(*^ ::[paletteColors = 128; automaticGrouping; currentKernel; fontset = title, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, L1, e8, 24, "Times"; ; fontset = subtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, L1, e6, 18, "Times"; ; fontset = subsubtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, italic, L1, e6, 14, "Times"; ; fontset = section, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, grayBox, M22, bold, L1, a20, 18, "Times"; ; fontset = subsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, blackBox, M19, bold, L1, a15, 14, "Times"; ; fontset = subsubsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, whiteBox, M18, bold, L1, a12, 12, "Times"; ; fontset = text, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12; fontset = smalltext, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 10, "Times"; ; fontset = input, noPageBreakBelow, nowordwrap, preserveAspect, groupLikeInput, M42, N23, bold, L1, 12, "Courier"; ; fontset = output, output, inactive, noPageBreakBelow, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L-5, 12, "Courier"; ; fontset = message, inactive, noPageBreakBelow, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L1, 12, "Courier"; ; fontset = print, inactive, noPageBreakBelow, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L1, 12, "Courier"; ; fontset = info, inactive, noPageBreakBelow, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L1, 12, "Courier"; ; fontset = postscript, PostScript, formatAsPostScript, output, inactive, noPageBreakBelow, nowordwrap, preserveAspect, groupLikeGraphics, M7, l34, w282, h287, L1, 12, "Courier"; ; fontset = name, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, italic, L1, 10, "Times"; ; fontset = header, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12; fontset = Left Header, nohscroll, cellOutline, 12; fontset = footer, inactive, nohscroll, noKeepOnOnePage, preserveAspect, center, M7, L1, 12; fontset = Left Footer, cellOutline, blackBox, 12; fontset = help, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 10, "Times"; ; fontset = clipboard, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12; fontset = completions, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12, "Courier"; ; fontset = special1, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12; fontset = special2, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12; fontset = special3, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12; fontset = special4, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12; fontset = special5, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12;] :[font = title; inactive; preserveAspect; startGroup; ] The Foot Problem in Wavelet Packet Splitting :[font = subsubtitle; inactive; preserveAspect; ] Jack K. Cohen Colorado School of Mines, 1993 jkc@keller.mines.colorado.edu :[font = text; inactive; preserveAspect; ] Wavelet Packets are formed to give finer frequency control than afforded by the pure wavelets. Unfortunately, when splitting is carried too far, pieces of non-adjacent bands creep in. One characterizes this problem by saying that the packets have ``feet'' because that's how it looks. One can overcome this problem by choice of wavelet for a designated number of splits, but eventually the ``feet'' will appear. This is OK for certain applications and fatal for others and for still others, only a few splits are needed, so the problem doesn't enter. 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lineto Mfstroke grestore grestore gsave gsave 0.004 setlinewidth 0.02381 0.01472 moveto 0.06349 0.01472 lineto 0.10317 0.01472 lineto 0.14286 0.01472 lineto 0.18254 0.01472 lineto 0.22222 0.01472 lineto 0.2619 0.01472 lineto 0.30159 0.01472 lineto 0.32143 0.01472 lineto 0.33135 0.01472 lineto 0.33631 0.01472 lineto 0.33879 0.01472 lineto 0.34003 0.01472 lineto 0.34127 0.01472 lineto 0.34251 0.01472 lineto 0.34375 0.01472 lineto 0.34499 0.01472 lineto 0.34623 0.01472 lineto 0.34747 0.01472 lineto 0.34871 0.01472 lineto 0.34995 0.01473 lineto 0.35119 0.01474 lineto 0.35243 0.01476 lineto 0.35367 0.01478 lineto 0.35491 0.01481 lineto 0.35615 0.01485 lineto 0.35739 0.0149 lineto 0.35863 0.01497 lineto 0.36111 0.01514 lineto 0.36359 0.01537 lineto 0.36607 0.01568 lineto 0.37103 0.01655 lineto 0.37599 0.01767 lineto 0.37847 0.01826 lineto 0.38095 0.01879 lineto 0.38343 0.01923 lineto 0.38467 0.0194 lineto 0.38591 0.01953 lineto 0.38715 0.01961 lineto 0.38839 0.01964 lineto 0.38963 0.01962 lineto 0.39087 0.01954 lineto 0.39211 0.01942 lineto 0.39335 0.01924 lineto 0.39583 0.01876 lineto 0.40079 0.01744 lineto 0.40575 0.01608 lineto 0.40823 0.01553 lineto 0.40947 0.01531 lineto 0.41071 0.01512 lineto Mistroke 0.41195 0.01498 lineto 0.41319 0.01487 lineto 0.41443 0.0148 lineto 0.41567 0.01475 lineto 0.41691 0.01473 lineto 0.41815 0.01472 lineto 0.41939 0.01472 lineto 0.42063 0.01472 lineto 0.42188 0.01472 lineto 0.42312 0.01472 lineto 0.4256 0.01472 lineto 0.43056 0.01472 lineto 0.44048 0.01472 lineto 0.46032 0.01472 lineto 0.5 0.01472 lineto 0.53968 0.01472 lineto 0.55952 0.01472 lineto 0.56944 0.01472 lineto 0.5744 0.01472 lineto 0.57688 0.01472 lineto 0.57813 0.01472 lineto 0.57937 0.01472 lineto 0.58061 0.01472 lineto 0.58185 0.01474 lineto 0.58309 0.01485 lineto 0.58433 0.01514 lineto 0.58557 0.01571 lineto 0.58681 0.01669 lineto 0.58805 0.01823 lineto 0.58929 0.02047 lineto 0.59053 0.02356 lineto 0.59177 0.02764 lineto 0.59425 0.03933 lineto 0.59549 0.04717 lineto 0.59673 0.05648 lineto 0.59921 0.07976 lineto 0.60417 0.14559 lineto 0.60913 0.23394 lineto 0.61409 0.33427 lineto 0.61905 0.4309 lineto 0.62401 0.50899 lineto 0.62649 0.53833 lineto 0.62897 0.56095 lineto 0.63145 0.57739 lineto 0.63269 0.58357 lineto 0.63393 0.58857 lineto 0.63517 0.59254 lineto 0.63641 0.59563 lineto 0.63765 0.59797 lineto 0.63889 0.59971 lineto Mistroke 0.64013 0.60096 lineto 0.64137 0.60183 lineto 0.64261 0.60242 lineto 0.64385 0.6028 lineto 0.64509 0.60304 lineto 0.64633 0.60318 lineto 0.64757 0.60325 lineto 0.64881 0.60329 lineto 0.65005 0.60331 lineto 0.65129 0.60332 lineto 0.65253 0.60332 lineto 0.65377 0.60332 lineto 0.65501 0.60332 lineto 0.65625 0.60332 lineto 0.65749 0.60332 lineto 0.65873 0.60332 lineto 0.65997 0.60332 lineto 0.66121 0.60332 lineto 0.66245 0.60332 lineto 0.66369 0.60332 lineto 0.66493 0.60332 lineto 0.66617 0.60332 lineto 0.66741 0.60332 lineto 0.66865 0.60332 lineto 0.66989 0.60332 lineto 0.67113 0.60332 lineto 0.67237 0.60332 lineto 0.67361 0.60332 lineto 0.67485 0.60331 lineto 0.67609 0.60331 lineto 0.67733 0.6033 lineto 0.67857 0.60329 lineto 0.67981 0.60327 lineto 0.68105 0.60325 lineto 0.68229 0.60322 lineto 0.68353 0.60318 lineto 0.68477 0.60312 lineto 0.68601 0.60304 lineto 0.68725 0.60294 lineto 0.68849 0.6028 lineto 0.69097 0.60242 lineto 0.69221 0.60216 lineto 0.69345 0.60183 lineto 0.69469 0.60144 lineto 0.69593 0.60096 lineto 0.69841 0.59971 lineto 0.70089 0.59797 lineto 0.70337 0.59563 lineto 0.70585 0.59254 lineto 0.70833 0.58857 lineto Mistroke 0.71329 0.57739 lineto 0.71577 0.56989 lineto 0.71825 0.56095 lineto 0.72321 0.53833 lineto 0.72817 0.509 lineto 0.7381 0.43092 lineto 0.75794 0.23399 lineto 0.76786 0.14566 lineto 0.77282 0.10956 lineto 0.77778 0.07982 lineto 0.78274 0.05652 lineto 0.7877 0.03937 lineto 0.79018 0.03289 lineto 0.79266 0.02767 lineto 0.79514 0.02358 lineto 0.79762 0.02048 lineto 0.79886 0.01926 lineto 0.8001 0.01824 lineto 0.80258 0.0167 lineto 0.80382 0.01614 lineto 0.80506 0.01571 lineto 0.8063 0.01538 lineto 0.80754 0.01514 lineto 0.80878 0.01497 lineto 0.81002 0.01485 lineto 0.81126 0.01478 lineto 0.8125 0.01474 lineto 0.81374 0.01472 lineto 0.81498 0.01472 lineto 0.81622 0.01472 lineto 0.81746 0.01472 lineto 0.8187 0.01472 lineto 0.81994 0.01472 lineto 0.82242 0.01472 lineto 0.82738 0.01472 lineto 0.8373 0.01472 lineto 0.85714 0.01472 lineto 0.89683 0.01472 lineto 0.93651 0.01472 lineto 0.97619 0.01472 lineto Mfstroke grestore grestore grestore % End of Graphics MathPictureEnd :[font = output; output; inactive; preserveAspect; endGroup; ] The Unformatted text for this cell was not generated. Use options in the Actions Settings dialog box to control when Unformatted text is generated. ;[o] -Graphics- :[font = text; inactive; preserveAspect; ] W15 is OK, though we can see the ghost of Christmas past and a new, but small, overlap with the later period. Try W14: :[font = input; preserveAspect; startGroup; ] Plot[Evaluate@(m0[4xi] m1[2xi] m1[xi] m1[xi/2]), {xi, 0, 1}] :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 282; pictureHeight = 174; ] %! %%Creator: Mathematica %%AspectRatio: 0.61803 MathPictureStart /Courier findfont 10 scalefont setfont % Scaling calculations -0.555597 1.531788 0.014715 0.589911 [ [(0.4)] 0.05712 0.01472 0 2 Msboxa [(0.5)] 0.2103 0.01472 0 2 Msboxa [(0.6)] 0.36348 0.01472 0 2 Msboxa [(0.7)] 0.51665 0.01472 0 2 Msboxa [(0.8)] 0.66983 0.01472 0 2 Msboxa [(0.9)] 0.82301 0.01472 0 2 Msboxa [(0.2)] 0.96369 0.1327 1 0 Msboxa [(0.4)] 0.96369 0.25068 1 0 Msboxa [(0.6)] 0.96369 0.36866 1 0 Msboxa [(0.8)] 0.96369 0.48664 1 0 Msboxa [(1)] 0.96369 0.60463 1 0 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 0.61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath %%Object: Graphics [ ] 0 setdash 0 setgray gsave gsave 0.002 setlinewidth 0.05712 0.01472 moveto 0.05712 0.02097 lineto stroke grestore [(0.4)] 0.05712 0.01472 0 2 Mshowa gsave 0.002 setlinewidth 0.2103 0.01472 moveto 0.2103 0.02097 lineto stroke grestore [(0.5)] 0.2103 0.01472 0 2 Mshowa gsave 0.002 setlinewidth 0.36348 0.01472 moveto 0.36348 0.02097 lineto stroke grestore [(0.6)] 0.36348 0.01472 0 2 Mshowa gsave 0.002 setlinewidth 0.51665 0.01472 moveto 0.51665 0.02097 lineto stroke grestore [(0.7)] 0.51665 0.01472 0 2 Mshowa gsave 0.002 setlinewidth 0.66983 0.01472 moveto 0.66983 0.02097 lineto stroke grestore [(0.8)] 0.66983 0.01472 0 2 Mshowa gsave 0.002 setlinewidth 0.82301 0.01472 moveto 0.82301 0.02097 lineto stroke grestore [(0.9)] 0.82301 0.01472 0 2 Mshowa gsave 0.001 setlinewidth 0.08775 0.01472 moveto 0.08775 0.01847 lineto stroke grestore gsave 0.001 setlinewidth 0.11839 0.01472 moveto 0.11839 0.01847 lineto stroke grestore gsave 0.001 setlinewidth 0.14903 0.01472 moveto 0.14903 0.01847 lineto stroke grestore gsave 0.001 setlinewidth 0.17966 0.01472 moveto 0.17966 0.01847 lineto stroke grestore gsave 0.001 setlinewidth 0.24093 0.01472 moveto 0.24093 0.01847 lineto stroke grestore gsave 0.001 setlinewidth 0.27157 0.01472 moveto 0.27157 0.01847 lineto stroke grestore gsave 0.001 setlinewidth 0.3022 0.01472 moveto 0.3022 0.01847 lineto stroke grestore gsave 0.001 setlinewidth 0.33284 0.01472 moveto 0.33284 0.01847 lineto stroke grestore gsave 0.001 setlinewidth 0.39411 0.01472 moveto 0.39411 0.01847 lineto stroke grestore gsave 0.001 setlinewidth 0.42475 0.01472 moveto 0.42475 0.01847 lineto stroke grestore gsave 0.001 setlinewidth 0.45538 0.01472 moveto 0.45538 0.01847 lineto stroke grestore gsave 0.001 setlinewidth 0.48602 0.01472 moveto 0.48602 0.01847 lineto stroke grestore gsave 0.001 setlinewidth 0.54729 0.01472 moveto 0.54729 0.01847 lineto stroke grestore gsave 0.001 setlinewidth 0.57793 0.01472 moveto 0.57793 0.01847 lineto stroke grestore gsave 0.001 setlinewidth 0.60856 0.01472 moveto 0.60856 0.01847 lineto stroke grestore gsave 0.001 setlinewidth 0.6392 0.01472 moveto 0.6392 0.01847 lineto stroke grestore gsave 0.001 setlinewidth 0.70047 0.01472 moveto 0.70047 0.01847 lineto stroke grestore gsave 0.001 setlinewidth 0.7311 0.01472 moveto 0.7311 0.01847 lineto stroke grestore gsave 0.001 setlinewidth 0.76174 0.01472 moveto 0.76174 0.01847 lineto stroke grestore gsave 0.001 setlinewidth 0.79238 0.01472 moveto 0.79238 0.01847 lineto stroke grestore gsave 0.001 setlinewidth 0.85365 0.01472 moveto 0.85365 0.01847 lineto stroke grestore gsave 0.001 setlinewidth 0.88428 0.01472 moveto 0.88428 0.01847 lineto stroke grestore gsave 0.001 setlinewidth 0.91492 0.01472 moveto 0.91492 0.01847 lineto stroke grestore gsave 0.001 setlinewidth 0.94555 0.01472 moveto 0.94555 0.01847 lineto stroke grestore gsave 0.001 setlinewidth 0.02648 0.01472 moveto 0.02648 0.01847 lineto stroke grestore gsave 0.002 setlinewidth 0 0.01472 moveto 1 0.01472 lineto stroke grestore gsave 0.002 setlinewidth 0.97619 0.1327 moveto 0.98244 0.1327 lineto stroke grestore [(0.2)] 0.96369 0.1327 1 0 Mshowa gsave 0.002 setlinewidth 0.97619 0.25068 moveto 0.98244 0.25068 lineto stroke grestore [(0.4)] 0.96369 0.25068 1 0 Mshowa gsave 0.002 setlinewidth 0.97619 0.36866 moveto 0.98244 0.36866 lineto stroke grestore [(0.6)] 0.96369 0.36866 1 0 Mshowa gsave 0.002 setlinewidth 0.97619 0.48664 moveto 0.98244 0.48664 lineto stroke grestore [(0.8)] 0.96369 0.48664 1 0 Mshowa gsave 0.002 setlinewidth 0.97619 0.60463 moveto 0.98244 0.60463 lineto stroke grestore [(1)] 0.96369 0.60463 1 0 Mshowa gsave 0.001 setlinewidth 0.97619 0.03831 moveto 0.97994 0.03831 lineto stroke grestore gsave 0.001 setlinewidth 0.97619 0.06191 moveto 0.97994 0.06191 lineto stroke grestore gsave 0.001 setlinewidth 0.97619 0.0855 moveto 0.97994 0.0855 lineto stroke grestore gsave 0.001 setlinewidth 0.97619 0.1091 moveto 0.97994 0.1091 lineto stroke grestore gsave 0.001 setlinewidth 0.97619 0.15629 moveto 0.97994 0.15629 lineto stroke grestore gsave 0.001 setlinewidth 0.97619 0.17989 moveto 0.97994 0.17989 lineto stroke grestore gsave 0.001 setlinewidth 0.97619 0.20349 moveto 0.97994 0.20349 lineto stroke grestore gsave 0.001 setlinewidth 0.97619 0.22708 moveto 0.97994 0.22708 lineto stroke grestore gsave 0.001 setlinewidth 0.97619 0.27428 moveto 0.97994 0.27428 lineto stroke grestore gsave 0.001 setlinewidth 0.97619 0.29787 moveto 0.97994 0.29787 lineto stroke grestore gsave 0.001 setlinewidth 0.97619 0.32147 moveto 0.97994 0.32147 lineto stroke grestore gsave 0.001 setlinewidth 0.97619 0.34507 moveto 0.97994 0.34507 lineto stroke grestore gsave 0.001 setlinewidth 0.97619 0.39226 moveto 0.97994 0.39226 lineto stroke grestore gsave 0.001 setlinewidth 0.97619 0.41585 moveto 0.97994 0.41585 lineto stroke grestore gsave 0.001 setlinewidth 0.97619 0.43945 moveto 0.97994 0.43945 lineto stroke grestore gsave 0.001 setlinewidth 0.97619 0.46305 moveto 0.97994 0.46305 lineto stroke grestore gsave 0.001 setlinewidth 0.97619 0.51024 moveto 0.97994 0.51024 lineto stroke grestore gsave 0.001 setlinewidth 0.97619 0.53384 moveto 0.97994 0.53384 lineto stroke grestore gsave 0.001 setlinewidth 0.97619 0.55743 moveto 0.97994 0.55743 lineto stroke grestore gsave 0.001 setlinewidth 0.97619 0.58103 moveto 0.97994 0.58103 lineto stroke grestore gsave 0.002 setlinewidth 0.97619 0 moveto 0.97619 0.61803 lineto stroke grestore grestore 0 0 moveto 1 0 lineto 1 0.61803 lineto 0 0.61803 lineto closepath clip newpath gsave gsave 0.004 setlinewidth stroke stroke stroke stroke stroke stroke stroke stroke stroke 0 0.01472 moveto 0.01882 0.01472 lineto stroke 0.01882 0.01472 moveto 0.08265 0.01472 lineto 0.14647 0.01472 lineto 0.2103 0.01472 lineto 0.27412 0.01472 lineto 0.33795 0.01472 lineto 0.40177 0.01472 lineto 0.43368 0.01472 lineto 0.44964 0.01472 lineto 0.45762 0.01472 lineto 0.46161 0.01472 lineto 0.4636 0.01472 lineto 0.46559 0.01472 lineto 0.46759 0.01474 lineto 0.46958 0.01514 lineto 0.47158 0.0167 lineto 0.47357 0.0205 lineto 0.47557 0.0277 lineto 0.47756 0.03942 lineto 0.47956 0.05662 lineto 0.48155 0.07996 lineto 0.48355 0.10977 lineto 0.48554 0.14595 lineto 0.48953 0.23447 lineto 0.49352 0.33501 lineto 0.49751 0.43183 lineto 0.4995 0.47396 lineto 0.5015 0.51004 lineto 0.50349 0.53941 lineto 0.50548 0.56203 lineto 0.50748 0.57844 lineto 0.50947 0.58957 lineto 0.51147 0.59654 lineto 0.51346 0.60049 lineto 0.51546 0.60245 lineto 0.51745 0.60321 lineto 0.51945 0.60332 lineto 0.52144 0.60311 lineto 0.52344 0.60274 lineto 0.52543 0.60226 lineto 0.52942 0.60101 lineto 0.53341 0.59927 lineto 0.5374 0.59692 lineto 0.54139 0.59382 lineto 0.54538 0.58984 lineto 0.55335 0.57864 lineto 0.55734 0.57112 lineto 0.56133 0.56216 lineto 0.56931 0.53949 lineto 0.57729 0.5101 lineto Mistroke 0.59324 0.43185 lineto 0.62516 0.23448 lineto 0.64111 0.14595 lineto 0.64909 0.10978 lineto 0.65707 0.07996 lineto 0.66505 0.05662 lineto 0.67302 0.03927 lineto 0.67701 0.03247 lineto 0.681 0.02676 lineto 0.68499 0.02218 lineto 0.68699 0.02033 lineto 0.68898 0.0188 lineto 0.69097 0.01758 lineto 0.69297 0.01663 lineto 0.69496 0.01594 lineto 0.69696 0.01545 lineto 0.69895 0.01513 lineto 0.70095 0.01494 lineto 0.70294 0.01482 lineto 0.70494 0.01476 lineto 0.70693 0.01473 lineto 0.70893 0.01472 lineto 0.71092 0.01472 lineto 0.71291 0.01472 lineto 0.71491 0.01472 lineto 0.7169 0.01472 lineto 0.7189 0.01472 lineto 0.72089 0.01472 lineto 0.72289 0.01472 lineto 0.72488 0.01472 lineto 0.72887 0.01472 lineto 0.73685 0.01472 lineto 0.7528 0.01472 lineto 0.78472 0.01472 lineto 0.84854 0.01472 lineto 0.91237 0.01472 lineto 0.97619 0.01472 lineto Mfstroke grestore grestore % End of Graphics MathPictureEnd :[font = output; output; inactive; preserveAspect; endGroup; ] The Unformatted text for this cell was not generated. Use options in the Actions Settings dialog box to control when Unformatted text is generated. ;[o] -Graphics- :[font = input; preserveAspect; startGroup; ] Plot[Evaluate@{m0[4xi], m1[2xi] m1[xi] m1[xi/2]}, {xi, 0, 1}, PlotStyle -> {GrayLevel[0.5], GrayLevel[0.0]} ] :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 282; pictureHeight = 174; ] %! %%Creator: Mathematica %%AspectRatio: 0.61803 MathPictureStart /Courier findfont 10 scalefont setfont % Scaling calculations 0.02381 0.952381 0.014715 0.588604 [ [(0.2)] 0.21429 0.01472 0 2 Msboxa [(0.4)] 0.40476 0.01472 0 2 Msboxa [(0.6)] 0.59524 0.01472 0 2 Msboxa [(0.8)] 0.78571 0.01472 0 2 Msboxa [(1)] 0.97619 0.01472 0 2 Msboxa [(0.2)] 0.01131 0.13244 1 0 Msboxa [(0.4)] 0.01131 0.25016 1 0 Msboxa [(0.6)] 0.01131 0.36788 1 0 Msboxa [(0.8)] 0.01131 0.4856 1 0 Msboxa [(1)] 0.01131 0.60332 1 0 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 0.61903 0 0 ] ] MathScale % Start of Graphics 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generated. 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Use options in the Actions Settings dialog box to control when Unformatted text is generated. ;[o] -Graphics- :[font = text; inactive; preserveAspect; ] This is the W2 filter -- tiny foot. 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Use options in the Actions Settings dialog box to control when Unformatted text is generated. ;[o] -Graphics- :[font = text; inactive; preserveAspect; endGroup; ] In comparison with Meyer, have TWO bad feet at this level instead of one. :[font = subsection; inactive; Cclosed; preserveAspect; startGroup; ] SplineOrder 5 Packets :[font = input; preserveAspect; ] n = 5; m0[xi_] := SplineM0[n, xi] m1[xi_] := m0[xi + 1/2] :[font = text; inactive; preserveAspect; ] Here is the low pass filter: :[font = input; preserveAspect; startGroup; ] Plot[Evaluate@m0[xi/2], {xi, 0, 1}] :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 282; pictureHeight = 174; ] %! %%Creator: Mathematica %%AspectRatio: 0.61803 MathPictureStart /Courier findfont 10 scalefont setfont % Scaling calculations 0.02381 0.952381 0.014715 0.588604 [ [(0.2)] 0.21429 0.01472 0 2 Msboxa [(0.4)] 0.40476 0.01472 0 2 Msboxa [(0.6)] 0.59524 0.01472 0 2 Msboxa [(0.8)] 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[(0.4)] 0.01131 0.25016 1 0 Mshowa gsave 0.002 setlinewidth 0.02381 0.36788 moveto 0.03006 0.36788 lineto stroke grestore [(0.6)] 0.01131 0.36788 1 0 Mshowa gsave 0.002 setlinewidth 0.02381 0.4856 moveto 0.03006 0.4856 lineto stroke grestore [(0.8)] 0.01131 0.4856 1 0 Mshowa gsave 0.002 setlinewidth 0.02381 0.60332 moveto 0.03006 0.60332 lineto stroke grestore [(1)] 0.01131 0.60332 1 0 Mshowa gsave 0.001 setlinewidth 0.02381 0.03826 moveto 0.02756 0.03826 lineto stroke grestore gsave 0.001 setlinewidth 0.02381 0.0618 moveto 0.02756 0.0618 lineto stroke grestore gsave 0.001 setlinewidth 0.02381 0.08535 moveto 0.02756 0.08535 lineto stroke grestore gsave 0.001 setlinewidth 0.02381 0.10889 moveto 0.02756 0.10889 lineto stroke grestore gsave 0.001 setlinewidth 0.02381 0.15598 moveto 0.02756 0.15598 lineto stroke grestore gsave 0.001 setlinewidth 0.02381 0.17952 moveto 0.02756 0.17952 lineto stroke grestore gsave 0.001 setlinewidth 0.02381 0.20307 moveto 0.02756 0.20307 lineto stroke 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Use options in the Actions Settings dialog box to control when Unformatted text is generated. ;[o] -Graphics- :[font = text; inactive; preserveAspect; ] Here is the high pass filter: :[font = input; preserveAspect; startGroup; ] Plot[Evaluate@m1[xi/2], {xi, 0, 1}] :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 282; pictureHeight = 174; ] %! %%Creator: Mathematica %%AspectRatio: 0.61803 MathPictureStart /Courier findfont 10 scalefont setfont % Scaling calculations 0.02381 0.952381 0.014715 0.588604 [ [(0.2)] 0.21429 0.01472 0 2 Msboxa [(0.4)] 0.40476 0.01472 0 2 Msboxa [(0.6)] 0.59524 0.01472 0 2 Msboxa [(0.8)] 0.78571 0.01472 0 2 Msboxa [(1)] 0.97619 0.01472 0 2 Msboxa [(0.2)] 0.01131 0.13244 1 0 Msboxa [(0.4)] 0.01131 0.25016 1 0 Msboxa [(0.6)] 0.01131 0.36788 1 0 Msboxa [(0.8)] 0.01131 0.4856 1 0 Msboxa [(1)] 0.01131 0.60332 1 0 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 0.61903 0 0 ] ] MathScale % Start of Graphics 1 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