(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 3.0, MathReader 3.0, or any compatible application. The data for the notebook starts with the line of 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[ 188881, 3297]*) (*NotebookOutlinePosition[ 215346, 4259]*) (* CellTagsIndexPosition[ 215302, 4255]*) (*WindowFrame->Normal*) Notebook[{ Cell["Filtering of SampledSoundList Objects", "Title", Evaluatable->False, AspectRatioFixed->True], Cell["\<\ In this Notebook, we'll examine the use of Fourier Transforms to \ construct various filters for SampledSoundList objects.\ \>", "Text", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell["Theory of Operation", "Section", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " can represent sound in several formats, as lists of samples or as \ functions which return sample values. Though the functional representation \ is smaller, using much less memory, the list representation has some key \ advantages that we'll make use of in this sample Notebook." }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ "One major advantage of using the list representation is that ", StyleBox["Mathematica", FontSlant->"Italic"], " provides several functions for manipulating lists such as those used to \ hold sampled sounds. For example, it is trivial to reverse the order of the \ elements of a list (to play sounds in reverse), concatenate two lists, to \ multiply each element of a list by a scalar (to amplify or attenuate sounds), \ or even to multiply each element of a list by a corresponding element of \ another list (to apply an amplitude envelope). Perhaps the most useful of \ these, however, is the facility to perform Fast Fourier Transforms (FFTs) on \ lists of data." }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ "In this Notebook, we'll use the FFT (and a few of the other methods \ mentioned above) to build filters for ", StyleBox["SampledSoundList", FontFamily->"Courier"], " objects. In order to understand how these filters work, it is first \ necessary to understand the structure of the ", StyleBox["SampledSoundList", FontFamily->"Courier"], " object." }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ "A ", StyleBox["SampledSoundList", FontFamily->"Courier"], " object is of the form\n\n\t", StyleBox["SampledSoundList[{", FontFamily->"Courier"], StyleBox["num", FontSlant->"Italic"], StyleBox[", ", FontFamily->"Courier"], StyleBox["num", FontSlant->"Italic"], StyleBox[", ", FontFamily->"Courier"], StyleBox["num", FontSlant->"Italic"], StyleBox[", ", FontFamily->"Courier"], "...", StyleBox[", ", FontFamily->"Courier"], StyleBox["num", FontSlant->"Italic"], StyleBox["}, ", FontFamily->"Courier"], StyleBox["srate", FontSlant->"Italic"], StyleBox["]", FontFamily->"Courier"], "\n\nThe first item in the square brackets is the list of sampled sound \ data. When the sound is played, these values (which must all be real numbers \ between -1 and +1) are converted to voltages which are applied to the speaker \ to make the sound. The second parameter is the sample rate, which determines \ how quickly the samples are presented to the hardware\[LongDash]that is, ", StyleBox["srate", FontSlant->"Italic"], " samples are converted each second to make up the sound. Thus, the \ duration of the sound is determined by the length of the list of samples and \ by the sample rate.\n\nA ", StyleBox["SampledSoundList", FontFamily->"Courier"], " object is played using ", StyleBox["Show[Sound[", FontFamily->"Courier"], StyleBox["sound", FontSlant->"Italic"], StyleBox["]]", FontFamily->"Courier"], "." }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell["\<\ To build a filter for a sound, we can use the FFT algorithm to \ obtain the frequency-domain representation of a sound, adjust the frequency \ response to our liking, and convert the signal back to the time domain using \ the inverse FFT.\ \>", "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ "The ", StyleBox["Fourier", FontFamily->"Courier"], " function simply takes a list of data and performs an FFT on it, returning \ a new list of equal length that contains information about the frequency \ spectrum of the original. Each element of the returned list is a complex \ number, indicating magnitude and phase of a specific frequency component of \ the original list. We can use ", StyleBox["InverseFourier", FontFamily->"Courier"], " on the resultant list to obtain the original list back. The original \ list is referred to as the ", StyleBox["time-domain signal", FontSlant->"Italic"], ", and the list as returned by ", StyleBox["Fourier", FontFamily->"Courier"], " is referred to as the ", StyleBox["frequency-domain signal", FontSlant->"Italic"], "." }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell["\<\ To implement our filters, we'll simply find the frequency-domain \ representation of a signal, mask off the unwanted frequencies, and convert \ the result back to the time domain.\ \>", "Text", Evaluatable->False, AspectRatioFixed->True], Cell["\<\ The mask will consist of a list containing 1 in positions \ corresponding to frequencies which are to be retained and 0 for those to be \ rejected, and will simply be multiplied with the frequency-domain signal to \ remove unwanted frequencies.\ \>", "Text", Evaluatable->False, AspectRatioFixed->True] }, Closed]], Cell[CellGroupData[{ Cell["Preliminary Setup", "Section", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ "The following functions are used to optimize the Fourier Transforms that \ we use in this Notebook. Because ", StyleBox["Fourier", FontFamily->"Courier"], " and ", StyleBox["InverseFourier", FontFamily->"Courier"], " perform most efficiently when they operate on arrays whose sizes are \ products of perfect powers of small prime numbers, we will pad our samples \ out to the nearest such size, using the functions defined here." }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ StyleBox["$foo", FontFamily->"Courier"], " will contain a list of optimal sizes, up to a maximum of ", StyleBox["$maxsz", FontFamily->"Courier"], ". Sizes larger than ", StyleBox["$maxsz", FontFamily->"Courier"], " will be generated using powers of two times sizes which appear in ", StyleBox["$foo", FontFamily->"Courier"], ". The function\n\n\t", StyleBox["newsize", FontSlant->"Italic"], StyleBox[" = psp[", FontFamily->"Courier"], StyleBox["origsize", FontSlant->"Italic"], StyleBox["]", FontFamily->"Courier"], "\n\nis used to find optimal sizes." }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell["$maxsz = 22050;", "Input", InitializationCell->True, AspectRatioFixed->True], Cell["\<\ $foo = Module[ \t\t{c2 = Log[2.], c3 = Log[3.], c5 = Log[5.], \t\t\tc1000 = Log[$maxsz + 0.5]}, \t\tSort[Flatten[Round[Exp[Table[i c2 + j c3 + k c5, \t\t\t{i, 0, Floor[c1000/c2]}, \t\t\t{j, 0, Floor[(c1000 - i c2)/c3]}, \t\t\t{k, 0, Floor[(c1000 - i c2 - j c3)/c5]}]]]]]];\ \>", "Input", InitializationCell->True, AspectRatioFixed->True], Cell["\<\ psp[x_] := Module[{p, q}, \t\t\tIf[x < $maxsz, \t\t\t\tFirst[Select[$foo, (# >= x)&]], \t\t\t(* else *) \t\t\t\tp = Ceiling[Log[2, N[x]/$maxsz]]; \t\t\t\tq = 2^-p; \t\t\t\t2^p First[Select[$foo, (# >= q x)&]] \t\t\t] \t\t]\ \>", "Input", InitializationCell->True, AspectRatioFixed->True] }, Closed]], Cell[CellGroupData[{ Cell["Band Pass Filter", "Section", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell["\<\ First, we define a simple band pass filter. It takes a \ SampledSoundList and two corner frequencies as arguments, and returns a \ SampledSoundList as its result. The two corner frequencies define a \"pass band\", or a group of frequencies \ which will be retained from the original sound in the result. Frequencies \ outside the pass band (lower than the lower corner and higher than the upper \ corner) will be rejected.\ \>", "Text", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell["\<\ BandPassFilter[sound_SampledSoundList, lcorner_, hcorner_] := \tBlock[{samps, srate, origsize, newsize, kern, \t\t \tnlcorn, nhcorn, n}, \t\t \t\t(* Separate the sound into samples and sample rate *) \t\tsamps = sound[[1]]; \t\tsrate = sound[[2]]; \t\t \t\t(* Because the FFT algorithm is much more efficient \t\t when it operates on tables whose sizes are products \t\t of perfect powers of small prime numbers, we will \t\t pad the original sample with silence to be of such \t\t a size. After we perform the filtering, we will \t\t return the result table to the correct size. *) \t\t \t\torigsize = Length[samps]; \t\t(* Calculate optimum size for FFT and pad sound *) \t\tnewsize = psp[origsize]; \t\tsamps = Join[samps, Table[0.0, {newsize - origsize}]]; \t\t \t\t(* The Fourier[] function generates a table of \t\t frequencies relative to the size of the original \t\t table. Therefore, frequencies in the frequency \t\t domain must be scaled to relate to a \"real\" time- \t\t domain signal. *) \t\t \t\tnlcorn = (lcorner * newsize) / srate; \t\tnhcorn = (hcorner * newsize) / srate; \t\t \t\t(* Generate the frequency response table. This \t\t is a simple table in the frequency-domain table \t\t which will be multiplied with the frequency spectrum \t\t of the original sound. Thus, it contains 1 for \t\t frequencies which are to be kept and 0 for those \t\t that are to be rejected. *) \t\t \t\tkern = Table[If[n >= nlcorn && n <= nhcorn, 1.0, 0.0], \t\t\t\t{n, Ceiling[newsize/2.0]}]; \t\t(* The table is symmetric due to aliasing. *) \t\tkern = Join[kern, \t\t\t\t\tTake[Reverse[kern], Floor[newsize/2.0]]]; \t\t \t\t(* Generate the new samples by conversion to the \t\t frequency domain, performing multiplication and \t\t conversion back to the time domain. *) \t\t \t\tsamps = Take[Chop[Re[ \t\t\t\t\tInverseFourier[kern Fourier[samps]]]], \t\t\t\t\torigsize]; \t\t \t\t(* Make sure all the samples are still within range, \t\t because some destructive interference may have \t\t been lost in the filter. *) \t\t \t\tsamps /= Max[Abs[samps]]; \t\t \t\t(* Build the SampledSoundList back from the samples *) \t\tReturn[SampledSoundList[samps, srate]] \t]\ \>", "Input", InitializationCell->True, AspectRatioFixed->True], Cell[BoxData[ \(General::"spell1" \( : \ \) "Possible spelling error: new symbol name \"\!\(sound\)\" is similar to \ existing symbol \"\!\(Sound\)\"."\)], "Message"], Cell[BoxData[ \(General::"spell1" \( : \ \) "Possible spelling error: new symbol name \"\!\(hcorner\)\" is similar \ to existing symbol \"\!\(lcorner\)\"."\)], "Message"], Cell[BoxData[ \(General::"spell1" \( : \ \) "Possible spelling error: new symbol name \"\!\(nhcorn\)\" is similar \ to existing symbol \"\!\(nlcorn\)\"."\)], "Message"], Cell[BoxData[ \(General::"stop" \( : \ \) "Further output of \!\(General :: \"spell1\"\) will be suppressed \ during this calculation."\)], "Message"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Demonstration of the Band Pass Filter", "Subsection", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell["\<\ In order to demonstrate the band pass filter, we'll construct a \ sound that is composed of three frequencies, at 400 Hz, 800 Hz and 1600 Hz. \ Just to keep things small, it will be only 1/20 second 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Its implementation is very nearly identical to the \ band pass filter, but with one important change: the sense of the \"If\" \ statement in building the filter.\ \>", "Text", Evaluatable->False, AspectRatioFixed->True], Cell["\<\ NotchRejectFilter[sound_SampledSoundList, lcorner_, hcorner_] := \tBlock[ \t\t{samps, srate, origsize, newsize, kern, \t\t nlcorn, nhcorn, n}, \t\tsamps = sound[[1]]; \t\tsrate = sound[[2]]; \t\torigsize = Length[samps]; \t\tnewsize = psp[origsize]; \t\tsamps = Join[samps, Table[0.0, {newsize - origsize}]]; \t\tnlcorn = (lcorner * newsize) / srate; \t\tnhcorn = (hcorner * newsize) / srate; \t\tkern = Table[If[n >= nlcorn && n <= nhcorn, 0.0, 1.0], \t\t\t\t{n, Ceiling[newsize/2.0]}]; \t\tkern = Join[kern, Take[Reverse[kern], \t\t\t\tFloor[newsize/2.0]]]; \t\tsamps = Take[ \t\t\t\t\tChop[Re[ \t\t\t\t\t\tInverseFourier[kern Fourier[samps]]]], \t\t\t\t\torigsize]; \t\tsamps /= Max[Abs[samps]]; \t\tReturn[SampledSoundList[samps, srate]] \t]\ \>", "Input", InitializationCell->True, AspectRatioFixed->True] }, Closed]], Cell[CellGroupData[{ Cell["Demonstration of the Notch Reject Filter", "Subsection", Evaluatable->False, AspectRatioFixed->True], Cell["\<\ We'll use the same sound to demonstrate the notch reject filter \ that we used to demonstrate the low pass and high pass filters. 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Closed]] }, Closed]] }, Closed]] }, FrontEndVersion->"Macintosh 3.0", ScreenRectangle->{{0, 832}, {0, 604}}, AutoGeneratedPackage->None, WindowToolbars->{}, CellGrouping->Manual, WindowSize->{520, 600}, WindowMargins->{{92, Automatic}, {Automatic, -1}}, PrivateNotebookOptions->{"ColorPalette"->{RGBColor, 128}}, ShowCellLabel->True, ShowCellTags->False, RenderingOptions->{"ObjectDithering"->True, "RasterDithering"->False}, StyleDefinitions -> Notebook[{ Cell[CellGroupData[{ Cell["Style Definitions", "Subtitle"], Cell["\<\ Modify the definitions below to change the default appearance of \ all cells in a given style. Make modifications to any definition using \ commands in the Format menu.\ \>", "Text"], Cell[CellGroupData[{ Cell["Style Environment Names", "Section"], Cell[StyleData[All, "Working"], PageWidth->WindowWidth, ScriptMinSize->9], Cell[StyleData[All, "Presentation"], PageWidth->WindowWidth, ScriptMinSize->12, FontSize->16], Cell[StyleData[All, "Condensed"], PageWidth->WindowWidth, CellBracketOptions->{"Margins"->{1, 1}, "Widths"->{0, 5}}, ScriptMinSize->8, FontSize->11], Cell[StyleData[All, "Printout"], PageWidth->PaperWidth, ScriptMinSize->5, FontSize->10, PrivateFontOptions->{"FontType"->"Outline"}] }, Closed]], Cell[CellGroupData[{ Cell["Notebook Options", "Section"], Cell["\<\ The options defined for the style below will be used at the \ Notebook level.\ \>", "Text"], Cell[StyleData["Notebook"], PageHeaders->{{Cell[ TextData[ { CounterBox[ "Page"]}], "PageNumber"], None, Cell[ TextData[ { ValueBox[ "FileName"]}], "Header"]}, {Cell[ TextData[ { ValueBox[ "FileName"]}], "Header"], None, Cell[ TextData[ { CounterBox[ "Page"]}], "PageNumber"]}}, CellFrameLabelMargins->6, StyleMenuListing->None] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Headings", "Section"], Cell[CellGroupData[{ Cell[StyleData["Title"], CellMargins->{{7, Inherited}, {8, 40}}, Evaluatable->False, CellGroupingRules->{"TitleGrouping", 0}, CellHorizontalScrolling->False, PageBreakBelow->False, GroupPageBreakWithin->False, TextAlignment->Center, LineSpacing->{1, 1}, CounterIncrements->"Title", CounterAssignments->{{"Section", 0}, {"Equation", 0}, {"Figure", 0}, { "Subtitle", 0}, {"Subsubtitle", 0}}, AspectRatioFixed->True, FontFamily->"Times", FontSize->24, FontWeight->"Bold"], Cell[StyleData["Title", "Presentation"], CellMargins->{{24, 10}, {20, 40}}, LineSpacing->{1, 0}, FontSize->44], Cell[StyleData["Title", "Condensed"], CellMargins->{{8, 10}, {4, 8}}, FontSize->20], Cell[StyleData["Title", "Printout"], CellMargins->{{2, 10}, {15, 30}}, FontSize->24] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Subtitle"], CellMargins->{{7, Inherited}, {6, 15}}, Evaluatable->False, CellGroupingRules->{"TitleGrouping", 10}, CellHorizontalScrolling->False, PageBreakBelow->False, GroupPageBreakWithin->False, TextAlignment->Center, LineSpacing->{1, 1}, CounterIncrements->"Subtitle", CounterAssignments->{{"Section", 0}, {"Equation", 0}, {"Figure", 0}, { "Subsubtitle", 0}}, AspectRatioFixed->True, FontFamily->"Times", FontSize->18, FontWeight->"Bold"], Cell[StyleData["Subtitle", "Presentation"], CellMargins->{{24, 10}, {15, 20}}, LineSpacing->{1, 0}, FontSize->36], Cell[StyleData["Subtitle", "Condensed"], CellMargins->{{8, 10}, {4, 4}}, FontSize->14], Cell[StyleData["Subtitle", "Printout"], CellMargins->{{2, 10}, {10, 15}}, FontSize->18] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Subsubtitle"], CellMargins->{{7, Inherited}, {6, 20}}, Evaluatable->False, CellGroupingRules->{"TitleGrouping", 20}, CellHorizontalScrolling->False, PageBreakBelow->False, GroupPageBreakWithin->False, TextAlignment->Center, LineSpacing->{1, 1}, CounterIncrements->"Subsubtitle", CounterAssignments->{{"Section", 0}, {"Equation", 0}, {"Figure", 0}}, AspectRatioFixed->True, FontFamily->"Times", FontSize->14, FontSlant->"Italic"], Cell[StyleData["Subsubtitle", "Presentation"], CellMargins->{{24, 10}, {10, 20}}, LineSpacing->{1, 0}, FontSize->24], Cell[StyleData["Subsubtitle", "Condensed"], CellMargins->{{8, 10}, {8, 12}}, FontSize->12], Cell[StyleData["Subsubtitle", "Printout"], CellMargins->{{2, 10}, {8, 10}}, FontSize->14] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Section"], CellDingbat->"\[GraySquare]", CellMargins->{{22, Inherited}, {8, 20}}, Evaluatable->False, CellGroupingRules->{"SectionGrouping", 30}, CellHorizontalScrolling->False, PageBreakBelow->False, LineSpacing->{1, 1}, CounterIncrements->"Section", CounterAssignments->{{"Subsection", 0}, {"Subsubsection", 0}}, AspectRatioFixed->True, FontFamily->"Times", FontSize->18, FontWeight->"Bold"], Cell[StyleData["Section", "Presentation"], CellMargins->{{40, 10}, {11, 32}}, LineSpacing->{1, 0}, FontSize->24], Cell[StyleData["Section", "Condensed"], CellMargins->{{18, Inherited}, {6, 12}}, FontSize->12], Cell[StyleData["Section", "Printout"], CellMargins->{{13, 0}, {7, 22}}, FontSize->14] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Subsection"], CellDingbat->"\[FilledSquare]", CellMargins->{{19, Inherited}, {8, 15}}, Evaluatable->False, CellGroupingRules->{"SectionGrouping", 40}, CellHorizontalScrolling->False, PageBreakBelow->False, LineSpacing->{1, 1}, CounterIncrements->"Subsection", CounterAssignments->{{"Subsubsection", 0}}, AspectRatioFixed->True, FontFamily->"Times", FontSize->14, FontWeight->"Bold"], Cell[StyleData["Subsection", "Presentation"], CellMargins->{{36, 10}, {11, 32}}, LineSpacing->{1, 0}, FontSize->22], Cell[StyleData["Subsection", "Condensed"], CellMargins->{{16, Inherited}, {6, 12}}, FontSize->12], Cell[StyleData["Subsection", "Printout"], CellMargins->{{9, 0}, {7, 22}}, FontSize->12] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Subsubsection"], CellDingbat->"\[EmptySquare]", CellMargins->{{18, Inherited}, {8, 12}}, Evaluatable->False, CellGroupingRules->{"SectionGrouping", 50}, CellHorizontalScrolling->False, PageBreakBelow->False, LineSpacing->{1, 1}, CounterIncrements->"Subsubsection", AspectRatioFixed->True, FontFamily->"Times", FontSize->12, FontWeight->"Bold"], Cell[StyleData["Subsubsection", "Presentation"], CellMargins->{{34, 10}, {11, 26}}, LineSpacing->{1, 0}, FontSize->18], Cell[StyleData["Subsubsection", "Condensed"], CellMargins->{{17, Inherited}, {6, 12}}, FontSize->10], Cell[StyleData["Subsubsection", "Printout"], CellMargins->{{9, 0}, {7, 14}}, FontSize->11] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Body Text", "Section"], Cell[CellGroupData[{ Cell[StyleData["Text"], CellMargins->{{7, 10}, {7, 7}}, Evaluatable->False, CellHorizontalScrolling->False, PageBreakWithin->Automatic, LineSpacing->{1, 1}, CounterIncrements->"Text", AspectRatioFixed->True, FontSize->12], Cell[StyleData["Text", "Presentation"], CellMargins->{{24, 10}, {10, 10}}, LineSpacing->{1, 5}], Cell[StyleData["Text", "Condensed"], CellMargins->{{8, 10}, {6, 6}}, LineSpacing->{1, 1}], Cell[StyleData["Text", "Printout"], CellMargins->{{2, 2}, {6, 6}}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["SmallText"], CellMargins->{{7, 10}, {6, 6}}, Evaluatable->False, CellHorizontalScrolling->False, PageBreakWithin->Automatic, LineSpacing->{1, 1}, CounterIncrements->"SmallText", AspectRatioFixed->True, FontFamily->"Times", FontSize->10], Cell[StyleData["SmallText", "Presentation"], CellMargins->{{24, 10}, {8, 8}}, LineSpacing->{1, 5}, FontSize->12], Cell[StyleData["SmallText", "Condensed"], CellMargins->{{8, 10}, {5, 5}}, LineSpacing->{1, 2}, FontSize->9], Cell[StyleData["SmallText", "Printout"], CellMargins->{{2, 2}, {5, 5}}, FontSize->7] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Input/Output", "Section"], Cell["\<\ The cells in this section define styles used for input and output \ to the kernel. Be careful when modifying, renaming, or removing these \ styles, because the front end associates special meanings with these style \ names.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Input"], PageWidth->Infinity, CellMargins->{{42, 10}, {5, 7}}, Evaluatable->True, CellGroupingRules->"InputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultInputFormatType, LineSpacing->{1, 1}, AutoItalicWords->{}, FormatType->InputForm, ShowStringCharacters->True, NumberMarks->True, CounterIncrements->"Input", AspectRatioFixed->True, FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], Cell[StyleData["Input", "Presentation"], CellMargins->{{72, Inherited}, {8, 10}}, LineSpacing->{1, 0}], Cell[StyleData["Input", "Condensed"], CellMargins->{{40, 10}, {2, 3}}], Cell[StyleData["Input", "Printout"], CellMargins->{{39, 0}, {4, 6}}, FontSize->9] }, Closed]], Cell[StyleData["InputOnly"], Evaluatable->True, CellGroupingRules->"InputGrouping", CellHorizontalScrolling->True, DefaultFormatType->DefaultInputFormatType, AutoItalicWords->{}, FormatType->InputForm, ShowStringCharacters->True, NumberMarks->True, CounterIncrements->"Input", StyleMenuListing->None, FontWeight->"Bold"], Cell[CellGroupData[{ Cell[StyleData["Output"], PageWidth->Infinity, CellMargins->{{42, 10}, {7, 5}}, CellEditDuplicate->True, Evaluatable->False, CellGroupingRules->"OutputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultOutputFormatType, LineSpacing->{1, 0}, AutoItalicWords->{}, FormatType->InputForm, CounterIncrements->"Output", AspectRatioFixed->True, FontFamily->"Courier", FontSize->12], Cell[StyleData["Output", "Presentation"], CellMargins->{{72, Inherited}, {10, 8}}, LineSpacing->{1, 0}], Cell[StyleData["Output", "Condensed"], CellMargins->{{41, Inherited}, {3, 2}}], Cell[StyleData["Output", "Printout"], CellMargins->{{39, 0}, {6, 4}}, FontSize->9] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Message"], PageWidth->Infinity, CellMargins->{{42, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellGroupingRules->"OutputGrouping", PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultOutputFormatType, LineSpacing->{1, 1}, AutoItalicWords->{}, FormatType->InputForm, CounterIncrements->"Message", AspectRatioFixed->True, StyleMenuListing->None, FontFamily->"Courier", FontSize->12, FontColor->RGBColor[0, 0, 1]], Cell[StyleData["Message", "Presentation"], CellMargins->{{72, Inherited}, {Inherited, Inherited}}, LineSpacing->{1, 0}], Cell[StyleData["Message", "Condensed"], CellMargins->{{41, Inherited}, {Inherited, Inherited}}], Cell[StyleData["Message", "Printout"], CellMargins->{{39, Inherited}, {Inherited, Inherited}}, FontSize->8, FontColor->GrayLevel[0]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Print"], PageWidth->Infinity, CellMargins->{{42, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellGroupingRules->"OutputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultOutputFormatType, LineSpacing->{1, 1}, AutoItalicWords->{}, FormatType->InputForm, CounterIncrements->"Print", AspectRatioFixed->True, StyleMenuListing->None, FontFamily->"Courier", FontSize->12], Cell[StyleData["Print", "Presentation"], CellMargins->{{72, Inherited}, {Inherited, Inherited}}, LineSpacing->{1, 0}], Cell[StyleData["Print", "Condensed"], CellMargins->{{41, Inherited}, {Inherited, Inherited}}], Cell[StyleData["Print", "Printout"], CellMargins->{{39, Inherited}, {Inherited, Inherited}}, FontSize->8] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Graphics"], PageWidth->Infinity, CellMargins->{{7, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellGroupingRules->"GraphicsGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, DefaultFormatType->DefaultOutputFormatType, LineSpacing->{1, 1}, FormatType->InputForm, CounterIncrements->"Graphics", AspectRatioFixed->True, ImageSize->{282, 287}, ImageMargins->{{34, Inherited}, {Inherited, 0}}, StyleMenuListing->None, FontFamily->"Courier", FontSize->12], Cell[StyleData["Graphics", "Presentation"], ImageMargins->{{62, Inherited}, {Inherited, 0}}], Cell[StyleData["Graphics", "Condensed"], ImageSize->{175, 175}, ImageMargins->{{38, Inherited}, {Inherited, 0}}], Cell[StyleData["Graphics", "Printout"], ImageSize->{250, 250}, ImageMargins->{{30, Inherited}, {Inherited, 0}}, FontSize->9] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["CellLabel"], StyleMenuListing->None, FontFamily->"Helvetica", FontSize->9, FontColor->RGBColor[0, 0, 1]], Cell[StyleData["CellLabel", "Presentation"], FontSize->12], Cell[StyleData["CellLabel", "Condensed"], FontSize->9], Cell[StyleData["CellLabel", "Printout"], FontFamily->"Courier", FontSize->8, FontSlant->"Italic", FontColor->GrayLevel[0]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Formulas and Programming", "Section"], Cell[CellGroupData[{ Cell[StyleData["InlineFormula"], CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, ScriptLevel->1, SingleLetterItalics->True], Cell[StyleData["InlineFormula", "Presentation"], CellMargins->{{24, 10}, {10, 10}}, LineSpacing->{1, 5}], Cell[StyleData["InlineFormula", "Condensed"], CellMargins->{{8, 10}, {6, 6}}, LineSpacing->{1, 1}], Cell[StyleData["InlineFormula", "Printout"], CellMargins->{{2, 0}, {6, 6}}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["DisplayFormula"], CellMargins->{{42, Inherited}, {Inherited, Inherited}}, CellHorizontalScrolling->True, ScriptLevel->0, SingleLetterItalics->True, StyleMenuListing->None, UnderoverscriptBoxOptions->{LimitsPositioning->True}], Cell[StyleData["DisplayFormula", "Presentation"], LineSpacing->{1, 5}], Cell[StyleData["DisplayFormula", "Condensed"], LineSpacing->{1, 1}], Cell[StyleData["DisplayFormula", "Printout"]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Headers and Footers", "Section"], Cell[StyleData["Header"], CellMargins->{{7, 0}, {4, 1}}, Evaluatable->False, CellHorizontalScrolling->False, PageBreakWithin->Automatic, LineSpacing->{1, 1}, AspectRatioFixed->True, StyleMenuListing->None, FontFamily->"Times", FontSize->12, FontSlant->"Italic"], Cell[StyleData["Footer"], CellMargins->{{7, 0}, {0, 4}}, Evaluatable->False, CellHorizontalScrolling->False, PageBreakWithin->Automatic, TextAlignment->Center, LineSpacing->{1, 1}, AspectRatioFixed->True, StyleMenuListing->None, FontFamily->"Times", FontSize->12, FontSlant->"Italic"], Cell[StyleData["PageNumber"], CellMargins->{{0, 0}, {4, 1}}, StyleMenuListing->None, FontFamily->"Times", FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell["Palette Styles", "Section"], Cell["\<\ The cells below define styles that define standard \ ButtonFunctions, for use in palette buttons.\ \>", "Text"], Cell[StyleData["Paste"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, After]}]&)}], Cell[StyleData["Evaluate"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], SelectionEvaluate[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["EvaluateCell"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionMove[ FrontEnd`InputNotebook[ ], All, Cell, 1], FrontEnd`SelectionEvaluateCreateCell[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["CopyEvaluate"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`SelectionCreateCell[ FrontEnd`InputNotebook[ ], All], FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionEvaluate[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["CopyEvaluateCell"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`SelectionCreateCell[ FrontEnd`InputNotebook[ ], All], FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionEvaluateCreateCell[ FrontEnd`InputNotebook[ ], All]}]&)}] }, Closed]], Cell[CellGroupData[{ Cell["Hyperlink Styles", "Section"], Cell["\<\ The cells below define styles useful for making hypertext \ ButtonBoxes. The \"Hyperlink\" style is for links within the same Notebook, \ or between Notebooks.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Hyperlink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookLocate[ #2]}]&), Active->True, ButtonNote->ButtonData}], Cell[StyleData["Hyperlink", "Presentation"]], Cell[StyleData["Hyperlink", "Condensed"]], Cell[StyleData["Hyperlink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell["\<\ The following styles are for linking automatically to the on-line \ help system.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["MainBookLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "MainBook", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["MainBookLink", "Presentation"]], Cell[StyleData["MainBookLink", "Condensed"]], Cell[StyleData["MainBookLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["AddOnsLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontFamily->"Courier", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "AddOns", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["AddOnsLink", "Presentation"]], Cell[StyleData["AddOnsLink", "Condensed"]], Cell[StyleData["AddOnLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["RefGuideLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontFamily->"Courier", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "RefGuideLink", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["RefGuideLink", "Presentation"]], Cell[StyleData["RefGuideLink", "Condensed"]], Cell[StyleData["RefGuideLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["GettingStartedLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "GettingStarted", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["GettingStartedLink", "Presentation"]], Cell[StyleData["GettingStartedLink", "Condensed"]], Cell[StyleData["GettingStartedLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["OtherInformationLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "OtherInformation", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["OtherInformationLink", "Presentation"]], Cell[StyleData["OtherInformationLink", "Condensed"]], Cell[StyleData["OtherInformationLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Placeholder Styles", "Section"], Cell["\<\ The cells below define styles useful for making placeholder \ objects in palette templates.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Placeholder"], Editable->False, Selectable->False, StyleBoxAutoDelete->True, Placeholder->True, StyleMenuListing->None], Cell[StyleData["Placeholder", "Presentation"]], Cell[StyleData["Placeholder", "Condensed"]], Cell[StyleData["Placeholder", "Printout"]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["SelectionPlaceholder"], Editable->False, Selectable->False, StyleBoxAutoDelete->True, Placeholder->Primary, StyleMenuListing->None, DrawHighlighted->True], Cell[StyleData["SelectionPlaceholder", "Presentation"]], Cell[StyleData["SelectionPlaceholder", "Condensed"]], Cell[StyleData["SelectionPlaceholder", "Printout"]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["FormatType Styles", "Section"], Cell["\<\ The cells below define styles that are mixed in with the styles \ of most cells. If a cell's FormatType matches the name of one of the styles \ defined below, then that style is applied between the cell's style and its \ own options.\ \>", "Text"], Cell[StyleData["CellExpression"], PageWidth->Infinity, CellMargins->{{6, Inherited}, {Inherited, Inherited}}, ShowCellLabel->False, ShowSpecialCharacters->False, AllowInlineCells->False, AutoItalicWords->{}, StyleMenuListing->None, FontFamily->"Courier", Background->GrayLevel[1]], Cell[StyleData["InputForm"], AllowInlineCells->False, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["OutputForm"], PageWidth->Infinity, TextAlignment->Left, LineSpacing->{1, -5}, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["StandardForm"], LineSpacing->{1.25, 0}, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["TraditionalForm"], LineSpacing->{1.25, 0}, SingleLetterItalics->True, TraditionalFunctionNotation->True, DelimiterMatching->None, StyleMenuListing->None], Cell["\<\ The style defined below is mixed in to any cell that is in an \ inline cell within another.\ \>", "Text"], Cell[StyleData["InlineCell"], TextAlignment->Left, ScriptLevel->1, StyleMenuListing->None], Cell[StyleData["InlineCellEditing"], StyleMenuListing->None, Background->RGBColor[1, 0.749996, 0.8]] }, Closed]] }, Open ]] }], MacintoshSystemPageSetup->"\<\ 00<0001804P000000]P2:?oQon82n@960dL5:0?l0080001804P000000]P2:001 0000I00000400`<300000BL?00400@00000000000000060001T1T00000000000 00000000000000000000000000000000\>" ] (*********************************************************************** Cached data follows. 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