 .57752 L .30907 .5938 L .30939 .58497 L .30972 .56605 L .31004 .52878 L .31037 .4898 L .31069 .46457 L .31102 .44794 L .31135 .41514 L .31167 .37352 L .312 .35276 L .31232 .32547 L .31265 .31102 L .31297 .29589 L .3133 .27834 L .31362 .26114 L .31395 .25162 L .31427 .23488 L .3146 .23695 L .31492 .27192 L .31525 .35609 L .31557 .41365 L .3159 .46239 L .31622 .50665 L .31655 .53807 L Mistroke .31687 .51525 L .3172 .49564 L .31753 .47065 L .31785 .44909 L .31818 .45666 L .3185 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.33899 .42868 L .33932 .48463 L .33964 .53268 L .33997 .55206 L .34029 .55413 L .34062 .55734 L .34094 .55504 L .34127 .54002 L .3416 .51663 L .34192 .4875 L .34225 .45253 L .34257 .39898 L .3429 .34302 L .34322 .31378 L .34355 .28545 L .34387 .2655 L .3442 .24474 L .34452 .23637 L .34485 .21883 L .34517 .20472 L .3455 .19727 L .34582 .19188 L .34615 .24004 L .34647 .33602 L .3468 .41262 L .34712 .45838 L .34745 .50321 L .34778 .52236 L .3481 .53234 L .34843 .53337 L .34875 .5133 L .34908 .50344 L Mistroke .3494 .4953 L .34973 .47466 L .35005 .4414 L .35038 .39531 L .3507 .35494 L .35103 .30884 L .35135 .28442 L .35168 .25919 L .352 .23362 L .35233 .22536 L .35265 .20702 L .35298 .19842 L .3533 .1834 L .35363 .17606 L .35396 .2186 L .35428 .33866 L .35461 .4273 L .35493 .48853 L .35526 .52293 L .35558 .5477 L .35591 .54713 L .35623 .54025 L .35656 .53956 L .35688 .52076 L .35721 .51777 L .35753 .49484 L .35786 .44267 L .35818 .38648 L .35851 .33843 L .35883 .31756 L .35916 .29268 L .35948 .27089 L .35981 .24176 L .36014 .22261 L .36046 .20759 L .36079 .2014 L .36111 .19188 L .36144 .19016 L .36176 .23087 L .36209 .32501 L .36241 .39943 L .36274 .44106 L .36306 .49485 L .36339 .52566 L .36371 .50069 L .36404 .50677 L .36436 .51445 L .36469 .5203 L .36501 .51709 L .36534 .48062 L Mistroke .36566 .43521 L .36599 .37639 L .36632 .32708 L .36664 .30151 L .36697 .27272 L .36729 .24474 L .36762 .23442 L .36794 .2186 L .36827 .20828 L .36859 .19956 L .36892 .19039 L .36924 .18936 L .36957 .22364 L .36989 .32295 L .37022 .40242 L .37054 .46147 L .37087 .51597 L .37119 .55013 L .37152 .54472 L .37184 .56227 L .37217 .55149 L .3725 .53933 L .37282 .48635 L .37315 .45723 L .37347 .41847 L .3738 .37891 L .37412 .33682 L .37445 .32169 L .37477 .28476 L .3751 .2577 L .37542 .23419 L .37575 .21631 L .37607 .20266 L .3764 .18684 L .37672 .17652 L .37705 .16791 L .37737 .22376 L .3777 .34737 L .37802 .42948 L .37835 .4906 L .37868 .54346 L .379 .57866 L .37933 .58876 L .37965 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.19773 L .40014 .18718 L .40047 .17846 L .40079 .22514 L .40112 .34909 L .40144 .4359 L .40177 .49633 L .40209 .54082 L .40242 .56869 L .40275 .56789 L .40307 .56513 L .4034 .55642 L .40372 .55768 L .40405 .55 L .40437 .51067 L .4047 .46021 L .40502 .41056 L .40535 .36607 L .40567 .31882 L .406 .29474 L .40632 .26745 L .40665 .24578 L .40697 .23144 L .4073 .21837 L .40762 .2022 L .40795 .19165 L .40827 .18317 L .4086 .23546 L .40893 .35609 L .40925 .44473 L .40958 .50206 L .4099 .56146 L .41023 .57534 L .41055 .58016 L .41088 .57958 L .4112 .55103 L .41153 .5414 L .41185 .54323 L .41218 .49725 L .4125 .44897 L .41283 .39542 L .41315 .34634 L .41348 .30724 L .4138 .27926 L .41413 .25277 L Mistroke .41445 .2366 L .41478 .22261 L .41511 .20885 L .41543 .20381 L .41576 .19845 L .41608 .19211 L .41641 .23944 L .41673 .36702 L .41706 .4586 L .41738 .51789 L .41771 .57201 L .41803 .58772 L .41836 .58577 L .41868 .5641 L .41901 .56685 L .41933 .56594 L .41966 .54851 L .41998 .51193 L .42031 .46399 L .42063 .41205 L .42096 .37375 L .42129 .33178 L .42161 .29314 L .42194 .26619 L .42226 .25885 L .42259 .24027 L .42291 .21826 L .42324 .20128 L .42356 .18649 L .42389 .17973 L .42421 .22525 L .42454 .35689 L .42486 .44542 L .42519 .50447 L .42551 .5586 L .42584 .55768 L .42616 .55562 L .42649 .57603 L .42681 .56043 L .42714 .53245 L .42747 .5008 L .42779 .46101 L .42812 .43269 L .42844 .3929 L .42877 .35104 L .42909 .32169 L .42942 .29692 L .42974 .27513 L .43007 .25208 L .43039 .23798 L Mistroke .43072 .2241 L .43104 .20943 L .43137 .2022 L .43169 .21057 L .43202 .24096 L .43234 .32398 L .43267 .40448 L .433 .47592 L .43332 .53463 L .43365 .54644 L .43397 .55206 L .4343 .56502 L .43462 .53188 L .43495 .48269 L .43527 .47156 L .4356 .457 L .43592 .43166 L .43625 .3882 L .43657 .35632 L .4369 .32777 L .43722 .30013 L .43755 .29233 L .43787 .26538 L .4382 .25197 L .43852 .24142 L .43885 .22456 L .43918 .21092 L .4395 .20874 L .43983 .23809 L .44015 .31286 L .44048 .3843 L .4408 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.46129 .24715 L .46162 .23316 L .46194 .22422 L .46227 .21447 L .46259 .19888 L .46292 .19016 L Mistroke .46324 .23133 L .46357 .33063 L .4639 .41927 L .46422 .48567 L .46455 .53635 L .46487 .55814 L .4652 .56536 L .46552 .56089 L .46585 .56192 L .46617 .57259 L .4665 .56789 L .46682 .52465 L .46715 .48601 L .46747 .43189 L .4678 .38889 L .46812 .35127 L .46845 .31171 L .46877 .29291 L .4691 .27846 L .46942 .26733 L .46975 .25323 L .47008 .2405 L .4704 .23098 L .47073 .2186 L .47105 .25529 L .47138 .35735 L .4717 .44083 L .47203 .49324 L .47235 .54071 L .47268 .56422 L .473 .57706 L .47333 .56789 L .47365 .5586 L .47398 .54415 L .4743 .54025 L .47463 .51617 L .47495 .48635 L .47528 .42099 L .4756 .37845 L .47593 .34359 L .47626 .32249 L .47658 .29669 L .47691 .28327 L .47723 .26561 L .47756 .25438 L .47788 .24394 L .47821 .23454 L .47853 .22571 L .47886 .25002 L .47918 .3382 L Mistroke .47951 .42248 L .47983 .47993 L .48016 .53612 L .48048 .5594 L .48081 .54186 L .48113 .54759 L .48146 .54541 L .48179 .54552 L .48211 .51479 L .48244 .47661 L .48276 .43968 L .48309 .39072 L .48341 .34313 L .48374 .31547 L .48406 .28362 L .48439 .26504 L .48471 .25633 L .48504 .24486 L .48536 .22766 L .48569 .21287 L .48601 .21115 L .48634 .19899 L .48666 .23064 L .48699 .34382 L .48731 .42707 L .48764 .49014 L .48797 .53039 L .48829 .54816 L .48862 .57006 L .48894 .56479 L .48927 .57522 L .48959 .5539 L .48992 .52982 L .49024 .47947 L .49057 .44565 L .49089 .38682 L .49122 .34737 L .49154 .31366 L .49187 .28889 L .49219 .26733 L .49252 .25036 L .49284 .23981 L .49317 .23282 L .49349 .22628 L .49382 .21665 L .49415 .20461 L .49447 .23362 L .4948 .33373 L .49512 .42019 L .49545 .49186 L Mistroke .49577 .5547 L .4961 .56743 L .49642 .58096 L .49675 .56743 L .49707 .54919 L .4974 .54725 L .49772 .5328 L .49805 .50459 L .49837 .47019 L .4987 .40161 L .49902 .36113 L .49935 .33281 L .49967 .30437 L .5 .28522 L .50033 .26791 L .50065 .25667 L .50098 .23867 L .5013 .23293 L .50163 .21459 L .50195 .20805 L .50228 .24279 L .5026 .3464 L .50293 .42868 L .50325 .4869 L .50358 .5297 L .5039 .55172 L .50423 .5625 L .50455 .57006 L .50488 .55997 L .5052 .52454 L .50553 .49346 L .50585 .45666 L .50618 .43154 L .50651 .38923 L .50683 .35643 L .50716 .32329 L .50748 .28281 L .50781 .26309 L .50813 .25048 L .50846 .24119 L .50878 .22158 L .50911 .21126 L .50943 .20576 L .50976 .20599 L .51008 .23488 L .51041 .3296 L .51073 .41056 L .51106 .47225 L .51138 .52374 L .51171 .5477 L Mistroke .51203 .5461 L .51236 .53922 L .51269 .54656 L .51301 .54277 L .51334 .53452 L .51366 .50252 L .51399 .4437 L .51431 .3945 L .51464 .35253 L .51496 .32696 L .51529 .28935 L .51561 .26699 L .51594 .24933 L .51626 .23339 L .51659 .22353 L .51691 .20759 L .51724 .20427 L .51756 .19842 L .51789 .22124 L .51821 .32341 L .51854 .41606 L .51887 .47661 L .51919 .52787 L .51952 .54323 L .51984 .55745 L .52017 .54656 L .52049 .53578 L .52082 .51846 L .52114 .50023 L .52147 .46973 L .52179 .42879 L .52212 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.50012 L .54294 .51823 L .54326 .52167 L .54359 .52121 L .54391 .52431 L .54424 .51227 L Mistroke .54456 .50344 L .54489 .47053 L .54521 .44152 L .54554 .38097 L .54586 .33384 L .54619 .30518 L .54651 .27869 L .54684 .25724 L .54716 .23064 L .54749 .22307 L .54781 .2053 L .54814 .18947 L .54846 .17617 L .54879 .1756 L .54912 .20599 L .54944 .32926 L .54977 .42386 L .55009 .48911 L .55042 .53027 L .55074 .56731 L .55107 .58038 L .55139 .57637 L .55172 .56571 L .55204 .56812 L .55237 .55825 L .55269 .49943 L .55302 .45516 L .55334 .3945 L .55367 .34153 L .55399 .31022 L .55432 .27593 L .55464 .2608 L .55497 .24623 L .5553 .23087 L .55562 .2147 L .55595 .20553 L .55627 .18993 L .5566 .1834 L .55692 .22055 L .55725 .34669 L .55757 .45069 L .5579 .50138 L .55822 .55321 L .55855 .57339 L .55887 .58784 L .5592 .5633 L .55952 .5438 L .55985 .5383 L .56017 .52465 L .5605 .48934 L Mistroke .56082 .44725 L .56115 .38694 L .56148 .34577 L .5618 .31951 L .56213 .30346 L .56245 .28488 L .56278 .26688 L .5631 .25231 L .56343 .24257 L .56375 .23098 L .56408 .21952 L .5644 .21516 L .56473 .24073 L .56505 .3327 L .56538 .414 L .5657 .48865 L .56603 .53922 L .56635 .54312 L .56668 .53922 L .567 .54621 L .56733 .53039 L .56766 .50952 L .56798 .48314 L .56831 .45551 L .56863 .41778 L .56896 .37088 L .56928 .34439 L .56961 .31183 L .56993 .29841 L .57026 .27869 L .57058 .26366 L .57091 .24818 L .57123 .23225 L .57156 .2264 L .57188 .21562 L .57221 .20897 L .57253 .23064 L .57286 .32261 L .57319 .40253 L .57351 .46308 L .57384 .49966 L .57416 .50539 L .57449 .49817 L .57481 .50482 L .57514 .49048 L .57546 .4648 L .57579 .45505 L .57611 .42707 L .57644 .39038 L .57676 .35265 L Mistroke .57709 .32031 L .57741 .29061 L .57774 .26137 L .57806 .24818 L .57839 .23259 L .57871 .21711 L .57904 .20243 L .57937 .19177 L .57969 .18374 L .58002 .17915 L .58034 .20541 L .58067 .30002 L .58099 .38453 L .58132 .46273 L .58164 .50826 L .58197 .52408 L .58229 .5219 L .58262 .52729 L .58294 .52729 L .58327 .49209 L .58359 .46973 L .58392 .43395 L .58424 .37983 L .58457 .35334 L .58489 .32056 L .58522 .28304 L .58555 .26194 L .58587 .24727 L .5862 .22456 L .58652 .21482 L .58685 .2022 L .58717 .19062 L .5875 .18844 L .58782 .18477 L .58815 .20748 L .58847 .30323 L .5888 .39427 L .58912 .46319 L .58945 .50814 L .58977 .52787 L .5901 .52477 L .59042 .52408 L .59075 .51938 L .59107 .52259 L .5914 .49106 L .59173 .44748 L .59205 .40907 L .59238 .36045 L .5927 .32341 L .59303 .28981 L Mistroke .59335 .26596 L .59368 .24681 L .594 .23763 L .59433 .22789 L .59465 .21195 L .59498 .20449 L .5953 .20495 L .59563 .19544 L .59595 .21848 L .59628 .31664 L .5966 .39714 L .59693 .45505 L .59725 .5031 L .59758 .52787 L .59791 .52534 L .59823 .52821 L .59856 .52213 L .59888 .52041 L .59921 .5008 L .59953 .45459 L .59986 .41044 L .60018 .34325 L .60051 .31171 L .60083 .2882 L .60116 .26596 L .60148 .24142 L .60181 .23099 L .60213 .21621 L .60246 .21124 L .60278 .20341 L .60311 .19546 L .60343 .19534 L .60376 .21584 L .60409 .29186 L .60441 .37373 L .60474 .43994 L .60506 .48591 L .60539 .51237 L .60571 .51324 L .60604 .48839 L .60636 .4623 L .60669 .42876 L .60701 .4269 L .60734 .39783 L .60766 .36168 L .60799 .32864 L .60831 .3054 L .60864 .28578 L .60896 .24913 L .60929 .23099 L Mistroke .60961 .22422 L .60994 .21745 L .61027 .20255 L .61059 .19899 L .61092 .19888 L .61124 .18018 L .61157 .19509 L .61189 .2741 L .61222 .36744 L .61254 .44312 L .61287 .48968 L .61319 .51319 L .61352 .53498 L .61384 .5375 L .61417 .53004 L .61449 .50998 L .61482 .47156 L .61514 .44152 L .61547 .40872 L .61579 .36354 L .61612 .32605 L .61645 .2921 L .61677 .26355 L .6171 .24027 L .61742 .21929 L .61775 .20897 L .61807 .20346 L .6184 .19234 L .61872 .17927 L .61905 .17766 L .61937 .19589 L .6197 .2882 L .62002 .37937 L .62035 .45516 L .62067 .49897 L .621 .5164 L .62132 .51743 L .62165 .52236 L .62198 .53096 L .6223 .52076 L .62263 .5055 L .62295 .46652 L .62328 .42111 L .6236 .3671 L .62393 .32008 L .62425 .30059 L .62458 .29554 L .6249 .26642 L .62523 .24566 L .62555 .23557 L Mistroke .62588 .22273 L .6262 .21573 L .62653 .20335 L .62685 .19463 L .62718 .20931 L .6275 .30024 L .62783 .39221 L .62816 .46147 L .62848 .49945 L .62881 .51001 L .62913 .5266 L .62946 .53383 L .62978 .52878 L .63011 .52328 L .63043 .51686 L .63076 .48372 L .63108 .44095 L .63141 .38453 L .63173 .34164 L .63206 .31022 L .63238 .29073 L .63271 .2733 L .63303 .26652 L .63336 .24391 L .63368 .23484 L .63401 .21745 L .63434 .1977 L .63466 .19137 L .63499 .20081 L .63531 .28603 L .63564 .37447 L .63596 .42455 L .63629 .46422 L .63661 .49346 L .63694 .49255 L .63726 .50103 L .63759 .50459 L .63791 .49541 L .63824 .47477 L .63856 .43235 L .63889 .39634 L .63921 .35024 L .63954 .30827 L .63986 .27571 L .64019 .25759 L .64052 .24142 L .64084 .23144 L .64117 .21332 L .64149 .2014 L .64182 .20174 L Mistroke .64214 .19727 L .64247 .19326 L .64279 .21138 L .64312 .28109 L .64344 .35494 L .64377 .4109 L .64409 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.53674 L .68508 .48727 L .6854 .44232 L .68573 .39863 L .68605 .3538 L .68638 .32536 L .6867 .30254 L .68703 .28006 L .68735 .25002 L .68768 .23901 L .688 .22284 L .68833 .20621 L .68865 .19085 L .68898 .18225 L .68931 .17032 L .68963 .18213 L .68996 .27089 L .69028 .37639 L .69061 .44955 L Mistroke .69093 .51342 L .69126 .52179 L .69158 .51239 L .69191 .49794 L .69223 .48074 L .69256 .45975 L .69288 .43865 L .69321 .38957 L .69353 .35953 L .69386 .3241 L .69418 .29314 L .69451 .26206 L .69483 .23821 L .69516 .22364 L .69549 .2139 L .69581 .20232 L .69614 .19096 L .69646 .18764 L .69679 .18248 L .69711 .17755 L .69744 .18087 L .69776 .26275 L .69809 .36263 L .69841 .4265 L .69874 .46548 L .69906 .4797 L .69939 .48165 L .69971 .4883 L .70004 .5039 L .70036 .51583 L .70069 .49633 L .70101 .44978 L .70134 .39531 L .70167 .34405 L .70199 .31435 L .70232 .28924 L .70264 .26172 L .70297 .25346 L .70329 .24073 L .70362 .2311 L .70394 .21332 L .70427 .19888 L .70459 .18821 L .70492 .18099 L .70524 .19245 L .70557 .2741 L .70589 .37146 L .70622 .43785 L .70654 .48326 L .70687 .50161 L Mistroke .70719 .50356 L .70752 .51342 L .70785 .51491 L .70817 .51709 L .7085 .49392 L .70882 .45666 L .70915 .40299 L .70947 .35403 L .7098 .31825 L .71012 .29096 L .71045 .26493 L .71077 .24406 L .7111 .23075 L .71142 .21321 L .71175 .20553 L .71207 .1936 L .7124 .18374 L .71272 .17755 L .71305 .18546 L .71337 .26527 L .7137 .35941 L .71403 .43154 L .71435 .48039 L .71468 .50229 L .715 .51789 L .71533 .51732 L .71565 .52293 L .71598 .53991 L .7163 .51984 L .71663 .47833 L .71695 .43395 L .71728 .36549 L .7176 .31825 L .71793 .29314 L .71825 .26665 L .71858 .2475 L .7189 .22261 L .71923 .2155 L .71956 .20094 L .71988 .18615 L .72021 .17824 L .72053 .16333 L .72086 .17445 L .72118 .26825 L .72151 .38166 L .72183 .46457 L .72216 .51124 L .72248 .51938 L .72281 .53188 L .72313 .54507 L Mistroke .72346 .55883 L .72378 .55367 L .72411 .52901 L .72443 .47454 L .72476 .41939 L .72508 .37834 L .72541 .33235 L .72574 .30529 L .72606 .28396 L .72639 .25896 L .72671 .23935 L .72704 .22364 L .72736 .21183 L .72769 .19745 L .72801 .18192 L .72834 .17248 L .72866 .19463 L .72899 .27353 L .72931 .37788 L .72964 .45069 L .72996 .49713 L .73029 .51858 L .73061 .52534 L .73094 .52259 L .73126 .52523 L .73159 .50378 L .73192 .47259 L .73224 .43464 L .73257 .38556 L .73289 .33694 L .73322 .3054 L .73354 .27571 L .73387 .26137 L .73419 .23706 L .73452 .21573 L .73484 .20759 L .73517 .19463 L .73549 .18672 L .73582 .18122 L .73614 .17743 L .73647 .18752 L .73679 .26172 L .73712 .3507 L .73744 .41067 L .73777 .44771 L .7381 .46399 L .73842 .47271 L .73875 .47168 L .73907 .46766 L .7394 .45436 L Mistroke .73972 .44037 L .74005 .40609 L .74037 .36389 L .7407 .32513 L .74102 .28717 L .74135 .25931 L .74167 .24176 L .742 .22342 L .74232 .2139 L .74265 .20174 L .74297 .19761 L .7433 .18569 L .74362 .17697 L .74395 .1709 L .74428 .18041 L .7446 .24085 L .74493 .31274 L .74525 .371 L .74558 .42111 L .7459 .44496 L .74623 .46032 L .74655 .46445 L .74688 .45402 L .7472 .44117 L .74753 .42833 L .74785 .38785 L .74818 .33969 L .7485 .31687 L .74883 .28843 L .74915 .27261 L .74948 .24853 L .7498 .24727 L .75013 .23733 L .75046 .22689 L .75078 .21298 L .75111 .19727 L .75143 .18512 L .75176 .17457 L .75208 .18546 L .75241 .25942 L .75273 .35265 L .75306 .43292 L .75338 .46376 L .75371 .48372 L .75403 .50252 L .75436 .51353 L .75468 .51846 L .75501 .50906 L .75533 .48395 L .75566 .44679 L Mistroke .75598 .40024 L .75631 .34611 L .75664 .3116 L .75696 .27433 L .75729 .24635 L .75761 .2202 L .75794 .1975 L .75826 .18603 L .75859 .17525 L .75891 .16619 L .75924 .15542 L .75956 .15221 L .75989 .16275 L .76021 .23855 L .76054 .34478 L .76086 .4281