From 30a06bd2ae64729514a5ff5e82ca86cf8d9bfd60 Mon Sep 17 00:00:00 2001 From: jmfriedt Date: Mon, 22 Jan 2018 08:56:21 +0100 Subject: [PATCH] initial commit: IFCS2018 article --- Makefile | 24 + biblio_dpnm.bib | 73 + ifcs2018.tex | 197 ++ images/fir-mono-vs-fir-series-100dB.eps | 5337 ++++++++++++++++++++++++++++ images/fir-mono-vs-fir-series-200dB.eps | 5867 +++++++++++++++++++++++++++++++ images/fir-mono-vs-fir-series-200dB.pdf | Bin 0 -> 24789 bytes images/fir1-vs-firls.eps | 1195 +++++++ images/fir1-vs-firls.pdf | Bin 0 -> 8116 bytes images/noise-rejection.pdf | Bin 0 -> 121462 bytes images/schema.fig | 53 + images/schema.pdf | Bin 0 -> 6160 bytes references.bib | 46 + submitted_version.pdf | Bin 0 -> 275710 bytes 13 files changed, 12792 insertions(+) create mode 100644 Makefile create mode 100644 biblio_dpnm.bib create mode 100644 ifcs2018.tex create mode 100644 images/fir-mono-vs-fir-series-100dB.eps create mode 100644 images/fir-mono-vs-fir-series-200dB.eps create mode 100644 images/fir-mono-vs-fir-series-200dB.pdf create mode 100644 images/fir1-vs-firls.eps create mode 100644 images/fir1-vs-firls.pdf create mode 100644 images/noise-rejection.pdf create mode 100644 images/schema.fig create mode 100644 images/schema.pdf create mode 100644 references.bib create mode 100644 submitted_version.pdf diff --git a/Makefile b/Makefile new file mode 100644 index 0000000..326683f --- /dev/null +++ b/Makefile @@ -0,0 +1,24 @@ +# source: https://tex.stackexchange.com/questions/40738/how-to-properly-make-a-latex-project + +TEX = pdflatex -shell-escape -interaction=nonstopmode -file-line-error +BIB = bibtex +TARGET = ifcs2018 + +.PHONY: all view + +all : $(TARGET).pdf + +view : + evince $(TARGET).pdf + +$(TARGET).pdf : $(TARGET).tex references.bib + $(TEX) $(TARGET).tex + $(BIB) $(TARGET) + $(TEX) $(TARGET).tex + $(TEX) $(TARGET).tex + +clean: + rm -f $(TARGET).aux $(TARGET).log $(TARGET).out $(TARGET).bbl $(TARGET).blg + +mrproper: clean + rm -f $(TARGET).pdf diff --git a/biblio_dpnm.bib b/biblio_dpnm.bib new file mode 100644 index 0000000..d1e0cac --- /dev/null +++ b/biblio_dpnm.bib @@ -0,0 +1,73 @@ +%dpnm +@article{angrisani2001digital, + title={A digital signal-processing approach for phase noise measurement}, + author={Angrisani, Leopoldo and D'Apuzzo, Massimo and D'Arco, Mauro}, + journal={IEEE Transactions on instrumentation and measurement}, + volume={50}, + number={4}, + pages={930--935}, + year={2001}, + publisher={IEEE} +} +@inproceedings{landis2001newd, + title={A new digital phase measurement system}, + author={Landis, G Paul and Galysh, Ivan and Petsopoulos, Thomas}, + year={2001}, + booktitle={33rd Annual Precise Time and Time Interval (PTTI) Meeting}, + pages={543--552}, + year={2001} +} +@inproceedings{grove2004direct, + title={Direct-digital phase-noise measurement}, + author={Grove, J and Hein, J and Retta, J and Schweiger, P and Solbrig, W and Stein, SR}, + booktitle={Frequency Control Symposium and Exposition, 2004. Proceedings of the 2004 IEEE International}, + pages={287--291}, + year={2004}, + organization={IEEE} +} +@article{mochizuki2007frequency, + title={Frequency-stability measurement system using high-speed ADCs and digital signal processing}, + author={Mochizuki, Ken and Uchino, Masaharu and Morikawa, Takao}, + journal={IEEE Transactions on Instrumentation and Measurement}, + volume={56}, + number={5}, + pages={1887--1893}, + year={2007}, + publisher={IEEE} +} +@inproceedings{ruppalt2010simultaneous, + title={Simultaneous digital measurement of phase and amplitude noise}, + author={Ruppalt, Laura B and McKinstry, David R and Lauritzen, Keir C and Wu, Albert K and Phillips, Shawn A and Talisa, Salvador H}, + booktitle={Frequency Control Symposium (FCS), 2010 IEEE International}, + pages={97--102}, + year={2010}, + organization={IEEE} +} +@article{nelson2012sub, + title={A sub-sampling digital PM/AM noise measurement system}, + author={Nelson, Craig W and Howe, David A}, + journal={NCSLI Measure}, + volume={7}, + number={3}, + pages={70--73}, + year={2012}, + publisher={Taylor \& Francis} +} +@inproceedings{bourgeois2015noise, + title={Noise in high-speed digital-to-analog converters}, + author={Bourgeois, P-Y and Imaike, T and Goavec-Merou, G and Rubiola, E}, + booktitle={Frequency Control Symposium \& the European Frequency and Time Forum (FCS), 2015 Joint Conference of the IEEE International}, + pages={672--675}, + year={2015}, + organization={IEEE} +} +@article{sherman2016oscillator, + title={Oscillator metrology with software defined radio}, + author={Sherman, Jeff A and J{\"o}rdens, Robert}, + journal={Review of Scientific Instruments}, + volume={87}, + number={5}, + pages={054711}, + year={2016}, + publisher={AIP Publishing} +} diff --git a/ifcs2018.tex b/ifcs2018.tex new file mode 100644 index 0000000..18a5a3d --- /dev/null +++ b/ifcs2018.tex @@ -0,0 +1,197 @@ +\documentclass[a4paper,conference]{IEEEtran/IEEEtran} +\usepackage{graphicx,color,hyperref} +\usepackage{amsfonts} +\usepackage{url} +\usepackage[normalem]{ulem} +\graphicspath{{/home/jmfriedt/gpr/170324_avalanche/}{/home/jmfriedt/gpr/1705_homemade/}} +% correct bad hyphenation here +\hyphenation{op-tical net-works semi-conduc-tor} +\textheight=26cm +\setlength{\footskip}{30pt} +\pagenumbering{gobble} +\begin{document} +\title{Filter optimization for real time digital processing of radiofrequency signals: application +to oscillator metrology} + +\author{\IEEEauthorblockN{A. Hugeat\IEEEauthorrefmark{1}\IEEEauthorrefmark{2}, J. Bernard\IEEEauthorrefmark{2}, +G. Goavec-M\'erou\IEEEauthorrefmark{1}, +P.-Y. Bourgeois\IEEEauthorrefmark{1}, J.-M Friedt\IEEEauthorrefmark{1}} +\IEEEauthorblockA{\IEEEauthorrefmark{1}FEMTO-ST, Time \& Frequency department, Besan\c con, France } +\IEEEauthorblockA{\IEEEauthorrefmark{2}FEMTO-ST, Computer Science department DISC, Besan\c con, France \\ +Email: \{pyb2,jmfriedt\}@femto-st.fr} +} +\maketitle +\thispagestyle{plain} +\pagestyle{plain} + +\begin{abstract} +Software Defined Radio (SDR) provides stability, flexibility and reconfigurability to +radiofrequency signal processing. Applied to oscillator characterization in the context +of ultrastable clocks, stringent filtering requirements are defined by spurious signal or +noise rejection needs. Since real time radiofrequency processing must be performed in a +Field Programmable Array to meet timing constraints, we investigate optimization strategies +to design filters meeting rejection characteristics while limiting the hardware resources +required and keeping timing constraints within the targeted measurement bandwidths. +\end{abstract} + +\begin{IEEEkeywords} +Software Defined Radio, Mixed-Integer Linear Programming, Finite Impulse Response filter +\end{IEEEkeywords} + +\section{Digital signal processing of ultrastable clock signals} + +Analog oscillator phase noise characteristics are classically performed by downconverting +the radiofrequency signal using a saturated mixer to bring the radiofrequency signal to baseband, +followed by a Fourier analysis of the beat signal to analyze phase fluctuations close to carrier. In +a fully digital approach, the radiofrequency signal is digitized and numerically downconverted by +multiplying the samples with a local numerically controlled oscillator (Fig. \ref{schema}) \cite{rsi}. + +\begin{figure}[h!tb] +\begin{center} +\includegraphics[width=.8\linewidth]{images/schema} +\end{center} +\caption{Fully digital oscillator phase noise characterization: the Device Under Test +(DUT) signal is sampled by the radiofrequency grade Analog to Digital Converter (ADC) and +downconverted by mixing with a Numerically Controlled Oscillator (NCO). Unwanted signals +and noise aliases are rejected by a Low Pass Filter (LPF) implemented as a cascade of Finite +Impulse Response (FIR) filters. The signal is then decimated before a Fourier analysis displays +the spectral characteristics of the phase fluctuations.} +\label{schema} +\end{figure} + +As with the analog mixer, +the non-linear behavior of the downconverter introduces noise or spurious signal aliasing as +well as the generation of the frequency sum signal in addition to the frequency difference. +These unwanted spectral characteristics must be rejected before decimating the data stream +for the phase noise spectral characterization. The characteristics introduced between the downconverter +and the decimation processing blocks are core characteristics of an oscillator characterization +system, and must reject out-of-band signals below the targeted phase noise -- typically in the +sub -170~dBc/Hz for ultrastable oscillator we aim at characterizing. The filter blocks will +use most resources of the Field Programmable Gate Array (FPGA) used to process the radiofrequency +datastream: optimizing the performance of the filter while reducing the needed resources is +hence tackled in a systematic approach using optimization techniques. Most significantly, we +tackle the issue by attempting to cascade multiple Finite Impulse Response (FIR) filters with +tunable number of coefficients and tunable number of bits representing the coefficients and the +data being processed. + +\section{Filter optimization} + +A basic approach for implementing the FIR filter is to compute the transfer function of +a monolithic filter: this single filter defines all coefficients with the same resolution +(number of bits) and processes data represented with their own resolution. Meeting the +filter shape requires a large number of coefficients, limited by resources of the FPGA since +this filter must process data stream at the radiofrequency sampling rate after the mixer. + +An optimization problem \cite{leung2004handbook} aims at improving one or many +performance criteria within a constrained resource environment. Amongst the tools +developed to meet this aim, Mixed-Integer Linear Programming (MILP) provides the framework to +provide a formal definition of the stated problem and search for an optimal use of available +resources \cite{yu2007design, kodek1980design}. + +The degrees of freedom when addressing the problem of replacing the single monolithic +FIR with a cascade of optimized filters are the number of coefficients $N_i$ of each filter $i$, +the number of bits $c_i$ representing the coefficients and the number of bits $d_i$ representing +the data fed to the filter. Because each FIR in the chain is fed the output of the previous stage, +the optimization of the complete processing chain within a constrained resource environment is not +trivial. The resource occupation of a FIR filter is considered as $c_i+d_i+\log_2(N_i)$ which is +the number of bits needed in a worst case condition to represent the output of the FIR. + + +\begin{figure}[h!tb] +\includegraphics[width=\linewidth]{images/noise-rejection.pdf} +\caption{Rejection as a function of number of coefficients and number of bits} +\label{noise-rejection} +\end{figure} + +The objective function maximizes the noise rejection while keeping resource occupation below +a user-defined threshold. The MILP solver is allowed to choose the number of successive +filters, within an upper bound. The last problem is to model the noise rejection. Since filter +noise rejection capability is not modeled with linear equation, a look-up-table is generated +for multiple filter configurations in which the $c_i$, $d_i$ and $N_i$ parameters are varied: for each +one of these conditions, the low-pass filter rejection defined as the mean power between +half the Nyquist frequency and the Nyquist frequency is stored as computed by the frequency response +of the digital filter (Fig. \ref{noise-rejection}). + +Linear program formalism for solving the problem is well documented: an objective function is +defined which is linearly dependent on the parameters to be optimized. Constraints are expressed +as linear equation and solved using one of the available solvers, in our case GLPK\cite{glpk}. + +The MILP solver provides a solution to the problem by selecting a series of small FIR with +increasing number of bits representing data and coefficients as well as an increasing number +of coefficients, instead of a single monolithic filter. Fig. \ref{compare-fir} exhibits the +performance comparison between one solution and a monolithic FIR when selecting a cutoff +frequency of half the Nyquist frequency: a series of 5 FIR and a series of 10 FIR with the +same space usage are provided as selected by the MILP solver. The FIR cascade provides improved +rejection than the monolithic FIR at the expense of a lower cutoff frequency which remains to +be tuned or compensated for. + +\begin{figure}[h!tb] +% \includegraphics[width=\linewidth]{images/compare-fir.pdf} +\includegraphics[width=\linewidth]{images/fir-mono-vs-fir-series-200dB.pdf} +\caption{Comparison of the rejection capability between a series of FIR and a monolithic FIR +with a cutoff frequency set at half the Nyquist frequency.} +\label{compare-fir} +\end{figure} + +The resource occupation when synthesizing such FIR on a Xilinx FPGA is summarized as Tab. \ref{t1}. + +\begin{table}[h!tb] +\caption{Resource occupation on a Xilinx Zynq-7000 series FPGA when synthesizing the FIR cascade +identified as optimal by the MILP solver within a finite resource criterion. The last line refers +to available resources on a Zynq-7010 as found on the Redpitaya board.} +\begin{center} +\begin{tabular}{|c|ccc|}\hline +FIR & BlockRAM & LookUpTables & DSP \\\hline\hline +1 (monolithic) & 1 & 4064 & 40 \\ +5 & 5 & 12332 & 0 \\ +10 & 10 & 12717 & 0 \\\hline\hline +Zynq 7010 & 60 & 17600 & 80 \\\hline +\end{tabular} +\end{center} +%\vspace{-0.7cm} +\label{t1} +\end{table} + +\section{Filter coefficient selection} + +The coefficients of a single monolithic filter are computed as the impulse response +of the filter transfer function, and practically approximated by a multitude of methods +including least square optimization (Matlab's {\tt firls} function), Hamming or Kaiser windowing +(Matlab's {\tt fir1} function). Cascading filters opens a new optimization opportunity by +selecting various coefficient sets depending on the number of coefficients. Fig. \ref{2} +illustrates that for a number of coefficients ranging from 8 to 47, {\tt fir1} provides a better +rejection than {\tt firls}: since the linear solver increases the number of coefficients along +the processing chain, the type of selected filter also changes depending on the number of coefficients +and evolves along the processing chain. + +\begin{figure}[h!tb] +\includegraphics[width=\linewidth]{images/fir1-vs-firls} +\caption{Evolution of the rejection capability of least-square optimized filters and Hamming +FIR filters as a function of the number of coefficients, for floating point numbers and 8-bit +encoded integers.} +\label{2} +\end{figure} + +\section{Conclusion} + +We address the optimization problem of designing a low-pass filter chain in a Field Programmable Gate +Array for improved noise rejection within constrained resource occupation, as needed for +real time processing of radiofrequency signal when characterizing spectral phase noise +characteristics of stable oscillators. The flexibility of the digital approach makes the result +best suited for closing the loop and using the measurement output in a feedback loop for +controlling clocks, e.g. in a quartz-stabilized high performance clock whose long term behavior +is controlled by non-piezoelectric resonator (sapphire resonator, microwave or optical +atomic transition). + +\section*{Acknowledgement} + +This work is supported by the ANR Programme d'Investissement d'Avenir in +progress at the Time and Frequency Departments of the FEMTO-ST Institute +(Oscillator IMP, First-TF and Refimeve+), and by R\'egion de Franche-Comt\'e. +The authors would like to thank E. Rubiola, F. Vernotte, G. Cabodevila for support and +fruitful discussions. + +\bibliographystyle{IEEEtran} +\bibliography{references} +\end{document} + diff --git a/images/fir-mono-vs-fir-series-100dB.eps b/images/fir-mono-vs-fir-series-100dB.eps new file mode 100644 index 0000000..4f7210b --- /dev/null +++ b/images/fir-mono-vs-fir-series-100dB.eps @@ -0,0 +1,5337 @@ +%!PS-Adobe-2.0 EPSF-2.0 +%%Title: /tmp/fir-mono-vs-fir-series.eps +%%Creator: gnuplot 5.2 patchlevel 2 +%%CreationDate: Sat Jan 20 12:55:46 2018 +%%DocumentFonts: (atend) +%%BoundingBox: 50 50 626 482 +%%EndComments +%%BeginProlog +/gnudict 256 dict def +gnudict begin +% +% The following true/false flags may be edited by hand if desired. +% The unit line width and grayscale image gamma correction may also be changed. +% +/Color true def +/Blacktext false def +/Solid false def +/Dashlength 2 def +/Landscape false def +/Level1 true def +/Level3 false def +/Rounded false def +/ClipToBoundingBox false def +/SuppressPDFMark false def 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{stroke [] 0 setdash + hpt 0 360 arc stroke} def +/Opaque {gsave closepath 1 setgray fill grestore 0 setgray closepath} def +/DiaW {stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V Opaque stroke} def +/BoxW {stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V Opaque stroke} def +/TriUW {stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V Opaque stroke} def +/TriDW {stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V Opaque stroke} def +/PentW {stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + Opaque stroke grestore} def +/CircW {stroke [] 0 setdash + hpt 0 360 arc Opaque stroke} def +/BoxFill {gsave Rec 1 setgray fill grestore} def +/Density { + /Fillden exch def + currentrgbcolor + /ColB exch def /ColG exch def /ColR exch def + /ColR ColR Fillden mul Fillden sub 1 add def + /ColG ColG Fillden mul Fillden sub 1 add def + /ColB ColB Fillden mul Fillden sub 1 add def + ColR ColG ColB setrgbcolor} def +/BoxColFill {gsave Rec PolyFill} def +/PolyFill {gsave Density fill grestore grestore} def +/h {rlineto rlineto rlineto gsave closepath fill grestore} bind def +% +% PostScript Level 1 Pattern Fill routine for rectangles +% Usage: x y w h s a XX PatternFill +% x,y = lower left corner of box to be filled +% w,h = width and height of box +% a = angle in degrees between lines and x-axis +% XX = 0/1 for no/yes cross-hatch +% +/PatternFill {gsave /PFa [ 9 2 roll ] def + PFa 0 get PFa 2 get 2 div add PFa 1 get PFa 3 get 2 div add translate + PFa 2 get -2 div PFa 3 get -2 div PFa 2 get PFa 3 get Rec + TransparentPatterns {} {gsave 1 setgray fill grestore} ifelse + clip + currentlinewidth 0.5 mul setlinewidth + /PFs PFa 2 get dup mul PFa 3 get dup mul add sqrt def + 0 0 M PFa 5 get rotate PFs -2 div dup translate + 0 1 PFs PFa 4 get div 1 add floor cvi + {PFa 4 get mul 0 M 0 PFs V} for + 0 PFa 6 get ne { + 0 1 PFs PFa 4 get div 1 add floor cvi + {PFa 4 get mul 0 2 1 roll M PFs 0 V} for + } if + stroke grestore} def +% +/languagelevel where + {pop languagelevel} {1} ifelse +dup 2 lt + {/InterpretLevel1 true def + /InterpretLevel3 false def} + {/InterpretLevel1 Level1 def + 2 gt + {/InterpretLevel3 Level3 def} + {/InterpretLevel3 false def} + ifelse } + ifelse +% +% PostScript level 2 pattern fill definitions +% +/Level2PatternFill { +/Tile8x8 {/PaintType 2 /PatternType 1 /TilingType 1 /BBox [0 0 8 8] /XStep 8 /YStep 8} + bind def +/KeepColor {currentrgbcolor [/Pattern /DeviceRGB] setcolorspace} bind def +<< Tile8x8 + /PaintProc {0.5 setlinewidth pop 0 0 M 8 8 L 0 8 M 8 0 L stroke} +>> matrix makepattern +/Pat1 exch def +<< Tile8x8 + /PaintProc {0.5 setlinewidth pop 0 0 M 8 8 L 0 8 M 8 0 L stroke + 0 4 M 4 8 L 8 4 L 4 0 L 0 4 L stroke} +>> matrix makepattern +/Pat2 exch def +<< Tile8x8 + /PaintProc {0.5 setlinewidth pop 0 0 M 0 8 L + 8 8 L 8 0 L 0 0 L fill} +>> matrix makepattern +/Pat3 exch def +<< Tile8x8 + /PaintProc {0.5 setlinewidth pop -4 8 M 8 -4 L + 0 12 M 12 0 L stroke} +>> matrix makepattern +/Pat4 exch def +<< Tile8x8 + /PaintProc {0.5 setlinewidth pop -4 0 M 8 12 L + 0 -4 M 12 8 L stroke} +>> matrix makepattern +/Pat5 exch def +<< Tile8x8 + /PaintProc {0.5 setlinewidth pop -2 8 M 4 -4 L + 0 12 M 8 -4 L 4 12 M 10 0 L stroke} +>> matrix makepattern +/Pat6 exch def +<< Tile8x8 + /PaintProc {0.5 setlinewidth pop -2 0 M 4 12 L + 0 -4 M 8 12 L 4 -4 M 10 8 L stroke} +>> matrix makepattern +/Pat7 exch def +<< Tile8x8 + /PaintProc {0.5 setlinewidth pop 8 -2 M -4 4 L + 12 0 M -4 8 L 12 4 M 0 10 L stroke} +>> matrix makepattern +/Pat8 exch def +<< Tile8x8 + /PaintProc {0.5 setlinewidth pop 0 -2 M 12 4 L + -4 0 M 12 8 L -4 4 M 8 10 L stroke} +>> matrix makepattern +/Pat9 exch def +/Pattern1 {PatternBgnd KeepColor Pat1 setpattern} bind def +/Pattern2 {PatternBgnd KeepColor Pat2 setpattern} bind def +/Pattern3 {PatternBgnd KeepColor Pat3 setpattern} bind def +/Pattern4 {PatternBgnd KeepColor Landscape {Pat5} {Pat4} ifelse setpattern} bind def +/Pattern5 {PatternBgnd KeepColor Landscape {Pat4} {Pat5} ifelse setpattern} bind def +/Pattern6 {PatternBgnd KeepColor Landscape {Pat9} {Pat6} ifelse setpattern} bind def +/Pattern7 {PatternBgnd KeepColor Landscape {Pat8} {Pat7} ifelse setpattern} bind def +} def +% +% +%End of PostScript Level 2 code +% +/PatternBgnd { + TransparentPatterns {} {gsave 1 setgray fill grestore} ifelse +} def +% +% Substitute for Level 2 pattern fill codes with +% grayscale if Level 2 support is not selected. +% +/Level1PatternFill { +/Pattern1 {0.250 Density} bind def +/Pattern2 {0.500 Density} bind def +/Pattern3 {0.750 Density} bind def +/Pattern4 {0.125 Density} bind def +/Pattern5 {0.375 Density} bind def +/Pattern6 {0.625 Density} bind def +/Pattern7 {0.875 Density} bind def +} def +% +% Now test for support of Level 2 code +% +Level1 {Level1PatternFill} {Level2PatternFill} ifelse +% +/Symbol-Oblique /Symbol findfont [1 0 .167 1 0 0] makefont +dup length dict begin {1 index /FID eq {pop pop} {def} ifelse} forall +currentdict end definefont pop +% +/Metrics {ExtendTextBox Gswidth} def +/Lwidth {currentpoint stroke M 0 vshift R Metrics} def +/Rwidth {currentpoint stroke M dup stringwidth pop neg vshift R Metrics} def +/Cwidth {currentpoint stroke M dup stringwidth pop -2 div vshift R Metrics} def +/GLwidth {currentpoint stroke M 0 vshift R {ExtendTextBox} forall} def +/GRwidth {currentpoint stroke M dup Gwidth vshift R {ExtendTextBox} forall} def +/GCwidth {currentpoint stroke M dup Gwidth 2 div vshift R {ExtendTextBox} forall} def +/GLwidth2 {0 Gwidth AddGlyphWidth} def +/GRwidth2 {Gwidth -1 mul 0 AddGlyphWidth} def +/GCwidth2 {Gwidth 2 div dup -1 mul AddGlyphWidth} def +/AddGlyphWidth { dup TBx2 gt {userdict /TBx2 3 -1 roll put} {pop} ifelse + dup TBx1 lt {userdict /TBx1 3 -1 roll put} {pop} ifelse } def +/MFshow { + { dup 5 get 3 ge + { 5 get 3 eq {gsave} {grestore} ifelse } + {dup dup 0 get findfont exch 1 get scalefont setfont + [ currentpoint ] exch dup 2 get 0 exch R dup 5 get 2 ne {dup dup 6 + get exch 4 get {textshow} {Metrics pop 0 R} ifelse }if dup 5 get 0 eq + {dup 3 get {2 get neg 0 exch R pop} {pop aload pop M} ifelse} {dup 5 + get 1 eq {dup 2 get exch dup 3 get exch 6 get Gswidth pop -2 div + dup 0 R} {dup 6 get Gswidth pop -2 div 0 R 6 get + textshow 2 index {aload pop M neg 3 -1 roll neg R pop pop} {pop pop pop + pop aload pop M} ifelse }ifelse }ifelse } + ifelse } + forall} def +/Gswidth {dup type /stringtype eq {stringwidth} {pop (n) stringwidth} ifelse} def +/MFwidth {0 exch { dup 5 get 3 ge { 5 get 3 eq { 0 } { pop } ifelse } + {dup 3 get{dup dup 0 get findfont exch 1 get scalefont setfont + 6 get Gswidth pop add} {pop} ifelse} ifelse} forall} def +/MLshow { currentpoint stroke M + 0 exch R + Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def +/MRshow { currentpoint stroke M + exch dup MFwidth neg 3 -1 roll R + Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def +/MCshow { currentpoint stroke M + exch dup MFwidth -2 div 3 -1 roll R + Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def +/XYsave { [( ) 1 2 true false 3 ()] } bind def +/XYrestore { [( ) 1 2 true false 4 ()] } bind def +Level1 SuppressPDFMark or +{} { +/SDict 10 dict def +systemdict /pdfmark known not { + userdict /pdfmark systemdict /cleartomark get put +} if +SDict begin [ + /Title (/tmp/fir-mono-vs-fir-series.eps) + /Subject (gnuplot plot) + /Creator (gnuplot 5.2 patchlevel 2) +% /Producer (gnuplot) +% /Keywords () + /CreationDate (Sat Jan 20 12:55:46 2018) + /DOCINFO pdfmark +end +} ifelse +% +% Support for boxed text - Ethan A Merritt Sep 2016 +% +/InitTextBox { userdict /TBy2 3 -1 roll put userdict /TBx2 3 -1 roll put + userdict /TBy1 3 -1 roll put userdict /TBx1 3 -1 roll put + /Boxing true def } def +/ExtendTextBox { dup type /stringtype eq + { Boxing { gsave dup false charpath pathbbox + dup TBy2 gt {userdict /TBy2 3 -1 roll put} {pop} ifelse + dup TBx2 gt {userdict /TBx2 3 -1 roll put} {pop} ifelse + dup TBy1 lt {userdict /TBy1 3 -1 roll put} {pop} ifelse + dup TBx1 lt {userdict /TBx1 3 -1 roll put} {pop} ifelse + grestore } if } + {} ifelse} def +/PopTextBox { newpath TBx1 TBxmargin sub TBy1 TBymargin sub M + TBx1 TBxmargin sub TBy2 TBymargin add L + TBx2 TBxmargin add TBy2 TBymargin add L + TBx2 TBxmargin add TBy1 TBymargin sub L closepath } def +/DrawTextBox { PopTextBox stroke /Boxing false def} def +/FillTextBox { gsave PopTextBox fill grestore /Boxing false def} def +0 0 0 0 InitTextBox +/TBxmargin 20 def +/TBymargin 20 def +/Boxing false def +/textshow { ExtendTextBox Gshow } def +% +end +%%EndProlog +%%Page: 1 1 +gnudict begin +gsave +doclip +50 50 translate +0.050 0.050 scale +0 setgray +newpath +(Helvetica) findfont 200 scalefont setfont +BackgroundColor 0 lt 3 1 roll 0 lt exch 0 lt or or not {BackgroundColor C 1.000 0 0 11520.00 8640.00 BoxColFill} if +gsave % colour palette begin +/maxcolors 64 def +/HSV2RGB { exch dup 0.0 eq {pop exch pop dup dup} % achromatic gray + { /HSVs exch def /HSVv exch def 6.0 mul dup floor dup 3 1 roll sub + /HSVf exch def /HSVi exch cvi def /HSVp HSVv 1.0 HSVs sub mul def + /HSVq HSVv 1.0 HSVs HSVf mul sub mul def + /HSVt HSVv 1.0 HSVs 1.0 HSVf sub mul sub mul def + /HSVi HSVi 6 mod def 0 HSVi eq {HSVv HSVt HSVp} + {1 HSVi eq {HSVq HSVv HSVp}{2 HSVi eq {HSVp HSVv HSVt} + {3 HSVi eq {HSVp HSVq HSVv}{4 HSVi eq {HSVt HSVp HSVv} + {HSVv HSVp HSVq} ifelse} ifelse} ifelse} ifelse} ifelse + } ifelse} def +/Constrain { + dup 0 lt {0 exch pop}{dup 1 gt {1 exch pop} if} ifelse} def +/YIQ2RGB { + 3 copy -1.702 mul exch -1.105 mul add add Constrain 4 1 roll + 3 copy -0.647 mul exch -0.272 mul add add Constrain 5 1 roll + 0.621 mul exch -0.956 mul add add Constrain 3 1 roll } def +/CMY2RGB { 1 exch sub exch 1 exch sub 3 2 roll 1 exch sub 3 1 roll exch } def +/XYZ2RGB { 3 copy -0.9017 mul exch -0.1187 mul add exch 0.0585 mul exch add + Constrain 4 1 roll 3 copy -0.0279 mul exch 1.999 mul add exch + -0.9844 mul add Constrain 5 1 roll -0.2891 mul exch -0.5338 mul add + exch 1.91 mul exch add Constrain 3 1 roll} def +/SelectSpace {ColorSpace (HSV) eq {HSV2RGB}{ColorSpace (XYZ) eq { + XYZ2RGB}{ColorSpace (CMY) eq {CMY2RGB}{ColorSpace (YIQ) eq {YIQ2RGB} + if} ifelse} ifelse} ifelse} def +/InterpolatedColor true def +/grayindex {/gidx 0 def + {GrayA gidx get grayv ge {exit} if /gidx gidx 1 add def} loop} def +/dgdx {grayv GrayA gidx get sub GrayA gidx 1 sub get + GrayA gidx get sub div} def +/redvalue {RedA gidx get RedA gidx 1 sub get + RedA gidx get sub dgdxval mul add} def +/greenvalue {GreenA gidx get GreenA gidx 1 sub get + GreenA gidx get sub dgdxval mul add} def +/bluevalue {BlueA gidx get BlueA gidx 1 sub get + BlueA gidx get sub dgdxval mul add} def +/interpolate { + grayindex grayv GrayA gidx get sub abs 1e-5 le + {RedA gidx get GreenA gidx get BlueA gidx get} + {/dgdxval dgdx def redvalue greenvalue bluevalue} ifelse} def +/GrayA [0 .0159 .0317 .0476 .0635 .0794 .0952 .1111 .127 .1429 .1587 .1746 + .1905 .2063 .2222 .2381 .254 .2698 .2857 .3016 .3175 .3333 .3492 .3651 + .381 .3968 .4127 .4286 .4444 .4603 .4762 .4921 .5079 .5238 .5397 .5556 + .5714 .5873 .6032 .619 .6349 .6508 .6667 .6825 .6984 .7143 .7302 .746 + .7619 .7778 .7937 .8095 .8254 .8413 .8571 .873 .8889 .9048 .9206 .9365 + .9524 .9683 .9841 1 ] def +/RedA [.267 .2727 .2771 .2804 .2824 .2832 .2828 .2812 .2785 .2747 .27 .2644 + .258 .2511 .2437 .2361 .2283 .2204 .2127 .2051 .1977 .1906 .1838 .1773 + .171 .1648 .1588 .153 .1471 .1414 .1358 .1306 .1259 .1222 .1199 .1196 .122 + .1277 .1368 .1496 .166 .1855 .208 .2331 .2605 .29 .3213 .3544 .3889 .4249 + .4622 .5008 .5403 .5809 .6222 .6641 .7064 .7489 .7913 .8333 .8747 .9153 + .9548 .9932 ] def +/GreenA [.0049 .0258 .0509 .0742 .096 .1169 .1374 .1575 .1773 .197 .2163 + .2354 .2542 .2726 .2906 .3083 .3256 .3425 .3591 .3754 .3913 .4071 .4226 + .4379 .4531 .4681 .4831 .4981 .513 .5279 .5428 .5577 .5726 .5875 .6024 + .6173 .6321 .6469 .6616 .6761 .6905 .7047 .7187 .7324 .7458 .7588 .7715 + .7837 .7955 .8067 .8173 .8274 .8369 .8457 .8538 .8613 .8682 .8745 .8803 + .8858 .8909 .896 .901 .9062 ] def +/BlueA [.3294 .3534 .3762 .3979 .4183 .4372 .4546 .4704 .4847 .4973 .5083 + .5177 .5258 .5325 .5381 .5427 .5463 .5493 .5516 .5535 .555 .5561 .557 + .5576 .558 .5581 .5581 .5577 .557 .5559 .5543 .5522 .5494 .546 .5418 .5368 + .5308 .5239 .516 .5069 .4968 .4854 .4729 .4591 .4441 .4278 .4103 .3915 + .3714 .3501 .3275 .3038 .2789 .253 .2262 .1989 .1715 .145 .1213 .1033 + .0954 .1005 .1179 .1439 ] def +/pm3dround {maxcolors 0 gt {dup 1 ge + {pop 1} {maxcolors mul floor maxcolors 1 sub div} ifelse} if} def +/pm3dGamma 1.0 1.5 Gamma mul div def +/ColorSpace (RGB) def +Color InterpolatedColor or { % COLOUR vs. GRAY map + InterpolatedColor { %% Interpolation vs. RGB-Formula + /g {stroke pm3dround /grayv exch def interpolate + SelectSpace setrgbcolor} bind def + }{ + /g {stroke pm3dround dup cF7 Constrain exch dup cF5 Constrain exch cF15 Constrain + SelectSpace setrgbcolor} bind def + } ifelse +}{ + /g {stroke pm3dround pm3dGamma exp setgray} bind def +} ifelse +1.000 UL +LTb +1.00 1.00 1.00 C 1.000 1497 5067 8926 2923 BoxColFill +1.000 UL +LTb +0.00 0.00 0.00 C 1497 5067 M +88 0 V +stroke +0.15 0.15 0.15 C 1377 5067 M +[ [(Helvetica) 200.0 0.0 true true 0 (-100)] +] -66.7 MRshow +1.000 UL +LTb +0.00 0.00 0.00 C 1497 5599 M +88 0 V +stroke +0.15 0.15 0.15 C 1377 5599 M +[ [(Helvetica) 200.0 0.0 true true 0 (-80)] +] -66.7 MRshow +1.000 UL +LTb +0.00 0.00 0.00 C 1497 6130 M +88 0 V +stroke +0.15 0.15 0.15 C 1377 6130 M +[ [(Helvetica) 200.0 0.0 true true 0 (-60)] +] -66.7 MRshow +1.000 UL +LTb +0.00 0.00 0.00 C 1497 6662 M +88 0 V +stroke +0.15 0.15 0.15 C 1377 6662 M +[ [(Helvetica) 200.0 0.0 true true 0 (-40)] +] -66.7 MRshow +1.000 UL +LTb +0.00 0.00 0.00 C 1497 7194 M +88 0 V +stroke +0.15 0.15 0.15 C 1377 7194 M +[ [(Helvetica) 200.0 0.0 true true 0 (-20)] +] -66.7 MRshow +1.000 UL +LTb +0.00 0.00 0.00 C 1497 7725 M +88 0 V +stroke +0.15 0.15 0.15 C 1377 7725 M +[ [(Helvetica) 200.0 0.0 true true 0 (0)] +] -66.7 MRshow +1.000 UL +LTb +0.00 0.00 0.00 C 1497 5067 M +0 88 V +stroke +0.15 0.15 0.15 C 1497 4867 M +[ [(Helvetica) 200.0 0.0 true true 0 (0)] +] -66.7 MCshow +1.000 UL +LTb +0.00 0.00 0.00 C 3282 5067 M +0 88 V +stroke +0.15 0.15 0.15 C 3282 4867 M +[ [(Helvetica) 200.0 0.0 true true 0 (0.2)] +] -66.7 MCshow +1.000 UL +LTb +0.00 0.00 0.00 C 5068 5067 M +0 88 V +stroke +0.15 0.15 0.15 C 5068 4867 M +[ [(Helvetica) 200.0 0.0 true true 0 (0.4)] +] -66.7 MCshow +1.000 UL +LTb +0.00 0.00 0.00 C 6853 5067 M +0 88 V +stroke +0.15 0.15 0.15 C 6853 4867 M +[ [(Helvetica) 200.0 0.0 true true 0 (0.6)] +] -66.7 MCshow +1.000 UL +LTb +0.00 0.00 0.00 C 8639 5067 M +0 88 V +stroke +0.15 0.15 0.15 C 8639 4867 M +[ [(Helvetica) 200.0 0.0 true true 0 (0.8)] +] -66.7 MCshow +1.000 UL +LTb 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fill Bsquare} bind def +/S9 {BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare} bind def +/S10 {BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill + Bsquare} bind def +/S11 {BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill + Bsquare} bind def +/S12 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare} bind def +/S13 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy vpt Square fill Bsquare} bind def +/S14 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill + 2 copy exch vpt sub exch vpt Square fill Bsquare} bind def +/S15 {BL [] 0 setdash 2 copy Bsquare fill Bsquare} bind def +/D0 {gsave translate 45 rotate 0 0 S0 stroke grestore} bind def +/D1 {gsave translate 45 rotate 0 0 S1 stroke grestore} bind def +/D2 {gsave translate 45 rotate 0 0 S2 stroke grestore} bind def +/D3 {gsave translate 45 rotate 0 0 S3 stroke grestore} bind def +/D4 {gsave translate 45 rotate 0 0 S4 stroke grestore} bind def +/D5 {gsave translate 45 rotate 0 0 S5 stroke grestore} bind def +/D6 {gsave translate 45 rotate 0 0 S6 stroke grestore} bind def +/D7 {gsave translate 45 rotate 0 0 S7 stroke grestore} bind def +/D8 {gsave translate 45 rotate 0 0 S8 stroke grestore} bind def +/D9 {gsave translate 45 rotate 0 0 S9 stroke grestore} bind def +/D10 {gsave translate 45 rotate 0 0 S10 stroke grestore} bind def +/D11 {gsave translate 45 rotate 0 0 S11 stroke grestore} bind def +/D12 {gsave translate 45 rotate 0 0 S12 stroke grestore} bind def +/D13 {gsave translate 45 rotate 0 0 S13 stroke grestore} bind def +/D14 {gsave translate 45 rotate 0 0 S14 stroke grestore} bind def +/D15 {gsave translate 45 rotate 0 0 S15 stroke grestore} bind def +/DiaE {stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V closepath stroke} def +/BoxE {stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V closepath stroke} def +/TriUE {stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V closepath stroke} def +/TriDE {stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V closepath stroke} def +/PentE {stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + closepath stroke grestore} def +/CircE {stroke [] 0 setdash + hpt 0 360 arc stroke} def +/Opaque {gsave closepath 1 setgray fill grestore 0 setgray closepath} def +/DiaW {stroke [] 0 setdash vpt add M + hpt neg vpt neg V hpt vpt neg V + hpt vpt V hpt neg vpt V Opaque stroke} def +/BoxW {stroke [] 0 setdash exch hpt sub exch vpt add M + 0 vpt2 neg V hpt2 0 V 0 vpt2 V + hpt2 neg 0 V Opaque stroke} def +/TriUW {stroke [] 0 setdash vpt 1.12 mul add M + hpt neg vpt -1.62 mul V + hpt 2 mul 0 V + hpt neg vpt 1.62 mul V Opaque stroke} def +/TriDW {stroke [] 0 setdash vpt 1.12 mul sub M + hpt neg vpt 1.62 mul V + hpt 2 mul 0 V + hpt neg vpt -1.62 mul V Opaque stroke} def +/PentW {stroke [] 0 setdash gsave + translate 0 hpt M 4 {72 rotate 0 hpt L} repeat + Opaque stroke grestore} def +/CircW {stroke [] 0 setdash + hpt 0 360 arc Opaque stroke} def +/BoxFill {gsave Rec 1 setgray fill grestore} def +/Density { + /Fillden exch def + currentrgbcolor + /ColB exch def /ColG exch def /ColR exch def + /ColR ColR Fillden mul Fillden sub 1 add def + /ColG ColG Fillden mul Fillden sub 1 add def + /ColB ColB Fillden mul Fillden sub 1 add def + ColR ColG ColB setrgbcolor} def +/BoxColFill {gsave Rec PolyFill} def +/PolyFill {gsave Density fill grestore grestore} def +/h {rlineto rlineto rlineto gsave closepath fill grestore} bind def +% +% PostScript Level 1 Pattern Fill routine for rectangles +% Usage: x y w h s a XX PatternFill +% x,y = lower left corner of box to be filled +% w,h = width and height of box +% a = angle in degrees between lines and x-axis +% XX = 0/1 for no/yes cross-hatch +% +/PatternFill {gsave /PFa [ 9 2 roll ] def + PFa 0 get PFa 2 get 2 div add PFa 1 get PFa 3 get 2 div add translate + PFa 2 get -2 div PFa 3 get -2 div PFa 2 get PFa 3 get Rec + TransparentPatterns {} {gsave 1 setgray fill grestore} ifelse + clip + currentlinewidth 0.5 mul setlinewidth + /PFs PFa 2 get dup mul PFa 3 get dup mul add sqrt def + 0 0 M PFa 5 get rotate PFs -2 div dup translate + 0 1 PFs PFa 4 get div 1 add floor cvi + {PFa 4 get mul 0 M 0 PFs V} for + 0 PFa 6 get ne { + 0 1 PFs PFa 4 get div 1 add floor cvi + {PFa 4 get mul 0 2 1 roll M PFs 0 V} for + } if + stroke grestore} def +% +/languagelevel where + {pop languagelevel} {1} ifelse +dup 2 lt + {/InterpretLevel1 true def + /InterpretLevel3 false def} + {/InterpretLevel1 Level1 def + 2 gt + {/InterpretLevel3 Level3 def} + {/InterpretLevel3 false def} + ifelse } + ifelse +% +% PostScript level 2 pattern fill definitions +% +/Level2PatternFill { +/Tile8x8 {/PaintType 2 /PatternType 1 /TilingType 1 /BBox [0 0 8 8] /XStep 8 /YStep 8} + bind def +/KeepColor {currentrgbcolor [/Pattern /DeviceRGB] setcolorspace} bind def +<< Tile8x8 + /PaintProc {0.5 setlinewidth pop 0 0 M 8 8 L 0 8 M 8 0 L stroke} +>> matrix makepattern +/Pat1 exch def +<< Tile8x8 + /PaintProc {0.5 setlinewidth pop 0 0 M 8 8 L 0 8 M 8 0 L stroke + 0 4 M 4 8 L 8 4 L 4 0 L 0 4 L stroke} +>> matrix makepattern +/Pat2 exch def +<< Tile8x8 + /PaintProc {0.5 setlinewidth pop 0 0 M 0 8 L + 8 8 L 8 0 L 0 0 L fill} +>> matrix makepattern +/Pat3 exch def +<< Tile8x8 + /PaintProc {0.5 setlinewidth pop -4 8 M 8 -4 L + 0 12 M 12 0 L stroke} +>> matrix makepattern +/Pat4 exch def +<< Tile8x8 + /PaintProc {0.5 setlinewidth pop -4 0 M 8 12 L + 0 -4 M 12 8 L stroke} +>> matrix makepattern +/Pat5 exch def +<< Tile8x8 + /PaintProc {0.5 setlinewidth pop -2 8 M 4 -4 L + 0 12 M 8 -4 L 4 12 M 10 0 L stroke} +>> matrix makepattern +/Pat6 exch def +<< Tile8x8 + /PaintProc {0.5 setlinewidth pop -2 0 M 4 12 L + 0 -4 M 8 12 L 4 -4 M 10 8 L stroke} +>> matrix makepattern +/Pat7 exch def +<< Tile8x8 + /PaintProc {0.5 setlinewidth pop 8 -2 M -4 4 L + 12 0 M -4 8 L 12 4 M 0 10 L stroke} +>> matrix makepattern +/Pat8 exch def +<< Tile8x8 + /PaintProc {0.5 setlinewidth pop 0 -2 M 12 4 L + -4 0 M 12 8 L -4 4 M 8 10 L stroke} +>> matrix makepattern +/Pat9 exch def +/Pattern1 {PatternBgnd KeepColor Pat1 setpattern} bind def +/Pattern2 {PatternBgnd KeepColor Pat2 setpattern} bind def +/Pattern3 {PatternBgnd KeepColor Pat3 setpattern} bind def +/Pattern4 {PatternBgnd KeepColor Landscape {Pat5} {Pat4} ifelse setpattern} bind def +/Pattern5 {PatternBgnd KeepColor Landscape {Pat4} {Pat5} ifelse setpattern} bind def +/Pattern6 {PatternBgnd KeepColor Landscape {Pat9} {Pat6} ifelse setpattern} bind def +/Pattern7 {PatternBgnd KeepColor Landscape {Pat8} {Pat7} ifelse setpattern} bind def +} def +% +% +%End of PostScript Level 2 code +% +/PatternBgnd { + TransparentPatterns {} {gsave 1 setgray fill grestore} ifelse +} def +% +% Substitute for Level 2 pattern fill codes with +% grayscale if Level 2 support is not selected. +% +/Level1PatternFill { +/Pattern1 {0.250 Density} bind def +/Pattern2 {0.500 Density} bind def +/Pattern3 {0.750 Density} bind def +/Pattern4 {0.125 Density} bind def +/Pattern5 {0.375 Density} bind def +/Pattern6 {0.625 Density} bind def +/Pattern7 {0.875 Density} bind def +} def +% +% Now test for support of Level 2 code +% +Level1 {Level1PatternFill} {Level2PatternFill} ifelse +% +/Symbol-Oblique /Symbol findfont [1 0 .167 1 0 0] makefont +dup length dict begin {1 index /FID eq {pop pop} {def} ifelse} forall +currentdict end definefont pop +% +/Metrics {ExtendTextBox Gswidth} def +/Lwidth {currentpoint stroke M 0 vshift R Metrics} def +/Rwidth {currentpoint stroke M dup stringwidth pop neg vshift R Metrics} def +/Cwidth {currentpoint stroke M dup stringwidth pop -2 div vshift R Metrics} def +/GLwidth {currentpoint stroke M 0 vshift R {ExtendTextBox} forall} def +/GRwidth {currentpoint stroke M dup Gwidth vshift R {ExtendTextBox} forall} def +/GCwidth {currentpoint stroke M dup Gwidth 2 div vshift R {ExtendTextBox} forall} def +/GLwidth2 {0 Gwidth AddGlyphWidth} def +/GRwidth2 {Gwidth -1 mul 0 AddGlyphWidth} def +/GCwidth2 {Gwidth 2 div dup -1 mul AddGlyphWidth} def +/AddGlyphWidth { dup TBx2 gt {userdict /TBx2 3 -1 roll put} {pop} ifelse + dup TBx1 lt {userdict /TBx1 3 -1 roll put} {pop} ifelse } def +/MFshow { + { dup 5 get 3 ge + { 5 get 3 eq {gsave} {grestore} ifelse } + {dup dup 0 get findfont exch 1 get scalefont setfont + [ currentpoint ] exch dup 2 get 0 exch R dup 5 get 2 ne {dup dup 6 + get exch 4 get {textshow} {Metrics pop 0 R} ifelse }if dup 5 get 0 eq + {dup 3 get {2 get neg 0 exch R pop} {pop aload pop M} ifelse} {dup 5 + get 1 eq {dup 2 get exch dup 3 get exch 6 get Gswidth pop -2 div + dup 0 R} {dup 6 get Gswidth pop -2 div 0 R 6 get + textshow 2 index {aload pop M neg 3 -1 roll neg R pop pop} {pop pop pop + pop aload pop M} ifelse }ifelse }ifelse } + ifelse } + forall} def +/Gswidth {dup type /stringtype eq {stringwidth} {pop (n) stringwidth} ifelse} def +/MFwidth {0 exch { dup 5 get 3 ge { 5 get 3 eq { 0 } { pop } ifelse } + {dup 3 get{dup dup 0 get findfont exch 1 get scalefont setfont + 6 get Gswidth pop add} {pop} ifelse} ifelse} forall} def +/MLshow { currentpoint stroke M + 0 exch R + Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def +/MRshow { currentpoint stroke M + exch dup MFwidth neg 3 -1 roll R + Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def +/MCshow { currentpoint stroke M + exch dup MFwidth -2 div 3 -1 roll R + Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def +/XYsave { [( ) 1 2 true false 3 ()] } bind def +/XYrestore { [( ) 1 2 true false 4 ()] } bind def +Level1 SuppressPDFMark or +{} { +/SDict 10 dict def +systemdict /pdfmark known not { + userdict /pdfmark systemdict /cleartomark get put +} if +SDict begin [ + /Title (/tmp/fir1-vs-firls.eps) + /Subject (gnuplot plot) + /Creator (gnuplot 5.2 patchlevel 2) +% /Producer (gnuplot) +% /Keywords () + /CreationDate (Sat Jan 20 11:47:53 2018) + /DOCINFO pdfmark +end +} ifelse +% +% Support for boxed text - Ethan A Merritt Sep 2016 +% +/InitTextBox { userdict /TBy2 3 -1 roll put userdict /TBx2 3 -1 roll put + userdict /TBy1 3 -1 roll put userdict /TBx1 3 -1 roll put + /Boxing true def } def +/ExtendTextBox { dup type /stringtype eq + { Boxing { gsave dup false charpath pathbbox + dup TBy2 gt {userdict /TBy2 3 -1 roll put} {pop} ifelse + dup TBx2 gt {userdict /TBx2 3 -1 roll put} {pop} ifelse + dup TBy1 lt {userdict /TBy1 3 -1 roll put} {pop} ifelse + dup TBx1 lt {userdict /TBx1 3 -1 roll put} {pop} ifelse + grestore } if } + {} ifelse} def +/PopTextBox { newpath TBx1 TBxmargin sub TBy1 TBymargin sub M + TBx1 TBxmargin sub TBy2 TBymargin add L + TBx2 TBxmargin add TBy2 TBymargin add L + TBx2 TBxmargin add TBy1 TBymargin sub L closepath } def +/DrawTextBox { PopTextBox stroke /Boxing false def} def +/FillTextBox { gsave PopTextBox fill grestore /Boxing false def} def +0 0 0 0 InitTextBox +/TBxmargin 20 def +/TBymargin 20 def +/Boxing false def +/textshow { ExtendTextBox Gshow } def +% +end +%%EndProlog +%%Page: 1 1 +gnudict begin +gsave +doclip +50 50 translate +0.050 0.050 scale +0 setgray +newpath +(Helvetica) findfont 200 scalefont setfont +BackgroundColor 0 lt 3 1 roll 0 lt exch 0 lt or or not {BackgroundColor C 1.000 0 0 11520.00 8640.00 BoxColFill} if +gsave % colour palette begin +/maxcolors 64 def +/HSV2RGB { exch dup 0.0 eq {pop exch pop dup dup} % achromatic gray + { /HSVs exch def /HSVv exch def 6.0 mul dup floor dup 3 1 roll sub + /HSVf exch def /HSVi exch cvi def /HSVp HSVv 1.0 HSVs sub mul def + /HSVq HSVv 1.0 HSVs HSVf mul sub mul def + /HSVt HSVv 1.0 HSVs 1.0 HSVf sub mul sub mul def + /HSVi HSVi 6 mod def 0 HSVi eq {HSVv HSVt HSVp} + {1 HSVi eq {HSVq HSVv HSVp}{2 HSVi eq {HSVp HSVv HSVt} + {3 HSVi eq {HSVp HSVq HSVv}{4 HSVi eq {HSVt HSVp HSVv} + {HSVv HSVp HSVq} ifelse} ifelse} ifelse} ifelse} ifelse + } ifelse} def +/Constrain { + dup 0 lt {0 exch pop}{dup 1 gt {1 exch pop} if} ifelse} def +/YIQ2RGB { + 3 copy -1.702 mul exch -1.105 mul add add Constrain 4 1 roll + 3 copy -0.647 mul exch -0.272 mul add add Constrain 5 1 roll + 0.621 mul exch -0.956 mul add add Constrain 3 1 roll } def +/CMY2RGB { 1 exch sub exch 1 exch sub 3 2 roll 1 exch sub 3 1 roll exch } def +/XYZ2RGB { 3 copy -0.9017 mul exch -0.1187 mul add exch 0.0585 mul exch add + Constrain 4 1 roll 3 copy -0.0279 mul exch 1.999 mul add exch + -0.9844 mul add Constrain 5 1 roll -0.2891 mul exch -0.5338 mul add + exch 1.91 mul exch add Constrain 3 1 roll} def +/SelectSpace {ColorSpace (HSV) eq {HSV2RGB}{ColorSpace (XYZ) eq { + XYZ2RGB}{ColorSpace (CMY) eq {CMY2RGB}{ColorSpace (YIQ) eq {YIQ2RGB} + if} ifelse} ifelse} ifelse} def +/InterpolatedColor true def +/grayindex {/gidx 0 def + {GrayA gidx get grayv ge {exit} if /gidx gidx 1 add def} loop} def +/dgdx {grayv GrayA gidx get sub GrayA gidx 1 sub get + GrayA gidx get sub div} def +/redvalue {RedA gidx get RedA gidx 1 sub get + RedA gidx get sub dgdxval mul add} def +/greenvalue {GreenA gidx get GreenA gidx 1 sub get + GreenA gidx get sub dgdxval mul add} def +/bluevalue {BlueA gidx get BlueA gidx 1 sub get + BlueA gidx get sub dgdxval mul add} def +/interpolate { + grayindex grayv GrayA gidx get sub abs 1e-5 le + {RedA gidx get GreenA gidx get BlueA gidx get} + {/dgdxval dgdx def redvalue greenvalue bluevalue} ifelse} def +/GrayA [0 .0159 .0317 .0476 .0635 .0794 .0952 .1111 .127 .1429 .1587 .1746 + .1905 .2063 .2222 .2381 .254 .2698 .2857 .3016 .3175 .3333 .3492 .3651 + .381 .3968 .4127 .4286 .4444 .4603 .4762 .4921 .5079 .5238 .5397 .5556 + .5714 .5873 .6032 .619 .6349 .6508 .6667 .6825 .6984 .7143 .7302 .746 + .7619 .7778 .7937 .8095 .8254 .8413 .8571 .873 .8889 .9048 .9206 .9365 + .9524 .9683 .9841 1 ] def +/RedA [.267 .2727 .2771 .2804 .2824 .2832 .2828 .2812 .2785 .2747 .27 .2644 + .258 .2511 .2437 .2361 .2283 .2204 .2127 .2051 .1977 .1906 .1838 .1773 + .171 .1648 .1588 .153 .1471 .1414 .1358 .1306 .1259 .1222 .1199 .1196 .122 + .1277 .1368 .1496 .166 .1855 .208 .2331 .2605 .29 .3213 .3544 .3889 .4249 + .4622 .5008 .5403 .5809 .6222 .6641 .7064 .7489 .7913 .8333 .8747 .9153 + .9548 .9932 ] def +/GreenA [.0049 .0258 .0509 .0742 .096 .1169 .1374 .1575 .1773 .197 .2163 + .2354 .2542 .2726 .2906 .3083 .3256 .3425 .3591 .3754 .3913 .4071 .4226 + .4379 .4531 .4681 .4831 .4981 .513 .5279 .5428 .5577 .5726 .5875 .6024 + .6173 .6321 .6469 .6616 .6761 .6905 .7047 .7187 .7324 .7458 .7588 .7715 + .7837 .7955 .8067 .8173 .8274 .8369 .8457 .8538 .8613 .8682 .8745 .8803 + .8858 .8909 .896 .901 .9062 ] def +/BlueA [.3294 .3534 .3762 .3979 .4183 .4372 .4546 .4704 .4847 .4973 .5083 + .5177 .5258 .5325 .5381 .5427 .5463 .5493 .5516 .5535 .555 .5561 .557 + .5576 .558 .5581 .5581 .5577 .557 .5559 .5543 .5522 .5494 .546 .5418 .5368 + .5308 .5239 .516 .5069 .4968 .4854 .4729 .4591 .4441 .4278 .4103 .3915 + .3714 .3501 .3275 .3038 .2789 .253 .2262 .1989 .1715 .145 .1213 .1033 + .0954 .1005 .1179 .1439 ] def +/pm3dround {maxcolors 0 gt {dup 1 ge + {pop 1} {maxcolors mul floor maxcolors 1 sub div} ifelse} if} def +/pm3dGamma 1.0 1.5 Gamma mul div def +/ColorSpace (RGB) def +Color InterpolatedColor or { % COLOUR vs. GRAY map + InterpolatedColor { %% Interpolation vs. RGB-Formula + /g {stroke pm3dround /grayv exch def interpolate + SelectSpace setrgbcolor} bind def + }{ + /g {stroke pm3dround dup cF7 Constrain exch dup cF5 Constrain exch cF15 Constrain + SelectSpace setrgbcolor} bind def + } ifelse +}{ + /g {stroke pm3dround pm3dGamma exp setgray} bind def +} ifelse +1.000 UL +LTb +1.00 1.00 1.00 C 1.000 1497 5067 8926 2923 BoxColFill +1.000 UL +LTb +0.00 0.00 0.00 C 1497 5067 M +88 0 V +stroke +0.15 0.15 0.15 C 1377 5067 M +[ [(Helvetica) 260.0 0.0 true true 0 (-200)] +] -66.7 MRshow +1.000 UL +LTb +0.00 0.00 0.00 C 1497 5798 M +88 0 V +stroke +0.15 0.15 0.15 C 1377 5798 M +[ [(Helvetica) 260.0 0.0 true true 0 (-150)] +] -66.7 MRshow +1.000 UL +LTb +0.00 0.00 0.00 C 1497 6529 M +88 0 V +stroke +0.15 0.15 0.15 C 1377 6529 M +[ [(Helvetica) 260.0 0.0 true true 0 (-100)] +] -66.7 MRshow +1.000 UL +LTb +0.00 0.00 0.00 C 1497 7260 M +88 0 V +stroke +0.15 0.15 0.15 C 1377 7260 M +[ [(Helvetica) 260.0 0.0 true true 0 (-50)] +] -66.7 MRshow +1.000 UL +LTb +0.00 0.00 0.00 C 1497 7991 M +88 0 V +stroke +0.15 0.15 0.15 C 1377 7991 M +[ [(Helvetica) 260.0 0.0 true true 0 (0)] +] -66.7 MRshow +1.000 UL +LTb +0.00 0.00 0.00 C 1497 5067 M +0 88 V +stroke +0.15 0.15 0.15 C 1497 4867 M +[ [(Helvetica) 260.0 0.0 true true 0 (0)] +] -66.7 MCshow +1.000 UL +LTb +0.00 0.00 0.00 C 3282 5067 M +0 88 V +stroke +0.15 0.15 0.15 C 3282 4867 M +[ [(Helvetica) 260.0 0.0 true true 0 (50)] +] -66.7 MCshow +1.000 UL +LTb +0.00 0.00 0.00 C 5068 5067 M +0 88 V +stroke +0.15 0.15 0.15 C 5068 4867 M +[ [(Helvetica) 260.0 0.0 true true 0 (100)] +] -66.7 MCshow +1.000 UL +LTb +0.00 0.00 0.00 C 6853 5067 M +0 88 V +stroke +0.15 0.15 0.15 C 6853 4867 M +[ [(Helvetica) 260.0 0.0 true true 0 (150)] +] -66.7 MCshow +1.000 UL +LTb +0.00 0.00 0.00 C 8639 5067 M +0 88 V +stroke +0.15 0.15 0.15 C 8639 4867 M +[ [(Helvetica) 260.0 0.0 true true 0 (200)] +] -66.7 MCshow +1.000 UL +LTb +0.00 0.00 0.00 C 10424 5067 M +0 88 V +stroke +0.15 0.15 0.15 C 10424 4867 M +[ [(Helvetica) 260.0 0.0 true true 0 (250)] +] -66.7 MCshow +1.000 UL +LTb +0.00 0.00 0.00 C 1.000 UP +1.000 UL +LTb +0.00 0.00 0.00 C 0.15 0.15 0.15 C 697 6529 M +currentpoint gsave translate 90 rotate 0 0 moveto +[ [(Helvetica) 280.0 0.0 true true 0 (Magnitude \(dB\))] +] -73.3 MCshow +grestore +LTb +0.15 0.15 0.15 C 5960 4567 M +[ [(Helvetica) 280.0 0.0 true true 0 (Number of coefficients)] +] -73.3 MCshow +LTb +0.00 0.00 0.00 C 5960 8311 M +[ [(:Bold) 280.0 0.0 true true 0 (Comparison between two coefficient generation methods)] +] -73.3 MCshow +LTb +1.000 UL +LTb +LCb setrgbcolor +6881 5928 N +0 2000 V +3423 0 V +0 -2000 V +-3423 0 V 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