dspTricks.sty
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Created: Thu, Mar 13, 14:01

dspTricks.sty
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	%% This is the package dspTricks
	%%
	%% Paolo Prandoni <paolo.prandoni _at_ epfl.ch>
	%%
	%% This program can be redistributed and/or modified under the terms
	%% of the LaTeX Project Public License Distributed from CTAN archives
	%% in directory macros/latex/base/lppl.txt.
	%%
	%% DESCRIPTION:
	%% `dsptricks' is a PSTricks package to plot discrete- and continuous-time signals,
	%% pole-zero plots and DSP block diagrams. The package has been developed while
	%% writing the textbook "Signal Processing for Communication" by P. Prandoni
	%% and M. Vetterli, available free of charge at www.sp4comm.org
	%%

	\RequirePackage{pstricks}
	\RequirePackage{pstricks-add}
	\RequirePackage{pst-xkey}
	\RequirePackage{calc}
	\RequirePackage{fp}
	\RequirePackage{ifthen}
	\ProvidesPackage{dsptricks}[2013/05/01 package for signal processing graphics]

	\makeatletter

	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%% Sizes and units:
	%%
	%% default values for plot size
	%%
	\newlength{\dspWidth}\setlength{\dspWidth}{0.7\textwidth}
	\newlength{\dspHeight}\setlength{\dspHeight}{0.43\dspWidth}
	\def\dspAxisColor{black}
	%
	%% Actual size (this is the size of the chart's frame, labels are extra)
	\newlength{\dspW}
	\newlength{\dspH}
	%% Basic Unit is a function of plot size
	\newlength{\dspBU}
	%% Derived units:
	\newlength{\dspLineWidth}
	\newlength{\dspStemWidth}
	\newlength{\dspDotSize}
	\newlength{\dspTickLen}
	\newlength{\dspXTickGap}
	\newlength{\dspYTickGap}
	\newlength{\dspTickLineWidth}
	\newlength{\dspFrameLineWidth}
	%% psTricks units
	\newlength{\dspUnitX}
	\newlength{\dspUnitY}
	\newlength{\dspTmpLen}
	%% booleans
	\newif\ifXTicks
	\newif\ifDoXTicks
	\newif\ifYTicks
	\newif\ifDoYTicks
	\newif\ifXLabel
	\newif\ifYLabel
	\newif\ifXAxisExp
	\newif\ifYAxisExp
	\newif\ifXAxisFreq
	\newif\ifXInside

	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%
	%% dspPlot environment:
	%%
	%% \begin{dspPlot}[OPTIONS]{xMin, xMax}{yMin, yMAx}
	%%
	%%

	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%% Keys for data plots :
	%%
	\define@key{dspDP}{width}{\setlength{\dspW}{#1}}
	\define@key{dspDP}{height}{\setlength{\dspH}{#1}}
	\define@key{dspDP}{xlabel}{\def\dspXLabel{#1}\XLabeltrue}
	\define@key{dspDP}{ylabel}{\def\dspYLabel{#1}\YLabeltrue}
	\define@key{dspDP}{rlabel}{\def\dspYLabelR{#1}\YLabeltrue} % right-side y-axis label
	\define@key{dspDP}{sidegap}{\def\sg{#1}}
	\define@choicekey*+{dspDP}{xtype}[\ll\ln]{time,freq}[time]{%
	\ifcase\ln\relax
	\XAxisFreqfalse
	\or
	\XAxisFreqtrue
	\fi}{}
	\define@choicekey*+{dspDP}{xticks}[\ll\ln]{auto,none,custom}[auto]{%
	\DoXTickstrue\XTickstrue\def\incX{-1}\def\piFrac{2}
	\ifcase\ln\relax
	\relax
	\or
	\DoXTicksfalse\XTicksfalse
	\or
	\DoXTicksfalse
	\fi}{%
	\DoXTickstrue\XTickstrue
	\def\incX{#1}\def\piFrac{#1}}
	\define@choicekey*+{dspDP}{yticks}[\ll\ln]{auto,none,custom}[auto]{%
	\DoYTickstrue\YTickstrue\def\incY{-1}
	\ifcase\ln\relax
	\relax
	\or
	\DoYTicksfalse\YTicksfalse
	\or
	\DoYTicksfalse
	\fi}{%
	\DoYTickstrue\YTickstrue
	\def\incY{#1}}
	\newif\ifXTicksOut
	\define@key{dspDP}{xout}{\XTicksOuttrue}
	\define@key{dspDP}{inticks}{\XInsidetrue}


	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%
	%% dspPlot environment
	%%
	\newenvironment{dspPlot}[3][]{%
	% default values
	\def\dspXlabel{}\XLabelfalse%
	\def\dspYLabel{}\def\dspYLabelR{}\YLabelfalse%
	\XAxisFreqfalse%
	\XTicksOutfalse%
	\setlength{\dspW}{\dspWidth}\setlength{\dspH}{\dspHeight}%

	\presetkeys{dspDP}{xticks=auto,yticks=auto}{}%
	\presetkeys{dspDP}{sidegap=-1}{}%
	\setkeys{dspDP}{#1}%
	%%
	%% set up
	\ifXAxisFreq\def\sg{0} \fi%
	\dspSetDims#2,#3,\sg\relax%
	\dspSetupAxes
	%%
	%% special x-axis for frequency plots
	\ifXAxisFreq\FPset\incX{1}%
	\ifXAxisExp%
	% x-axis is not on bottom; skip last values
	\FPupn\stX{\dspMinX{} \piFrac{} * 1 + 0 trunc}%
	\FPupn\tlimX{\stX{} \dspMaxX{} \piFrac{} * - 0 trunc}%
	\else%
	\FPupn\stX{\dspMinX{} \piFrac{} * 0 trunc}%
	\FPupn\tlimX{\stX{} \dspMaxX{} \piFrac{} * - 1 + 0 trunc}\relax\fi%
	%
	\ifXTicksOut% undo above if ticks explicitly out
	\FPupn\stX{\dspMinX{} \piFrac{} * 0 trunc}%
	\FPupn\tlimX{\stX{} \dspMaxX{} \piFrac{} * - 1 + 0 trunc}\relax\fi
	%
	\def\thisTickX##1{%
	\FPupn\u{\piFrac{} ##1 /}%
	\psline[linewidth=\dspTickLineWidth,linecolor=\dspAxisColor](\u,\haY)(\u,\tickEndX)}
	\def\thisTickLabelX##1##2{%
	\FPupn\u{\piFrac{} ##1 /}%
	\rput*[B]{{0}}(\u,\tickTxtX){{\simplifyPiFrac{##1}{\piFrac}}}}%
	\else
	\def\thisTickX{\dspTickX}\def\thisTickLabelX{\dspTickLabelX}\relax\fi
	%%
	%% start the plot
	\begin{pspicture}(\LX,\BY)(\RX,\TY)
	%\showpointstrue
	%\psframe[dimen=middle,linewidth=1pt,linecolor=red](\LX,\BY)(\RX,\TY)%
	\ifXAxisExp\psline[linewidth=\dspFrameLineWidth,linecolor=\dspAxisColor](\dspMinX,0)(\dspMaxX,0)\fi
	\dspPlotFrame
	%%
	%% draw ticks selectively according to user options
	\ifDoXTicks\multido{\n=\stX+\incX}{\tlimX}{\thisTickX{\n}}\fi
	\ifDoYTicks\multido{\n=\stY+\incY}{\tlimY}{\dspTickY{\n}}\fi
	}{%
	%% tick labels
	\psset{xunit=\dspUnitX,yunit=\dspUnitY} %user may have changed those
	\ifDoXTicks\multido{\n=\stX+\incX}{\tlimX}{\thisTickLabelX{\n}{$\n$}}\fi
	\ifDoYTicks\multido{\n=\stY+\incY}{\tlimY}{\dspTickLabelY{\n}{$\n$}}\fi
	\dspLabels
	\end{pspicture}}


	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%
	%% Custom ticks
	%%
	%% \dspCustomTicks[axis={x\|y}]{value label ...}
	%%
	%% if using macros for values, enclose them in curly braces:
	%% \def\a{1 }
	%% \dspCustomTicks{{\a} 1}
	%%
	\define@choicekey*{dspCT}{axis}[\ll\ln]{x,y,ry}[x]{%
	\def\dspCA{\ln}}
	\define@key{dspCT}{color}{\def\tickColor{#1}}
	\newcommand{\dspCustomTicks}[2][]{%
	\presetkeys{dspCT}{axis=x,color=black}{}%
	\setkeys{dspCT}{#1}%
	\ifcase\dspCA\relax%
	\def\dspMkTk##1##2{\dspTickX{##1}{\dspTickLabelX{##1}{##2}}}%
	\or
	\def\dspMkTk##1##2{\dspTickY{##1}{\dspTickLabelY{##1}{##2}}}%
	\or
	\def\dspMkTk##1##2{{\dspTickLabelYR{##1}{##2}}}%
	\fi
	\def\dspMakeTicks##1 ##2 ##3\relax{%
	\ifx&##3&
	\dspMkTk{##1}{##2} %
	\else
	\dspMkTk{##1}{##2} \relax %
	\dspMakeTicks##3\relax%
	\fi}%
	\dspMakeTicks#2 \relax}

	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%
	%% Draw legend
	%%
	%% \dspLegend(x,y){color label color label ...}
	%%
	\def\dspLegend(#1,#2)#3{%
	\rput[lt](#1,#2){\fbox{%
	\begin{tabular}{ll}
	\@dsplegend#3 \@empty
	\end{tabular}}}}
	\def\@dsplegend#1 #2 #3{%
	{\color{#1}\rule[0.5ex]{2em}{2pt}} & #2\\ \space % fbox here to have a visual test
	\ifx #3\@empty\else
	\expandafter\@dsplegend
	\fi
	#3}


	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%
	%% Redraw frame around plot
	%%
	\newcommand{\dspPlotFrame}{
	\psframe[dimen=middle,linewidth=\dspFrameLineWidth,linecolor=black]%
	(\dspMinX,\dspMinY)(\dspMaxX,\dspMaxY)}


	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%
	%% Environment to clip plots to within the frame box. Do not leave
	%% spaces in the environment's body otherwise graph will shift
	%%
	\newenvironment{dspClip}{%
	\psclip{\psframe[dimen=middle,linestyle=none](\dspMinX,\dspMinY)(\dspMaxX,\dspMaxY)}}{%
	\endpsclip}



	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%
	%% Plotting discrete-time signals in the dspPlot environment:
	%%
	%%

	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%% Keys for plotting functions (these are set together with pstricks keys
	%% so they must use the [psset] prefix and be declared)
	%%
	%% xmin=N,
	%% xmax=N range for the plotted signal
	%%
	\define@key[psset]{dspData}{xmin}{\def\dspXmin{#1}}
	\define@key[psset]{dspData}{xmax}{\def\dspXmax{#1}}
	\pst@addfams{dspData}

	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%
	%% Plot discrete-time points
	%%
	%% \dspTaps[OPTIONS]{x1 y1 x2 y2 ...}
	%%
	\newcommand{\dspTaps}[2][]{%
	\listplot[plotstyle=LineToXAxis, linestyle=solid,%
	showpoints=true, dotstyle=*, linewidth=\dspStemWidth,%
	dotsize=\dspDotSize, #1]{\expandafter\m@keList#2 \relax}}


	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%
	%% Plot discrete-time points starting at a given abscissa
	%% Data in this case is only ordinates
	%%
	%% \dspTapsAt{x0}{y0 y1 y2,...}
	%%
	\newcommand{\dspTapsAt}[3][]{%
	% use postscript to iterate over space-separated list and create indices
	\listplot[plotstyle=LineToXAxis, linestyle=solid,%
	showpoints=true, dotstyle=*, linewidth=\dspStemWidth,%
	dotsize=\dspDotSize, #1]{%
	#2
	[#3] { % n []
	% n a0
	1 index % n a0 n
	1 add
	} forall
	pop
	}}

	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%
	%% Plot discrete-time signal from a data file
	%%
	%% \dspTapsFile[OPTIONS]{FILE}
	%%
	\newcommand{\dspTapsFile}[2][]{%
	\readdata{\data}{#2}%
	\listplot[plotstyle=LineToXAxis, linestyle=solid,%
	showpoints=true, dotstyle=*,%
	linewidth=\dspStemWidth, dotsize=\dspDotSize,%
	#1]{\data}}


	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%
	%% Plot discrete-time signal
	%%
	%% \dspSignal[OPTIONS]{PS code}
	%%
	\newcommand{\dspSignal}[2][]{%
	\presetkeys[psset]{dspData}{xmin=\dspMinActX, xmax=\dspMaxActX}{}%
	\setkeys*[psset]{dspData}{#1}%
	\FPupn\mn{{\dspXmin} 0 trunc clip }%
	\FPupn\mx{{\dspXmax} 0 trunc clip }%
	\FPupn\ntaps{\mn{} \mx{} - 1 + 0 trunc clip}%
	\psplot[plotstyle=LineToXAxis, linestyle=solid,%
	showpoints=true, dotstyle=*,%
	linewidth=\dspStemWidth, dotsize=\dspDotSize,%
	plotpoints=\ntaps, #1]%
	{\mn}{\mx}{#2}}

	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%
	%% Plot discrete-time signal with postscript initialization options
	%%
	%\dspSignalOpt[OPTIONS]{PS init code}{PS code}
	%%
	\newcommand{\dspSignalOpt}[3][]{%
	\presetkeys[psset]{dspData}{xmin=\dspMinActX, xmax=\dspMaxActX}{}%
	\setkeys*[psset]{dspData}{#1}%
	\FPupn\ntaps{\dspXmin{} \dspXmax{} - 1 + 0 trunc}%
	\psplot[plotstyle=LineToXAxis, linestyle=solid,%
	showpoints=true, dotstyle=*,%
	linewidth=\dspStemWidth, dotsize=\dspDotSize,%
	plotpoints=\ntaps, #1]%
	{\dspXmin}{\dspXmax}[{#2}]{#3}}



	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%
	%% Plotting continuous-time signals in the dspPlot environment:
	%%
	%%

	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%
	%% Plot smooth function
	%%
	%% \dspFunc[OPTIONS]{PS code}
	%%
	\newcommand{\dspFunc}[2][]{%
	\presetkeys[psset]{dspData}{xmin=\dspMinActX, xmax=\dspMaxActX}{}%
	\setkeys*[psset]{dspData}{#1}%
	\psplot[linewidth=\dspLineWidth, plotpoints=\dspPSPoints,%
	linejoin=1,#1]{\dspXmin}{\dspXmax}{#2}}


	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%
	%% Plot smooth function with postscript initialization options
	%%
	%% \dspFuncOpt[OPTIONS]{PS init code}{PS code}
	%%
	\newcommand{\dspFuncOpt}[3][]{%
	\presetkeys[psset]{dspData}{xmin=\dspMinActX, xmax=\dspMaxActX}{}%
	\setkeys*[psset]{dspData}{#1}%
	\psplot[linewidth=\dspLineWidth, plotpoints=\dspPSPoints,%
	linejoin=1,#1]{\dspXmin}{\dspXmax}[{#2}]{#3}}


	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%
	%% Plot smooth function from a set of points
	%%
	%% \dspFuncData[OPTIONS]{x1 y1 x2 y2 ...}
	%%
	\newcommand{\dspFuncData}[2][]{%
	\listplot[linewidth=\dspLineWidth,linejoin=1,plotstyle=line,#1]{\expandafter\m@keList#2 \relax}}

	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%
	%% Plot smooth function from a set of points starting at a given point
	%% Data in this case is only ordinates
	%%
	%% \dspFuncDataAt[OPTIONS]{x1}{y1 y2 ...}
	%%
	\newcommand{\dspFuncDataAt}[3][]{%
	\listplot[linewidth=\dspLineWidth,linejoin=1,plotstyle=line,#1]{%
	#2
	[#3] { % n []
	% n a0
	1 index % n a0 n
	1 add
	} forall
	pop
	}}

	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%
	%% Plot smooth function from a data file
	%% file must contain a list of space-separated abscissa and ordinate pairs
	%%
	%% \dspFuncFile[OPTIONS]{FILE}
	%%
	\newcommand{\dspFuncFile}[2][]{%
	\readdata{\data}{#2}%
	\listplot[linewidth=\dspLineWidth,linejoin=1,plotstyle=line,#1]{\data}}


	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%
	%% Plot Dirac deltas
	%%
	%% \dspDiracs[OPTIONS]{x1 y1 x2 y2 ...}
	%%
	\newcommand{\dspDiracs}[2][]{%
	\def\dirac##1##2{\psline[linestyle=solid,linewidth=\dspLineWidth,#1]{->}(! ##1 0)(! ##1 ##2)}
	\doOnPairs{dirac}{#2}}




	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%
	%% Periodize function over the [-1, 1] interval
	%
	\newcommand{\dspPeriod}[1]{ #1 sub #1 2 mul div dup floor sub #1 2 mul mul #1 sub }
	\newcommand{\dspPeriodize}{ \dspPeriod{1} }
	\newcommand{\dspMainPeriod}[1][]{%
	\psframe[linecolor=lightgray,linewidth=0.4pt,#1](-1,\dspMinY)(1,\dspMaxY)}


	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%
	%% Plot text
	% \dspText(x,y){text}
	\newcommand{\dspText}[2]{%
	\rput*[B]{0}#1{#2}}


	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%
	%% Pole-Zero Plots
	%
	% Specialized options:
	%
	% circle=["true" \| "false"] draw unit circle
	% clabel="text" set a label at circle unit
	% roc
	%
	\define@key{dspPZ}{width}{\setlength{\dspW}{#1}\setlength{\dspH}{#1}}
	\define@key{dspPZ}{height}{\setlength{\dspH}{#1}}
	\define@key{dspPZ}{circle}{\def\dspCircle{#1}}
	\define@key{dspPZ}{clabel}{\def\dspCircleLabel{#1}}
	\define@choicekey*+{dspPZ}{xticks}[\ll\ln]{auto,none}[auto]{%
	\DoXTickstrue\def\incX{-1}
	\ifcase\ln\relax
	\relax
	\or
	\DoXTicksfalse
	\fi}{%
	\DoXTickstrue
	\def\incX{#1}}
	\define@choicekey*+{dspPZ}{yticks}[\ll\ln]{auto,none}[auto]{%
	\DoYTickstrue\def\incY{-1}
	\ifcase\ln\relax
	\relax
	\or
	\DoYTicksfalse
	\fi}{%
	\DoYTickstrue
	\def\incY{#1}}
	\newif\ifComplexLabels
	\define@choicekey*{dspPZ}{cunits}[\ll\ln]{true,false}[true]{%
	\ifcase\ln\relax
	\ComplexLabelstrue
	\or
	\ComplexLabelsfalse
	\fi}
	\define@key{dspPZ}{roc}{\def\PZCROC{#1}}
	\define@key{dspPZ}{antiroc}{\def\PZAROC{#1}}

	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

	\newenvironment{dspPZPlot}[2][]{%
	\setlength{\dspW}{\dspHeight}\setlength{\dspH}{\dspHeight}%
	\ComplexLabelstrue%
	\presetkeys{dspPZ}{xticks=auto,yticks=auto,circle=1,clabel={ },roc=-1,antiroc=-1}{}%
	\setkeys{dspPZ}{#1}%
	%
	%% set up
	\dspSetDims{-#2},{#2},{-#2},{#2},0\relax%
	\dspSetupAxes%
	%
	\gdef\dspTickX##1{\psline[linewidth=\dspTickLineWidth,linecolor=\dspAxisColor](##1,-\tickEndX)(##1,\tickEndX)}%
	\gdef\dspTickY##1{\psline[linewidth=\dspTickLineWidth,linecolor=\dspAxisColor](-\tickEndY,##1)(\tickEndY,##1)}%
	\gdef\dspTickLabelY##1##2{\uput{{2\dspYTickGap}}[0]{{0}}(\tickEndY,##1){{##2}}}%
	\gdef\dspTickLabelX##1##2{\rput[B]{{0}}(##1,\tickTxtX){{##2}}}%
	%
	%% start the plot
	\begin{pspicture}(\LX,\BY)(\RX,\TY)
	\FPifpos\PZCROC%
	\pscustom[fillstyle=vlines,hatchcolor=lightgray,linecolor=lightgray,linewidth=0]{%
	\psarc(0,0){\PZCROC\dspUnitX}{0}{360}%
	\psline[linecolor=\dspAxisColor](\dspMaxX,0)(\dspMaxX,\dspMinY)(\dspMinX,\dspMinY)%
	(\dspMinX,\dspMaxY)(\dspMaxX,\dspMaxY)(\dspMaxX,0)}
	\pscircle[linecolor=lightgray,dimen=middle]{\PZCROC\dspUnitX}\relax\fi
	\FPifpos\PZAROC%
	\pscircle[fillstyle=vlines,hatchcolor=lightgray,linecolor=lightgray,dimen=middle]{\PZAROC\dspUnitX}\relax\fi
	%%
	\psline[linewidth=\dspFrameLineWidth,linecolor=\dspAxisColor](\dspMinX,0)(\dspMaxX,0)%
	\psline[linewidth=\dspFrameLineWidth,linecolor=\dspAxisColor](0,\dspMinY,0)(0,\dspMaxY)%
	\dspPlotFrame%
	\FPifgt\dspCircle{0}%
	\FPmul\r\dspCircle{\strip@pt\dspUnitX}%
	\pscircle[linewidth=\dspFrameLineWidth,dimen=middle](0,0){{\r}pt}%
	\ifx\@empty\dspCircleLabel%
	\def\dspCircleLabel{\dspCircle}\relax\fi
	\FPupn\r{0.6 \dspTSX{} mul \dspCircle{} add}%
	\rput[b]{0}(\r,\tickTxtX){\dspCircleLabel}\relax\fi
	%
	% draw ticks selectively according to user options
	% but here skip zero and intersections with the circle (if any)
	\FPupn\r{\tlimX{} 1 sub 2 div clip}%
	\def\xt{%
	\multido{\n=\stX+\incX}{\r}{\FPifeq\n{-\dspCircle}\relax\else\dspTickX{\n}\fi}%
	\multido{\n=\incX+\incX}{\r}{\FPifeq\n\dspCircle\relax\else\dspTickX{\n}\fi}%
	\multido{\n=\stX+\incX}{\r}{\FPifeq\n{-\dspCircle}\relax\else\dspTickLabelX{\n}{$\n$}\fi}%
	\multido{\n=\incX+\incX}{\r}{\FPifeq\n\dspCircle\relax\else\dspTickLabelX{\n}{$\n$}\fi}}%
	\def\yt{%
	\multido{\n=\stY+\incY}{\r}{\FPifeq\n{-\dspCircle}\relax\else\dspTickY{\n}\fi}%
	\multido{\n=\incY+\incY}{\r}{\FPifeq\n\dspCircle\relax\else\dspTickY{\n}\fi}%
	\multido{\n=\stY+\incY}{\r}{\FPifeq\n{-\dspCircle}\relax\else\dspTickLabelY{\n}{$\n$}\fi}%
	\multido{\n=\incY+\incY}{\r}{\FPifeq\n\dspCircle\relax\else\dspTickLabelY{\n}{$\n$}\fi}}%
	\ifDoXTicks\xt\fi
	\ifDoYTicks\yt\fi
	\ifComplexLabels%
	\rput[mr]{0}(\dspMaxX,1em){Re~}%
	\FPupn\r{\dspMaxY{} 0.6 \dspTSY{} mul sub}%
	\rput[t]{0}(-1.2em,\r){Im~}\relax\fi
	}{%
	\end{pspicture}}

	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%% Keyvals for poles and zeros
	%
	\newif\ifPZPole
	\define@choicekey*[psset]{dspPZP}{type}[\ll\ln]{zero,pole}[zero]{%
	\ifcase\ln\relax
	\PZPolefalse
	\or
	\PZPoletrue
	\fi}
	\newif\ifPZLabel
	\define@choicekey*+[psset]{dspPZP}{label}[\ll\ln]{auto,none}[auto]{%
	\def\PZLabel{}\relax%
	\ifcase\ln\relax
	\PZLabeltrue
	\or
	\PZLabelfalse
	\fi}{%
	\PZLabeltrue
	\def\PZLabel{#1}}
	\define@key[psset]{dspPZP}{lpos}{\def\PZLP{#1}}
	\pst@addfams{dspPZP}


	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%
	%% Plot pole-zero point
	%
	% \dspPZPoint[OPTIONS]{RE,IM}
	%
	% RE, IM coordinates
	%
	% Options:
	%
	% type = ["pole" \| "zero"] circle or cross (default: pole)
	% label=["false" \| TEXT ] the point's label (default: false)
	% lpos = ANGLE label position (default: 45)
	%
	\newcommand{\dspPZ}[2][]{%
	\presetkeys[psset]{dspPZP}{type=pole,label=auto}{}%
	\setkeys*[psset]{dspPZP}{#1}%
	\ifPZPole
	\psdot[dotstyle=+,dotsize=1.4ex,dotscale=1.5,dotangle=45, #1](\twoArgSplit#2) \else
	\psdot[dotstyle=*,dotsize=1.4ex,#1](\twoArgSplit#2) \fi
	\ifx\@empty\PZLabel \def\PZLabel{$(\twoArgSplit#2)$} \fi
	% tricky bug in pstricks so we can't use presetkeys for angle... Could not understand
	\ifdefined\PZLP \relax \else \def\PZLP{45} \fi
	\ifPZLabel \uput[\PZLP]{0}(\twoArgSplit#2){\PZLabel} \fi}


	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


	\define@key{dspCP}{width}{\setlength{\dspCPW}{#1}\setlength{\dspCPH}{#1}}

	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%
	% dspCP environment
	%
	% \begin{dspCP}[OPTIONS]{MAX}
	%
	%
	\newlength{\dspCPW}\newlength{\dspCPH}
	\newenvironment{dspCP}[3][]{%
	%% scale dimensions so that axes have equal units
	\setlength{\dspCPW}{0.37\textwidth}\setlength{\dspCPH}{\dspCPW}
	\setlength{\dspW}{\dspCPW}\setlength{\dspH}{\dspCPH}
	\setkeys*{dspCP}{#1}%
	\dspSetDims#2,#3,0\relax%
	\FPupn\g{\dspRngY{} {\strip@pt\dspCPW} / \dspRngX{} * 0 trunc}%
	\setlength{\dspCPH}{1pt*\g}%
	%%
	\begin{dspPlot}[#1,sidegap=0,inticks=true,width=\dspCPW,height=\dspCPH]{#2}{#3}%
	\ifYAxisExp\psline[linewidth=\dspFrameLineWidth,linecolor=\dspAxisColor](0,\dspMinY)(0,\dspMaxY)\fi
	}{%
	%% redo ticks and axes since images may overlap a little
	\dspPlotFrame
	\ifDoXTicks\multido{\n=\stX+\incX}{\tlimX}{\dspTickX{\n}}\fi
	\ifDoYTicks\multido{\n=\stY+\incY}{\tlimY}{\dspTickY{\n}}\fi
	\end{dspPlot}}


	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%
	%% Plot Dirac deltas
	%
	% \dspPoints[OPTIONS]{x1 y1 x2 y2 ...}
	%
	\newcommand{\dspPoints}[2][]{%
	\listplot[plotstyle=dots,%
	showpoints=true, dotstyle=*,%
	dotsize=\dspDotSize, #1]{\m@keList#2 \relax}}

	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%
	%% Plot Dirac delta with value
	%
	% \dspDiracs[OPTIONS]{x, y}{text}
	%
	\newcommand{\dspPointValue}[3][]{%
	\psdot[dotstyle=*, dotsize=\dspDotSize, #1](\twoArgSplit#2)%
	\uput[45]{0}(\twoArgSplit#2){#3}}

	\newcommand{\dspPointValueSC}[3][]{%
	\SpecialCoor
	\psdot[dotstyle=*, dotsize=\dspDotSize, #1](#2)%
	\uput[45]{0}(\twoArgSplit#2){#3}
	\NormalCoor}

	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%
	%% Plot image from file
	\newcommand{\dspImageFile}[1]{%
	\FPupn\u{2 \dspRngX{} 1.01 * / \dspMinX{} + }\FPupn\v{2 \dspRngY{} 1.01 * / \dspMinY{} + }%
	\setlength{\dspCPW}{1.01\dspW}\setlength{\dspCPH}{1.01\dspH}%
	\rput(\u,\v){\includegraphics[width=\dspCPW,height=\dspCPH]{#1}}}


	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%
	%% Quick image plot, with frame but no additional space around it
	\newcommand{\dspShowImage}[2][0.37\textwidth]{%
	\psset{xunit=#1,yunit=#1}%
	\begin{pspicture}(0,0)(0,1)%
	\includegraphics[width=#1,height=#1]{#2}%
	\psframe[dimen=middle,linewidth=1.1pt](-0.01,0)(-.99,.99)
	\end{pspicture}}



	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%
	%% Some geometrical primitives
	%
	\newif\ifPointToOrg
	\define@choicekey*[psset]{dspPZP}{toorg}[\ll\ln]{true,false}[false]{%
	\ifcase\ln\relax
	\PointToOrgtrue
	\or
	\PointToOrgfalse
	\fi}

	% [opts]{x,y}{label}
	\newcommand{\dspCPPoint}[3][]{%
	\setkeys*[psset]{dspPZP}{#1}%
	\psdot[dotstyle=*, dotsize=\dspDotSize, #1](#2)%
	\uput[45]{0}(#2){#3}%
	\ifPointToOrg\psline[linewidth=\dspTickLineWidth, #1](0,0)(#2)\fi}

	% [opts]{x,y in special coor}{label}
	\newcommand{\dspCPPointSC}[3][]{%
	\setkeys*[psset]{dspPZP}{#1}%
	\SpecialCoor%
	\psdot[dotstyle=*, dotsize=\dspDotSize, #1](#2)%
	\uput[45]{0}(#2){#3}%
	\ifPointToOrg\psline[linewidth=\dspTickLineWidth, #1](! 0 0 )(#2)\fi%
	\NormalCoor}

	% [opts]{x,y}{r}
	\newcommand{\dspCPCircle}[3][]{%
	\pscircle[#1](#2){#3\dspUnitX}}

	% [opts]{r}{a}{label}
	\newcommand{\dspCPCirclePoint}[4][]{%
	\setkeys*[psset]{dspPZP}{#1}%
	\SpecialCoor%
	\def\pcorps{! #3 cos #2 mul #3 sin #2 mul}%
	\FPupn\q{#2 1.1 * 2 trunc}%
	\uput*{\q\dspUnitX}[#3]{0}(0,0){#4}%
	\psdot[dotstyle=*, dotsize=\dspDotSize, #1](\pcorps)%
	\ifPointToOrg\psline[linewidth=\dspTickLineWidth, #1](! 0 0 )(\pcorps)\fi%
	\NormalCoor}

	% [opts] {r}{a}{b}{label}
	\newcommand{\dspCPArc}[5][]{%
	\FPupn\p{#3 #4 + 0.5 * 2 trunc}%
	\FPupn\q{#2 1.1 * 2 trunc}%
	\uput*{\q\dspUnitX}[\p]{0}(0,0){#5}%
	\psarc[linewidth=2\dspTickLineWidth, #1]{->}{#2\dspUnitX}{#3}{#4}}
	\newcommand{\dspCPArcn}[5][]{%
	\FPupn\p{#3 #4 + 0.5 * 2 trunc}%
	\FPupn\q{#2 1.1 * 2 trunc}%
	\uput*{\q\dspUnitX}[\p]{0}(0,0){#5}%
	\psarcn[linewidth=2\dspTickLineWidth, #1]{->}{#2\dspUnitX}{#3}{#4}}



	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%% Helpers
	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%% This is called at each plot setup with xmin, xmax, ymin, ymax and sidegap
	%% and sets all lengths
	\def\dspSetDims#1,#2,#3,#4,#5\relax{%
	\def\sideGap{#5}%
	% default sidegap: 5% of range
	\FPifneg\sideGap\FPupn\sideGap{#1 #2 - 0.05 * 0.5 + 2 trunc}\fi%
	\FPifgt\sideGap{1}\FPtrunc\sideGap\sideGap{0}\fi%
	%%
	%% active range for the independent variable
	\def\dspMinActX{#1}%
	\def\dspMaxActX{#2}%
	%% axes range (including sidegap)
	\FPupn\dspMinX{\sideGap{} #1 - clip}%
	\FPupn\dspMaxX{\sideGap{} #2 + clip}%
	\FPupn\dspRngX{#1 #2 - \sideGap{} 2 * + clip}%
	\FPupn\dspMinY{#3 0 + clip}%
	\FPupn\dspMaxY{#4 0 + clip}%
	\FPupn\dspRngY{#3 #4 - clip}%
	%%
	% if y-range is across zero we'll need to draw the x-axis
	\FPmul\u\dspMinY\dspMaxY%
	\FPifneg\u\XAxisExptrue\else\XAxisExpfalse\fi%
	%% same for x (but usually we never draw the y axis)
	\FPmul\u\dspMinX\dspMaxX%
	\FPifneg\u\YAxisExptrue\else\YAxisExpfalse\fi%
	%%
	%% pstricks units: we scale the units so that coordinates are "real" coords on the axes
	\FPupn\tmp{\dspRngX{} {\strip@pt\dspW} / }
	\setlength{\dspUnitX}{\tmp pt}%
	\FPupn\tmp{\dspRngY{} {\strip@pt\dspH} / }%
	\setlength{\dspUnitY}{\tmp pt}%
	%%
	%% basic unit based on the size of the image: ~1pt for a 10x5 cm box
	\FPupn\g{2 {\strip@pt\dspW} {\strip@pt\dspH} * root 0.005 * 0 round 1 max}%
	\setlength{\dspBU}{1pt*\g}%
	%% derived sizes: lines and fonts
	\setlength{\dspLineWidth}{1.8\dspBU}%
	\setlength{\dspDotSize}{5\dspBU}%
	\setlength{\dspStemWidth}{1.4\dspBU}%
	\fontsize{9\dspBU}{10\dspBU}\selectfont%
	% %% ticks on axes
	\setlength{\dspTickLen}{4\dspBU}%
	\setlength{\dspTickLineWidth}{0.4\dspBU}%
	\setlength{\dspXTickGap}{6\dspBU}\addtolength{\dspXTickGap}{2ex}%
	\setlength{\dspYTickGap}{2\dspBU}%
	\setlength{\dspFrameLineWidth}{2.2\dspTickLineWidth}%
	%%
	%% height of a line of text in psticks units
	\setlength{\dspTmpLen}{1em}%
	\FPupn\dspTSX{{\strip@pt\dspUnitX} {\strip@pt\dspTmpLen} / }%
	\FPupn\dspTSY{{\strip@pt\dspUnitY} {\strip@pt\dspTmpLen} / }%
	%%
	%% find the coordinates of the plot's bounding box, including labels
	\ifYLabel%
	\FPupn\LX{\dspTSX{} 4 * \dspMinX{} -}%
	\FPupn\RX{\dspTSX{} 4 * \dspMaxX{} +}%
	\else%
	\FPupn\LX{\dspTSX{} 2 * \dspMinX{} -}%
	\FPupn\RX{\dspTSX{} 2 * \dspMaxX{} +}%
	\fi
	\FPupn\TY{\dspTSY{} \dspMaxY{} +}%
	\def\outTicks{%
	\ifXTicks\FPupn\BY{\dspTSY{} 2.5 * \dspMinY{} -}\else\FPupn\BY{\dspTSY{} \dspMinY{} -}\fi%
	\ifXLabel\FPupn\BY{\dspTSY{} 1.5 * \BY{} -}\else\relax\fi }%
	\ifXAxisExp % ticks are inside
	\ifXLabel\FPupn\BY{\dspTSY{} 2.5 * \dspMinY{} -}\else\FPupn\BY{\dspTSY{} \dspMinY{} -}\fi%
	\else% ticks are outside
	\outTicks \fi%
	% did we select explicit outside ticks?
	\ifXTicksOut\outTicks \fi%
	%%
	%% x-axis resolution for plotting functions: ~60 values/cm
	\FPupn\dspPSPoints{{\strip@pt\dspW} 2 * 0 trunc}%
	%%
	\psset{xunit=\dspUnitX, yunit=\dspUnitY}%
	\psset{linewidth=\dspLineWidth}%www
	}

	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%% Draw axis labels (if required) under x axis and to left and right of y axes
	%%
	\def\dspLabels{%
	% horizontal label
	\ifXTicksOut\XAxisExpfalse\fi%
	\ifXLabel%
	\FPupn\mid{\dspMinX{} \dspMaxX{} + 0.5 mul}%
	\ifXAxisExp%
	\FPupn\pos{\dspTSY{} 2 * \dspMinY{} -}%
	\else%
	\ifXTicks%
	\FPupn\pos{\dspTSY{} 3 * \dspMinY{} -}%
	\else%
	\FPupn\pos{\dspTSY{} 2 * \dspMinY{} -}%
	\fi%
	\fi%
	\rput[b]{0}(\mid,\pos){\dspXLabel}%
	\fi%
	%
	\FPupn\mid{\dspMinY{} \dspMaxY{} + 0.5 mul}%
	\ifYTicks%
	\FPupn\pos{\dspTSX{} 3.4 * \dspMinX{} -}%
	\else%
	\FPupn\pos{\dspTSX{} 1 * \dspMinX{} -}%
	\fi%
	\rput[b]{90}(\pos,\mid){\dspYLabel}
	%%
	\FPupn\pos{\dspTSX{} 3 * \dspMaxX{} +}%
	\rput[b]{-90}(\pos,\mid){\dspYLabelR}}


	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%% This sets axes ticks (spacing and number) and prepares macros
	%% for plotting ticks and tick labels
	\def\dspSetupAxes{%
	%% tick increments; if incX/Y is zero, compute suitable value
	\FPifgt\incX{0}\FPupn\incX{\incX{} 2 trunc}%
	\else\FPupn\incX{\dspMinActX{} \dspMaxActX{} - 1 + 6 swap / 0 trunc 1 max}\relax\fi%
	\FPifgt\incY{0}\FPupn\incY{\incY{} 2 trunc}%
	\else\FPupn\incY{\dspMinY{} \dspMaxY{} - 1 + 6 swap / 0 trunc 1 max}\relax\fi%
	%%
	%% now find starting point and increment for ticks (and number of ticks)
	%% start with y-axis:
	\ifXAxisExp% is y=0 explicit or does it coincide with the lower edge?
	\def\haY{0}%
	% make sure ticks hit zero; add small epsilons to avoid ticks at the limits
	\FPupn\stY{\incY{} \dspMinY{} / 0.001 + 0 trunc \incY{} * 2 trunc}%
	\FPupn\tlimY{\stY{} \dspMaxY{} - 0.001 - \incY{} swap / abs 1 + 0 trunc}%
	\else%
	\def\haY{\dspMinY}%
	\FPupn\tlimY{\incY{} \dspRngY{} / abs 1 + 0 trunc}%
	\FPupn\stY{\dspMinY{} 2 trunc}% \incY{} 1 \tlimY{} - * \dspRngY{} - 0.5 * \dspMinY{} + 2 trunc}%
	\fi%
	% x-ticks outside of the box anyway?
	\ifXTicksOut\def\haY{\dspMinY}\relax\fi%
	% round off to integer if possible:
	\FPupn\v{\stY{} 0 trunc \stY{} - abs \incY{} 0 trunc \incY{} - abs + clip}%
	\FPifeq\v{0}\FPtrunc\stY\stY{0}\FPtrunc\incY\incY{0}\relax\fi%
	%
	%% now x-axis:
	\ifYAxisExp% we almost never draw the y-axis but need to see if x-axis spans zero
	% make sure ticks hit zero; add small epsilons to avoid ticks at the limits
	\FPupn\stX{\incX{} \dspMinX{} / 0 trunc \incX{} * 2 trunc}%
	\FPupn\tlimX{\incX{} \stX{} \dspMaxX{} - / abs 1 + 0 trunc}%
	\else%
	\FPupn\tlimX{\incX{} \dspRngX{} / abs 1 + 0 trunc}%
	\FPupn\stX{\dspMinX{} 2 trunc}% \FPupn\stX{\incX{} 1 \tlimX{} - * \dspRngX{} - 0.5 * \dspMinX{} + 2 trunc}%
	\fi%
	\FPupn\v{\stX{} 0 trunc \stX{} - abs \incX{} 0 trunc \incX{} - abs +}%
	\FPifzero\v\FPtrunc\stX\stX{0}\FPtrunc\incX\incX{0}\relax\fi%
	%%
	%% macros for drawing x-ticks
	\ifXInside%
	\FPupn\tickEndX{{\strip@pt\dspUnitY} {\strip@pt\dspTickLen} /}%
	\FPupn\tickTxtX{{\strip@pt\dspUnitY} {\strip@pt\dspXTickGap} 0.9 * / \dspMinY{} -}% tick label pos in PS units
	\FPupn\tickXB{\tickEndX{} \dspMinY{} +}%
	\FPupn\tickXT{\tickEndX{} \dspMaxY{} -}%
	\gdef\dspTickX##1{%
	\psline[linewidth=\dspTickLineWidth,linecolor=\dspAxisColor](##1,\dspMinY)(##1,\tickXB)%
	\psline[linewidth=\dspTickLineWidth,linecolor=\dspAxisColor](##1,\dspMaxY)(##1,\tickXT)}%
	% \gdef\dspTickLabelX##1##2{\uput{{2\dspYTickGap}}[180]{{0}}(\dspMinX,##1){{##2}}}%
	\gdef\dspTickLabelX##1##2{\rput*[B]{{0}}(##1,\tickTxtX){{##2}}}%
	\else%
	\FPupn\tickEndX{{\strip@pt\dspUnitY} {\strip@pt\dspTickLen} / \haY{} -}% tick len in PS units
	\FPupn\tickTxtX{{\strip@pt\dspUnitY} {\strip@pt\dspXTickGap} / \haY{} -}% tick label pos in PS units
	\gdef\dspTickX##1{\psline[linewidth=\dspTickLineWidth,linecolor=\dspAxisColor](##1,\haY)(##1,\tickEndX)}%
	\gdef\dspTickLabelX##1##2{\rput*[B]{{0}}(##1,\tickTxtX){{##2}}}%
	\fi%
	%% macros for drawing y-ticks
	\FPupn\tickEndY{{\strip@pt\dspUnitX} {\strip@pt\dspTickLen} /}%
	\FPupn\tickXB{\tickEndY{} \dspMinX{} +}%
	\FPupn\tickXT{\tickEndY{} \dspMaxX{} -}%
	\gdef\dspTickY##1{%
	\psline[linewidth=\dspTickLineWidth,linecolor=\dspAxisColor](\dspMinX,##1)(\tickXB,##1)%
	\psline[linewidth=\dspTickLineWidth,linecolor=\dspAxisColor](\dspMaxX,##1)(\tickXT,##1)}%
	\gdef\dspTickLabelY##1##2{\uput{{2\dspYTickGap}}[180]{{0}}(\dspMinX,##1){{##2}}}%
	\gdef\dspTickLabelYR##1##2{\uput{{2\dspYTickGap}}[0]{{0}}(\dspMaxX,##1){{##2}}}%
	}

	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	% simplify fractions of pi
	\newcount\dspNum \newcount\dspDen
	\def\simplifyPiFrac#1#2{%
	\ifnum#1=0 $0$\else % zero is zero
	\dspNum=#1 \dspDen=#2 %
	\divide\dspNum by\dspDen \multiply\dspNum by\dspDen % see if frac is simply an integer
	\ifnum\dspNum=#1 \divide\dspNum by\dspDen \ifnum\dspNum=1 $\pi$\else \ifnum\dspNum=-1 $-\pi$\else $\number\dspNum\pi$\fi\fi\else%
	\dspNum=#1 %
	\ifnum\dspNum<0 \multiply\dspNum by-1 \def\s{-}\else\def\s{}\fi % normalize sign
	\divide\dspDen by\dspNum \multiply\dspDen by\dspNum % see if frac is of type 1/x
	\ifnum\dspDen=#2 \divide\dspDen by\dspNum $\s\pi / \number\dspDen$\else %
	\dspNum=#1\dspDen=#2 %
	\removeFactor{10}\removeFactor{9}\removeFactor{8}% remove some common factors
	\removeFactor{7}\removeFactor{6}\removeFactor{5}%
	\removeFactor{4}\removeFactor{3}\removeFactor{2}%
	$\number\dspNum \pi / \number\dspDen$\fi%
	\fi %
	\fi}

	%% simplify a fraction (not the full Euclid, but it's ok for our purposes)
	\newcount\dspTerm \newcount\dspFact
	\def\removeFactor#1{\dspFact=#1 \dspTerm=\dspNum%
	\divide\dspTerm by\dspFact \multiply\dspTerm by\dspFact %
	\ifnum\dspTerm=\dspNum %
	\dspTerm=\dspDen %
	\divide\dspTerm by\dspFact \multiply\dspTerm by\dspFact %
	\ifnum\dspTerm=\dspDen %
	\divide\dspNum by\dspFact \divide\dspDen by\dspFact %
	\fi %
	\fi}


	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	% space-separated lists must have at least two pairs of elements.
	% Duplicate singletons
	%
	\def\m@keList#1 #2 #3\relax{%
	\ifx&#3&
	#1 #2 #1 #2
	\else
	#1 #2 #3
	\fi
	}

	\def\twoArgSplit#1,#2{#1, #2}


	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	% prepend the ordinal index to each element of a space-separated list
	%
	\def\m@keIndexedList#1#2{%
	\count0=#1%
	\expandafter\m@kixl\trim #2 \|}
	\def\m@kixl#1 {%
	\ifx#1\|%
	\let\next=\relax%
	\else{\number\count0} \ #1\ \advance\count0 by1\let\next=\m@kixl\fi%
	\next}

	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	% perform an action on all consecutive pairs in a space-separated list
	%
	\def\doOnPairs#1#2{%
	\def\action{#1}%
	\expandafter\p@rseB\trim #2 \|}
	\def\p@rseB#1 #2 #3{%
	\csname \action\endcsname{#1}{#2}%
	\ifx#3\|%
	\let\next=\@gobble%
	\else%
	\let\next=\p@rseB\fi%
	\next #3}
	\def\@gobble#1{}


	\def\trim#1{%
	\romannumeral-`\.\expandafter\noexpand#1%
	}

	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%
	% PsTricks overrides
	%
	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%% Lollipop line style, by Denis.Girou at idris.fr %%%%%%%%%%%%%%%%%%%%%%%%
	%%
	\let\beginplot@LineToXAxis\beginplot@line
	\def\endplot@LineToXAxis{\psLineToXAxis@ii}
	\let\beginqp@LineToXAxis\beginqp@line
	\let\doqp@LineToXAxis\doqp@line
	\let\endqp@LineToXAxis\endqp@line
	\let\testqp@LineToXAxis\testqp@line
	%
	\def\psLineToXAxis@ii{%
	\addto@pscode{\pst@cp \psline@iii \tx@LineToXAxis}%
	\end@OpenObj}
	%
	\def\tx@LineToXAxis{LineToXAxis }
	%
	% Adapted from Line
	\pst@def{LineToXAxis}<{%
	NArray
	n 0 eq not
	{ n 1 eq { 0 0 /n 2 def } if
	ArrowA
	/n n 2 sub def
	CP 2 copy moveto pop 0 Lineto
	n { 2 copy moveto pop 0 Lineto } repeat
	CP
	4 2 roll
	ArrowB
	2 copy moveto pop 0
	L
	pop pop } if}>


	\makeatother
	\endinput

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