Education Sampler 1992 [NeXTSTEP]/Education_1992_Sampler.iso/SoundAndMusic/resample/testFilter.ma

Text File | 1991-06-22 | 39KB | 1,647 lines

(*^

::[paletteColors = 128;
    fontset = title, "Times-Bold", 24, L2, center, bold, nohscroll;
    fontset = subtitle, "Times-Bold", 18, L2, center, bold, nohscroll;
    fontset = subsubtitle, "Times-Bold", 14, L2, center, bold, nohscroll;
    fontset = section, "Times-Bold", 18, L2, bold, nohscroll, grayBox;
    fontset = subsection, "Times-Bold", 14, L2, bold, nohscroll, blackBox;
    fontset = subsubsection, "Times-Bold", 12, L2, bold, nohscroll, whiteBox;
    fontset = text, "Times-Roman", 12, L2, nohscroll;
    fontset = smalltext, "Times-Roman", 10, L2, nohscroll;
    fontset = input, "Courier-Bold", 12, L2, bold, nowordwrap;
    fontset = output, "Courier", 12, L2, nowordwrap;
    fontset = message, "Courier", 12, L2, R21845, G21845, B21845, nowordwrap;
    fontset = print, "Courier", 12, L2, nowordwrap;
    fontset = info, "Courier", 12, L2, nowordwrap;
    fontset = postscript, "Courier", 12, L2, nowordwrap;
    fontset = name, "Times-Italic", 11, L2, italic, R21845, G21845, B21845, nowordwrap, nohscroll;
    fontset = header, "Times", 10, L2;
    fontset = footer, "Times", 12, L2, center;
    fontset = help, "Times-Roman", 14, L2, nohscroll;
    fontset = clipboard, "New York", 12, L2;
    fontset = completions, "Courier", 16, L2, nowordwrap;
    fontset = network, "Courier", 10, L2, nowordwrap;
    fontset = graphlabel, "Courier", 12, L2, nowordwrap;
    fontset = special1, "New York", 12, L2, nowordwrap;
    fontset = special2, "New York", 12, L2, center, nowordwrap;
    fontset = special3, "New York", 12, L2, right, nowordwrap;
    fontset = special4, "New York", 12, L2, nowordwrap;
    fontset = special5, "New York", 12, L2, nowordwrap;]
:[font = title; inactive; ]
FIR Filter Test
:[font = subtitle; inactive; ]
To display FIR filter designed by program windowfilter
for use in program resample
:[font = section; inactive; startGroup; ]
Usage
:[font = subsubsection; inactive; ]
Rename the filter written by windowfilter to 'test.filter'
:[font = subsubsection; inactive; ]
Execute the testFilter shell script in this directory
:[font = subsubsection; inactive; ]
Make sure there is a symbolic link from this directory to /
:[font = subsubsection; inactive; endGroup; ]
Select all cells in this document (via %A) and press the Enter key
:[font = section; inactive; startGroup; ]
Load and Display FIR Impulse Resonse
:[font = input; ]
d = ReadList["/resample/ir.dat",Number] * 2^-15; (* [-1.0,1.0) *)
:[font = text; inactive; ]
The above requires a soft-link from the resample directory to /
:[font = input; startGroup; ]
len = Length[d]
:[font = output; inactive; output; endGroup; ]
78
;[o]
78
:[font = input; startGroup; ]
ListPlot[d,PlotJoined->True,PlotRange->All];
:[font = postscript; inactive; PostScript; output; endGroup; endGroup; pictureLeft = 39; pictureWidth = 282; pictureHeight = 174; preserveAspect; ]
%!
%%Creator: Mathematica
%%AspectRatio: 0.61803
MathPictureStart
% Scaling calculations
0.01144 0.01237 0.11103 0.54923 [
[(20)] 0.25881 0.09853 0 1 Msboxa
[(40)] 0.50618 0.09853 0 1 Msboxa
[(60)] 0.75356 0.09853 0 1 Msboxa
[(-0.2)] -0.00106 0.00118 1 0 Msboxa
[(0.2)] -0.00106 0.22087 1 0 Msboxa
[(0.4)] -0.00106 0.33072 1 0 Msboxa
[(0.6)] -0.00106 0.44056 1 0 Msboxa
[(0.8)] -0.00106 0.55041 1 0 Msboxa
[ -0.001 -0.001 0 0 ]
[ 1.001 0.61903 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
%%Object: Graphics
[ ] 0 setdash
0 setgray
gsave
gsave
0.002 setlinewidth
0 0.11103 moveto
1 0.11103 lineto
stroke
0.25881 0.10478 moveto
0.25881 0.11728 lineto
stroke
0 setgray
[(20)] 0.25881 0.09853 0 1 Mshowa
0.50618 0.10478 moveto
0.50618 0.11728 lineto
stroke
0 setgray
[(40)] 0.50618 0.09853 0 1 Mshowa
0.75356 0.10478 moveto
0.75356 0.11728 lineto
stroke
0 setgray
[(60)] 0.75356 0.09853 0 1 Mshowa
0.01144 0 moveto
0.01144 0.61803 lineto
stroke
0.00519 0.00118 moveto
0.01769 0.00118 lineto
stroke
0 setgray
[(-0.2)] -0.00106 0.00118 1 0 Mshowa
0.00519 0.22087 moveto
0.01769 0.22087 lineto
stroke
0 setgray
[(0.2)] -0.00106 0.22087 1 0 Mshowa
0.00519 0.33072 moveto
0.01769 0.33072 lineto
stroke
0 setgray
[(0.4)] -0.00106 0.33072 1 0 Mshowa
0.00519 0.44056 moveto
0.01769 0.44056 lineto
stroke
0 setgray
[(0.6)] -0.00106 0.44056 1 0 Mshowa
0.00519 0.55041 moveto
0.01769 0.55041 lineto
stroke
0 setgray
[(0.8)] -0.00106 0.55041 1 0 Mshowa
grestore
grestore
0 0 moveto
1 0 lineto
1 0.618034 lineto
0 0.618034 lineto
closepath
clip
newpath
0 setgray
0.004 setlinewidth
0.02381 0.11104 moveto
0.03618 0.11111 lineto
0.04855 0.11111 lineto
0.06092 0.11103 lineto
0.07328 0.11084 lineto
0.08565 0.11059 lineto
0.09802 0.11047 lineto
0.11039 0.11069 lineto
0.12276 0.11133 lineto
0.13513 0.11225 lineto
0.1475 0.11292 lineto
0.15986 0.11262 lineto
0.17223 0.11108 lineto
0.1846 0.10863 lineto
0.19697 0.10643 lineto
0.20934 0.10603 lineto
0.22171 0.10866 lineto
0.23408 0.11391 lineto
0.24644 0.11967 lineto
0.25881 0.12261 lineto
0.27118 0.11967 lineto
0.28355 0.11047 lineto
0.29592 0.09807 lineto
0.30829 0.08875 lineto
0.32066 0.08912 lineto
0.33302 0.10236 lineto
0.34539 0.12526 lineto
0.35776 0.14788 lineto
0.37013 0.15708 lineto
0.3825 0.14285 lineto
0.39487 0.10496 lineto
0.40724 0.0561 lineto
0.4196 0.01973 lineto
0.43197 0.02177 lineto
0.44434 0.07963 lineto
0.45671 0.19269 lineto
0.46908 0.33926 lineto
0.48145 0.48192 lineto
0.49382 0.57979 lineto
0.50618 0.60332 lineto
0.51855 0.54524 lineto
0.53092 0.42337 lineto
0.54329 0.27388 lineto
0.55566 0.13789 lineto
0.56803 0.0473 lineto
0.5804 0.01472 lineto
0.59276 0.03221 lineto
0.60513 0.07725 lineto
0.6175 0.12375 lineto
0.62987 0.15221 lineto
Mistroke
0.64224 0.15554 lineto
0.65461 0.13895 lineto
0.66698 0.11466 lineto
0.67934 0.09509 lineto
0.69171 0.08746 lineto
0.70408 0.09195 lineto
0.71645 0.10347 lineto
0.72882 0.1151 lineto
0.74119 0.12175 lineto
0.75356 0.1219 lineto
0.76592 0.11733 lineto
0.77829 0.11141 lineto
0.79066 0.10715 lineto
0.80303 0.10588 lineto
0.8154 0.10724 lineto
0.82777 0.10975 lineto
0.84014 0.1119 lineto
0.8525 0.11289 lineto
0.86487 0.1127 lineto
0.87724 0.11186 lineto
0.88961 0.11103 lineto
0.90198 0.11054 lineto
0.91435 0.11047 lineto
0.92672 0.11069 lineto
0.93908 0.11092 lineto
0.95145 0.11108 lineto
0.96382 0.11111 lineto
0.97619 0.11108 lineto
Mfstroke
% End of Graphics
MathPictureEnd
:[font = section; inactive; startGroup; ]
Compute and Display Frequency Response
:[font = input; startGroup; Cclosed; ]
padlen = N[2^(4+Floor[Log[2,len]])]
:[font = output; inactive; output; ]
1024.
;[o]
1024.
:[font = input; ]
d = Flatten[{d,Table[0,{padlen-len}]}];
:[font = input; startGroup; ]
Length[d]
:[font = output; inactive; output; endGroup; ]
1024
;[o]
1024
:[font = input; ]
f = Fourier[d];
:[font = input; startGroup; ]
lf = Length[f]
:[font = output; inactive; output; endGroup; ]
1024
;[o]
1024
:[font = input; ]
pf = Take[f,{1,Floor[lf/2]}];
:[font = input; ]
fs = Re[pf * Conjugate[pf]];
:[font = input; startGroup; ]
mfs = Max[fs]
:[font = output; inactive; output; endGroup; ]
0.0157216946498225
;[o]
0.0157217
:[font = input; ]
onfs = fs * (1/mfs) + 10^-10;
:[font = input; endGroup; ]
nfsdb = 10*Log[10,onfs];
:[font = input; startGroup; ]
ListPlot[nfsdb,PlotJoined->True,PlotRange->{-100,10}];
:[font = postscript; inactive; PostScript; output; endGroup; endGroup; pictureLeft = 39; pictureWidth = 282; pictureHeight = 174; preserveAspect; ]
%!
%%Creator: Mathematica
%%AspectRatio: 0.61803
MathPictureStart
% Scaling calculations
0.02381 0.00186 0.56185 0.00562 [
[(100)] 0.20982 0.54935 0 1 Msboxa
[(200)] 0.39583 0.54935 0 1 Msboxa
[(300)] 0.58185 0.54935 0 1 Msboxa
[(400)] 0.76786 0.54935 0 1 Msboxa
[(500)] 0.95387 0.54935 0 1 Msboxa
[(-100)] 0.01131 0 1 0 Msboxa
[(-80)] 0.01131 0.11237 1 0 Msboxa
[(-60)] 0.01131 0.22474 1 0 Msboxa
[(-40)] 0.01131 0.33711 1 0 Msboxa
[(-20)] 0.01131 0.44948 1 0 Msboxa
[ -0.001 -0.001 0 0 ]
[ 1.001 0.61903 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
%%Object: Graphics
[ ] 0 setdash
0 setgray
gsave
gsave
0.002 setlinewidth
0 0.56185 moveto
1 0.56185 lineto
stroke
0.20982 0.5556 moveto
0.20982 0.5681 lineto
stroke
0 setgray
[(100)] 0.20982 0.54935 0 1 Mshowa
0.39583 0.5556 moveto
0.39583 0.5681 lineto
stroke
0 setgray
[(200)] 0.39583 0.54935 0 1 Mshowa
0.58185 0.5556 moveto
0.58185 0.5681 lineto
stroke
0 setgray
[(300)] 0.58185 0.54935 0 1 Mshowa
0.76786 0.5556 moveto
0.76786 0.5681 lineto
stroke
0 setgray
[(400)] 0.76786 0.54935 0 1 Mshowa
0.95387 0.5556 moveto
0.95387 0.5681 lineto
stroke
0 setgray
[(500)] 0.95387 0.54935 0 1 Mshowa
0.02381 0 moveto
0.02381 0.61803 lineto
stroke
0.01756 0 moveto
0.03006 0 lineto
stroke
0 setgray
[(-100)] 0.01131 0 1 0 Mshowa
0.01756 0.11237 moveto
0.03006 0.11237 lineto
stroke
0 setgray
[(-80)] 0.01131 0.11237 1 0 Mshowa
0.01756 0.22474 moveto
0.03006 0.22474 lineto
stroke
0 setgray
[(-60)] 0.01131 0.22474 1 0 Mshowa
0.01756 0.33711 moveto
0.03006 0.33711 lineto
stroke
0 setgray
[(-40)] 0.01131 0.33711 1 0 Mshowa
0.01756 0.44948 moveto
0.03006 0.44948 lineto
stroke
0 setgray
[(-20)] 0.01131 0.44948 1 0 Mshowa
grestore
grestore
0 0 moveto
1 0 lineto
1 0.618034 lineto
0 0.618034 lineto
closepath
clip
newpath
0 setgray
0.004 setlinewidth
0.02567 0.56182 moveto
0.02753 0.56182 lineto
0.02939 0.56182 lineto
0.03125 0.56182 lineto
0.03311 0.56182 lineto
0.03497 0.56183 lineto
0.03683 0.56183 lineto
0.03869 0.56183 lineto
0.04055 0.56183 lineto
0.04241 0.56183 lineto
0.04427 0.56184 lineto
0.04613 0.56184 lineto
0.04799 0.56184 lineto
0.04985 0.56184 lineto
0.05171 0.56184 lineto
0.05357 0.56185 lineto
0.05543 0.56185 lineto
0.05729 0.56185 lineto
0.05915 0.56185 lineto
0.06101 0.56185 lineto
0.06287 0.56185 lineto
0.06473 0.56185 lineto
0.06659 0.56185 lineto
0.06845 0.56185 lineto
0.07031 0.56185 lineto
0.07217 0.56185 lineto
0.07403 0.56185 lineto
0.07589 0.56184 lineto
0.07775 0.56184 lineto
0.07961 0.56184 lineto
0.08147 0.56184 lineto
0.08333 0.56184 lineto
0.08519 0.56184 lineto
0.08705 0.56184 lineto
0.08891 0.56184 lineto
0.09077 0.56184 lineto
0.09263 0.56184 lineto
0.09449 0.56184 lineto
0.09635 0.56184 lineto
0.09821 0.56184 lineto
0.10007 0.56184 lineto
0.10193 0.56184 lineto
0.10379 0.56184 lineto
0.10565 0.56184 lineto
0.10751 0.56184 lineto
0.10938 0.56184 lineto
0.11124 0.56184 lineto
0.1131 0.56184 lineto
0.11496 0.56184 lineto
0.11682 0.56184 lineto
Mistroke
0.11868 0.56184 lineto
0.12054 0.56184 lineto
0.1224 0.56184 lineto
0.12426 0.56184 lineto
0.12612 0.56184 lineto
0.12798 0.56184 lineto
0.12984 0.56184 lineto
0.1317 0.56184 lineto
0.13356 0.56185 lineto
0.13542 0.56185 lineto
0.13728 0.56185 lineto
0.13914 0.56185 lineto
0.141 0.56185 lineto
0.14286 0.56185 lineto
0.14472 0.56185 lineto
0.14658 0.56185 lineto
0.14844 0.56185 lineto
0.1503 0.56185 lineto
0.15216 0.56185 lineto
0.15402 0.56184 lineto
0.15588 0.56184 lineto
0.15774 0.56184 lineto
0.1596 0.56184 lineto
0.16146 0.56184 lineto
0.16332 0.56184 lineto
0.16518 0.56184 lineto
0.16704 0.56184 lineto
0.1689 0.56184 lineto
0.17076 0.56184 lineto
0.17262 0.56184 lineto
0.17448 0.56183 lineto
0.17634 0.56182 lineto
0.1782 0.5618 lineto
0.18006 0.56177 lineto
0.18192 0.56173 lineto
0.18378 0.56168 lineto
0.18564 0.56161 lineto
0.1875 0.56152 lineto
0.18936 0.5614 lineto
0.19122 0.56126 lineto
0.19308 0.56108 lineto
0.19494 0.56086 lineto
0.1968 0.56059 lineto
0.19866 0.56028 lineto
0.20052 0.55991 lineto
0.20238 0.55948 lineto
0.20424 0.55898 lineto
0.2061 0.5584 lineto
0.20796 0.55774 lineto
0.20982 0.557 lineto
Mistroke
0.21168 0.55615 lineto
0.21354 0.55521 lineto
0.2154 0.55416 lineto
0.21726 0.55299 lineto
0.21912 0.5517 lineto
0.22098 0.55028 lineto
0.22284 0.54873 lineto
0.2247 0.54703 lineto
0.22656 0.54519 lineto
0.22842 0.54318 lineto
0.23028 0.54102 lineto
0.23214 0.53869 lineto
0.234 0.53618 lineto
0.23586 0.53349 lineto
0.23772 0.53062 lineto
0.23958 0.52754 lineto
0.24144 0.52426 lineto
0.2433 0.52077 lineto
0.24516 0.51706 lineto
0.24702 0.51313 lineto
0.24888 0.50895 lineto
0.25074 0.50454 lineto
0.2526 0.49987 lineto
0.25446 0.49493 lineto
0.25632 0.48972 lineto
0.25818 0.48423 lineto
0.26004 0.47844 lineto
0.2619 0.47233 lineto
0.26376 0.4659 lineto
0.26563 0.45912 lineto
0.26749 0.45199 lineto
0.26935 0.44447 lineto
0.27121 0.43655 lineto
0.27307 0.42821 lineto
0.27493 0.41941 lineto
0.27679 0.41012 lineto
0.27865 0.40031 lineto
0.28051 0.38993 lineto
0.28237 0.37894 lineto
0.28423 0.36727 lineto
0.28609 0.35485 lineto
0.28795 0.3416 lineto
0.28981 0.3274 lineto
0.29167 0.31212 lineto
0.29353 0.29557 lineto
0.29539 0.27749 lineto
0.29725 0.25754 lineto
0.29911 0.23517 lineto
0.30097 0.20948 lineto
0.30283 0.17883 lineto
Mistroke
0.30469 0.13964 lineto
0.30655 0.08423 lineto
0.30841 0.06644 lineto
0.31027 0.08171 lineto
0.31213 0.07892 lineto
0.31399 0.0635 lineto
0.31585 0.03497 lineto
0.31771 0.0012 lineto
0.31957 0.01596 lineto
0.32143 0.03058 lineto
0.32329 0.03393 lineto
0.32515 0.0315 lineto
0.32701 0.03074 lineto
0.32887 0.03767 lineto
0.33073 0.04836 lineto
0.33259 0.05738 lineto
0.33445 0.06301 lineto
0.33631 0.06504 lineto
0.33817 0.06348 lineto
0.34003 0.05816 lineto
0.34189 0.04858 lineto
0.34375 0.03418 lineto
0.34561 0.01758 lineto
0.34747 0.01546 lineto
0.34933 0.03111 lineto
0.35119 0.04637 lineto
0.35305 0.05732 lineto
0.35491 0.06467 lineto
0.35677 0.06933 lineto
0.35863 0.07197 lineto
0.36049 0.07317 lineto
0.36235 0.07342 lineto
0.36421 0.07322 lineto
0.36607 0.073 lineto
0.36793 0.07306 lineto
0.36979 0.0735 lineto
0.37165 0.07421 lineto
0.37351 0.075 lineto
0.37537 0.07568 lineto
0.37723 0.07611 lineto
0.37909 0.07626 lineto
0.38095 0.07619 lineto
0.38281 0.07599 lineto
0.38467 0.07582 lineto
0.38653 0.0758 lineto
0.38839 0.07599 lineto
0.39025 0.07643 lineto
0.39211 0.07707 lineto
0.39397 0.07786 lineto
0.39583 0.07876 lineto
Mistroke
0.39769 0.07973 lineto
0.39955 0.08073 lineto
0.40141 0.08174 lineto
0.40327 0.08267 lineto
0.40513 0.08343 lineto
0.40699 0.08387 lineto
0.40885 0.08383 lineto
0.41071 0.08313 lineto
0.41257 0.08158 lineto
0.41443 0.07895 lineto
0.41629 0.07502 lineto
0.41815 0.06949 lineto
0.42001 0.06201 lineto
0.42188 0.05216 lineto
0.42374 0.03969 lineto
0.4256 0.0259 lineto
0.42746 0.0177 lineto
0.42932 0.02287 lineto
0.43118 0.03419 lineto
0.43304 0.04418 lineto
0.4349 0.05126 lineto
0.43676 0.05547 lineto
0.43862 0.05709 lineto
0.44048 0.05628 lineto
0.44234 0.05317 lineto
0.4442 0.04805 lineto
0.44606 0.04194 lineto
0.44792 0.03775 lineto
0.44978 0.03955 lineto
0.45164 0.04746 lineto
0.4535 0.05752 lineto
0.45536 0.06688 lineto
0.45722 0.07461 lineto
0.45908 0.08056 lineto
0.46094 0.08484 lineto
0.4628 0.08754 lineto
0.46466 0.08877 lineto
0.46652 0.08856 lineto
0.46838 0.08693 lineto
0.47024 0.08385 lineto
0.4721 0.07922 lineto
0.47396 0.07292 lineto
0.47582 0.06474 lineto
0.47768 0.05451 lineto
0.47954 0.04243 lineto
0.4814 0.03041 lineto
0.48326 0.02443 lineto
0.48512 0.0291 lineto
0.48698 0.03916 lineto
0.48884 0.0492 lineto
Mistroke
0.4907 0.0577 lineto
0.49256 0.06467 lineto
0.49442 0.07037 lineto
0.49628 0.07502 lineto
0.49814 0.07878 lineto
0.5 0.08172 lineto
0.50186 0.08386 lineto
0.50372 0.08514 lineto
0.50558 0.08548 lineto
0.50744 0.08476 lineto
0.5093 0.08283 lineto
0.51116 0.07945 lineto
0.51302 0.07429 lineto
0.51488 0.06684 lineto
0.51674 0.05625 lineto
0.5186 0.041 lineto
0.52046 0.01906 lineto
0.52232 0.00011 lineto
0.52418 0.01837 lineto
0.52604 0.04175 lineto
0.5279 0.05835 lineto
0.52976 0.07013 lineto
0.53162 0.07866 lineto
0.53348 0.08478 lineto
0.53534 0.08901 lineto
0.5372 0.09165 lineto
0.53906 0.0929 lineto
0.54092 0.0929 lineto
0.54278 0.09171 lineto
0.54464 0.0894 lineto
0.5465 0.08604 lineto
0.54836 0.08168 lineto
0.55022 0.07648 lineto
0.55208 0.07071 lineto
0.55394 0.06486 lineto
0.5558 0.05973 lineto
0.55766 0.05623 lineto
0.55952 0.0549 lineto
0.56138 0.0555 lineto
0.56324 0.05721 lineto
0.5651 0.05916 lineto
0.56696 0.06075 lineto
0.56882 0.06165 lineto
0.57068 0.06168 lineto
0.57254 0.06074 lineto
0.5744 0.05878 lineto
0.57626 0.05573 lineto
0.57813 0.05159 lineto
0.57999 0.04639 lineto
0.58185 0.04044 lineto
Mistroke
0.58371 0.03459 lineto
0.58557 0.03062 lineto
0.58743 0.03057 lineto
0.58929 0.03475 lineto
0.59115 0.04128 lineto
0.59301 0.04817 lineto
0.59487 0.05429 lineto
0.59673 0.05923 lineto
0.59859 0.06287 lineto
0.60045 0.0652 lineto
0.60231 0.06625 lineto
0.60417 0.06608 lineto
0.60603 0.06479 lineto
0.60789 0.06255 lineto
0.60975 0.05966 lineto
0.61161 0.0567 lineto
0.61347 0.05443 lineto
0.61533 0.05366 lineto
0.61719 0.05465 lineto
0.61905 0.05695 lineto
0.62091 0.05967 lineto
0.62277 0.06194 lineto
0.62463 0.06316 lineto
0.62649 0.06287 lineto
0.62835 0.06068 lineto
0.63021 0.05618 lineto
0.63207 0.04884 lineto
0.63393 0.03824 lineto
0.63579 0.02595 lineto
0.63765 0.02209 lineto
0.63951 0.03489 lineto
0.64137 0.052 lineto
0.64323 0.0665 lineto
0.64509 0.07788 lineto
0.64695 0.08665 lineto
0.64881 0.09327 lineto
0.65067 0.09807 lineto
0.65253 0.10125 lineto
0.65439 0.10291 lineto
0.65625 0.10312 lineto
0.65811 0.10184 lineto
0.65997 0.099 lineto
0.66183 0.09449 lineto
0.66369 0.0881 lineto
0.66555 0.07968 lineto
0.66741 0.06946 lineto
0.66927 0.05933 lineto
0.67113 0.05484 lineto
0.67299 0.06011 lineto
0.67485 0.07032 lineto
Mistroke
0.67671 0.08029 lineto
0.67857 0.08839 lineto
0.68043 0.09447 lineto
0.68229 0.0987 lineto
0.68415 0.10127 lineto
0.68601 0.1023 lineto
0.68787 0.10185 lineto
0.68973 0.09994 lineto
0.69159 0.09651 lineto
0.69345 0.09144 lineto
0.69531 0.08452 lineto
0.69717 0.07547 lineto
0.69903 0.06395 lineto
0.70089 0.05003 lineto
0.70275 0.03641 lineto
0.70461 0.03202 lineto
0.70647 0.04011 lineto
0.70833 0.05133 lineto
0.71019 0.06069 lineto
0.71205 0.06757 lineto
0.71391 0.07229 lineto
0.71577 0.07523 lineto
0.71763 0.07671 lineto
0.71949 0.077 lineto
0.72135 0.07638 lineto
0.72321 0.07509 lineto
0.72507 0.07342 lineto
0.72693 0.07165 lineto
0.72879 0.07005 lineto
0.73065 0.06876 lineto
0.73251 0.06781 lineto
0.73438 0.06706 lineto
0.73624 0.06627 lineto
0.7381 0.06516 lineto
0.73996 0.06343 lineto
0.74182 0.06084 lineto
0.74368 0.0571 lineto
0.74554 0.05195 lineto
0.7474 0.04507 lineto
0.74926 0.03612 lineto
0.75112 0.02516 lineto
0.75298 0.01422 lineto
0.75484 0.01064 lineto
0.7567 0.0193 lineto
0.75856 0.03281 lineto
0.76042 0.04544 lineto
0.76228 0.05601 lineto
0.76414 0.06468 lineto
0.766 0.07178 lineto
0.76786 0.07756 lineto
Mistroke
0.76972 0.08224 lineto
0.77158 0.08597 lineto
0.77344 0.08884 lineto
0.7753 0.09095 lineto
0.77716 0.09233 lineto
0.77902 0.09304 lineto
0.78088 0.09312 lineto
0.78274 0.09257 lineto
0.7846 0.09143 lineto
0.78646 0.08972 lineto
0.78832 0.08747 lineto
0.79018 0.08469 lineto
0.79204 0.0814 lineto
0.7939 0.07764 lineto
0.79576 0.07342 lineto
0.79762 0.06873 lineto
0.79948 0.06355 lineto
0.80134 0.0578 lineto
0.8032 0.05136 lineto
0.80506 0.04402 lineto
0.80692 0.03548 lineto
0.80878 0.02547 lineto
0.81064 0.01414 lineto
0.8125 0.00366 lineto
0.81436 0.00063 lineto
0.81622 0.00869 lineto
0.81808 0.02136 lineto
0.81994 0.0335 lineto
0.8218 0.04388 lineto
0.82366 0.05254 lineto
0.82552 0.05975 lineto
0.82738 0.06575 lineto
0.82924 0.07075 lineto
0.8311 0.07489 lineto
0.83296 0.0783 lineto
0.83482 0.08106 lineto
0.83668 0.08326 lineto
0.83854 0.08495 lineto
0.8404 0.08617 lineto
0.84226 0.08695 lineto
0.84412 0.08734 lineto
0.84598 0.08736 lineto
0.84784 0.08706 lineto
0.8497 0.08649 lineto
0.85156 0.08575 lineto
0.85342 0.08492 lineto
0.85528 0.08413 lineto
0.85714 0.0835 lineto
0.859 0.08313 lineto
0.86086 0.08308 lineto
Mistroke
0.86272 0.08333 lineto
0.86458 0.08377 lineto
0.86644 0.08426 lineto
0.8683 0.08461 lineto
0.87016 0.08464 lineto
0.87202 0.08416 lineto
0.87388 0.08302 lineto
0.87574 0.08106 lineto
0.8776 0.07814 lineto
0.87946 0.07411 lineto
0.88132 0.06883 lineto
0.88318 0.0622 lineto
0.88504 0.05433 lineto
0.8869 0.0459 lineto
0.88876 0.03896 lineto
0.89063 0.03682 lineto
0.89249 0.04061 lineto
0.89435 0.04754 lineto
0.89621 0.05469 lineto
0.89807 0.0607 lineto
0.89993 0.06521 lineto
0.90179 0.06817 lineto
0.90365 0.06964 lineto
0.90551 0.06967 lineto
0.90737 0.06831 lineto
0.90923 0.06556 lineto
0.91109 0.06146 lineto
0.91295 0.05611 lineto
0.91481 0.04982 lineto
0.91667 0.04338 lineto
0.91853 0.03828 lineto
0.92039 0.03636 lineto
0.92225 0.03813 lineto
0.92411 0.04224 lineto
0.92597 0.04688 lineto
0.92783 0.05094 lineto
0.92969 0.05395 lineto
0.93155 0.05578 lineto
0.93341 0.05646 lineto
0.93527 0.05613 lineto
0.93713 0.05499 lineto
0.93899 0.05338 lineto
0.94085 0.05172 lineto
0.94271 0.05057 lineto
0.94457 0.05041 lineto
0.94643 0.05145 lineto
0.94829 0.05352 lineto
0.95015 0.0562 lineto
0.95201 0.05901 lineto
0.95387 0.06159 lineto
Mistroke
0.95573 0.0637 lineto
0.95759 0.06523 lineto
0.95945 0.06612 lineto
0.96131 0.06639 lineto
0.96317 0.06607 lineto
0.96503 0.06525 lineto
0.96689 0.06401 lineto
0.96875 0.0625 lineto
0.97061 0.06087 lineto
0.97247 0.0593 lineto
0.97433 0.05799 lineto
0.97619 0.05711 lineto
Mfstroke
% End of Graphics
MathPictureEnd
:[font = section; inactive; startGroup; ]
Print Gain in Transition from Pass-Band to Stop-Band
:[font = subsubtitle; inactive; ]
Assuming upsampling by factor of 4
:[font = input; startGroup; ]
Clear[tw,fc,ls,twlb,twub];
tw=0.1;
fc=N[1/4];
ls=Length[nfsdb];
twlb = 1+Floor[ls*fc-tw*ls]
:[font = output; inactive; output; ]
77
;[o]
77
:[font = input; startGroup; ]
twm = 1+Floor[ls*fc]
:[font = output; inactive; output; endGroup; ]
129
;[o]
129
:[font = input; startGroup; ]
twub = 1+Floor[ls*fc+tw*ls]
:[font = output; inactive; output; endGroup; ]
180
;[o]
180
:[font = input; startGroup; ]
Take[nfsdb,{twlb,twm}]
:[font = output; inactive; output; endGroup; ]
{-0.000900855883948437, -0.001041819049927622,
  -0.001425486458333564, -0.002205925731739059,
  -0.003584104497213135, -0.005813715508185981,
  -0.00920647118366813, -0.01413666787423758,
  -0.02104484216531012, -0.03044037374902151,
  -0.04290293016240351, -0.059082695610281,
  -0.07969937625417425, -0.1055400245808852,
  -0.1374557726269145, -0.1763576051094924,
  -0.22321133665262, -0.2790319807894561,
  -0.3448777115898822, -0.4218436217391806,
  -0.5110554745390804, -0.613663633041292,
  -0.7308373291562864, -0.863759411081509,
  -1.01362168072762, -1.181620905792314,
  -1.368955565273084, -1.576823363727236,
  -1.806419529335177, -2.058935894323503,
  -2.33556074378888, -2.637479410427473,
  -2.96587558794085, -3.321933334671039,
  -3.706839740974831, -4.121788238636531,
  -4.567982537931949, -5.046641187555863,
  -5.559002764366101, -6.106331713751688,
  -6.68992487750744, -7.311118764658005,
  -7.971297642170027, -8.67190254759167,
  -9.41444135530586, -10.20050006356338,
  -11.0317555125083, -11.90998979635087,
  -12.83710669882245, -13.81515056431832,
  -14.84632812351804, -15.93303392981021,
  -17.07788024277802}
;[o]
{-0.000900856, -0.00104182, -0.00142549, -0.00220593,

  -0.0035841, -0.00581372, -0.00920647, -0.0141367,

  -0.0210448, -0.0304404, -0.0429029, -0.0590827,

  -0.0796994, -0.10554, -0.137456, -0.176358, -0.223211,

  -0.279032, -0.344878, -0.421844, -0.511055, -0.613664,

  -0.730837, -0.863759, -1.01362, -1.18162, -1.36896,

  -1.57682, -1.80642, -2.05894, -2.33556, -2.63748,

  -2.96588, -3.32193, -3.70684, -4.12179, -4.56798,

  -5.04664, -5.559, -6.10633, -6.68992, -7.31112,

  -7.9713, -8.6719, -9.41444, -10.2005, -11.0318,

  -11.91, -12.8371, -13.8152, -14.8463, -15.933,

  -17.0779}
:[font = input; startGroup; ]
Take[nfsdb,{twm,twub}]
:[font = output; inactive; output; endGroup; ]
{-17.07788024277802, -18.28373243323577,
  -19.55375130367868, -20.89144415178549,
  -22.30072700203453, -23.78600126573028,
  -25.35224927664505, -27.00515486650374,
  -28.75125767779335, -30.59815373131836,
  -32.55476066804937, -34.63167545695789,
  -36.84166771050351, -39.20037779290588,
  -41.72733492308512, -44.44749570853874,
  -47.39367042139774, -50.61055335068851,
  -54.16186427538455, -58.14408436194924,
  -62.71585136896294, -68.17037515145527,
  -75.14626510586862, -85.0079047767115,
  -88.1748575421776, -85.4574102811739,
  -85.9533977724383, -88.6987583055619,
  -93.7754605509079, -99.7868862800816,
  -97.1594592379559, -94.5566291640072,
  -93.9604892606191, -94.3932408290867,
  -94.5295783411756, -93.296158135647,
  -91.3933000326142, -89.7871239372832,
  -88.7852567620149, -88.4235042979157,
  -88.7009213079637, -89.6490445540925,
  -91.3541173627318, -93.9157261635056,
  -96.8715413194745, -97.2477467112471,
  -94.4627131026955, -91.747290877392,
  -89.7986852997791, -88.48930196696, -87.6604175029047,
  -87.1896914562699}
;[o]
{-17.0779, -18.2837, -19.5538, -20.8914, -22.3007,

  -23.786, -25.3522, -27.0052, -28.7513, -30.5982,

  -32.5548, -34.6317, -36.8417, -39.2004, -41.7273,

  -44.4475, -47.3937, -50.6106, -54.1619, -58.1441,

  -62.7159, -68.1704, -75.1463, -85.0079, -88.1749,

  -85.4574, -85.9534, -88.6988, -93.7755, -99.7869,

  -97.1595, -94.5566, -93.9605, -94.3932, -94.5296,

  -93.2962, -91.3933, -89.7871, -88.7853, -88.4235,

  -88.7009, -89.649, -91.3541, -93.9157, -96.8715,

  -97.2477, -94.4627, -91.7473, -89.7987, -88.4893,

  -87.6604, -87.1897}
:[font = input; startGroup; ]
nfsdb[[twlb]] = -100;    (* Mark end of passband *)
nfsdb[[twm]] = 0;    (* Mark folding frequency *)
nfsdb[[twub]] = 0;    (* Mark fold-freq + xition width *)
ListPlot[nfsdb,PlotJoined->True,PlotRange->{-100,10}];
:[font = postscript; inactive; PostScript; output; endGroup; endGroup; endGroup; pictureLeft = 39; pictureWidth = 282; pictureHeight = 174; preserveAspect; ]
%!
%%Creator: Mathematica
%%AspectRatio: 0.61803
MathPictureStart
% Scaling calculations
0.02381 0.00186 0.56185 0.00562 [
[(100)] 0.20982 0.54935 0 1 Msboxa
[(200)] 0.39583 0.54935 0 1 Msboxa
[(300)] 0.58185 0.54935 0 1 Msboxa
[(400)] 0.76786 0.54935 0 1 Msboxa
[(500)] 0.95387 0.54935 0 1 Msboxa
[(-100)] 0.01131 0 1 0 Msboxa
[(-80)] 0.01131 0.11237 1 0 Msboxa
[(-60)] 0.01131 0.22474 1 0 Msboxa
[(-40)] 0.01131 0.33711 1 0 Msboxa
[(-20)] 0.01131 0.44948 1 0 Msboxa
[ -0.001 -0.001 0 0 ]
[ 1.001 0.61903 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
%%Object: Graphics
[ ] 0 setdash
0 setgray
gsave
gsave
0.002 setlinewidth
0 0.56185 moveto
1 0.56185 lineto
stroke
0.20982 0.5556 moveto
0.20982 0.5681 lineto
stroke
0 setgray
[(100)] 0.20982 0.54935 0 1 Mshowa
0.39583 0.5556 moveto
0.39583 0.5681 lineto
stroke
0 setgray
[(200)] 0.39583 0.54935 0 1 Mshowa
0.58185 0.5556 moveto
0.58185 0.5681 lineto
stroke
0 setgray
[(300)] 0.58185 0.54935 0 1 Mshowa
0.76786 0.5556 moveto
0.76786 0.5681 lineto
stroke
0 setgray
[(400)] 0.76786 0.54935 0 1 Mshowa
0.95387 0.5556 moveto
0.95387 0.5681 lineto
stroke
0 setgray
[(500)] 0.95387 0.54935 0 1 Mshowa
0.02381 0 moveto
0.02381 0.61803 lineto
stroke
0.01756 0 moveto
0.03006 0 lineto
stroke
0 setgray
[(-100)] 0.01131 0 1 0 Mshowa
0.01756 0.11237 moveto
0.03006 0.11237 lineto
stroke
0 setgray
[(-80)] 0.01131 0.11237 1 0 Mshowa
0.01756 0.22474 moveto
0.03006 0.22474 lineto
stroke
0 setgray
[(-60)] 0.01131 0.22474 1 0 Mshowa
0.01756 0.33711 moveto
0.03006 0.33711 lineto
stroke
0 setgray
[(-40)] 0.01131 0.33711 1 0 Mshowa
0.01756 0.44948 moveto
0.03006 0.44948 lineto
stroke
0 setgray
[(-20)] 0.01131 0.44948 1 0 Mshowa
grestore
grestore
0 0 moveto
1 0 lineto
1 0.618034 lineto
0 0.618034 lineto
closepath
clip
newpath
0 setgray
0.004 setlinewidth
0.02567 0.56182 moveto
0.02753 0.56182 lineto
0.02939 0.56182 lineto
0.03125 0.56182 lineto
0.03311 0.56182 lineto
0.03497 0.56183 lineto
0.03683 0.56183 lineto
0.03869 0.56183 lineto
0.04055 0.56183 lineto
0.04241 0.56183 lineto
0.04427 0.56184 lineto
0.04613 0.56184 lineto
0.04799 0.56184 lineto
0.04985 0.56184 lineto
0.05171 0.56184 lineto
0.05357 0.56185 lineto
0.05543 0.56185 lineto
0.05729 0.56185 lineto
0.05915 0.56185 lineto
0.06101 0.56185 lineto
0.06287 0.56185 lineto
0.06473 0.56185 lineto
0.06659 0.56185 lineto
0.06845 0.56185 lineto
0.07031 0.56185 lineto
0.07217 0.56185 lineto
0.07403 0.56185 lineto
0.07589 0.56184 lineto
0.07775 0.56184 lineto
0.07961 0.56184 lineto
0.08147 0.56184 lineto
0.08333 0.56184 lineto
0.08519 0.56184 lineto
0.08705 0.56184 lineto
0.08891 0.56184 lineto
0.09077 0.56184 lineto
0.09263 0.56184 lineto
0.09449 0.56184 lineto
0.09635 0.56184 lineto
0.09821 0.56184 lineto
0.10007 0.56184 lineto
0.10193 0.56184 lineto
0.10379 0.56184 lineto
0.10565 0.56184 lineto
0.10751 0.56184 lineto
0.10938 0.56184 lineto
0.11124 0.56184 lineto
0.1131 0.56184 lineto
0.11496 0.56184 lineto
0.11682 0.56184 lineto
Mistroke
0.11868 0.56184 lineto
0.12054 0.56184 lineto
0.1224 0.56184 lineto
0.12426 0.56184 lineto
0.12612 0.56184 lineto
0.12798 0.56184 lineto
0.12984 0.56184 lineto
0.1317 0.56184 lineto
0.13356 0.56185 lineto
0.13542 0.56185 lineto
0.13728 0.56185 lineto
0.13914 0.56185 lineto
0.141 0.56185 lineto
0.14286 0.56185 lineto
0.14472 0.56185 lineto
0.14658 0.56185 lineto
0.14844 0.56185 lineto
0.1503 0.56185 lineto
0.15216 0.56185 lineto
0.15402 0.56184 lineto
0.15588 0.56184 lineto
0.15774 0.56184 lineto
0.1596 0.56184 lineto
0.16146 0.56184 lineto
0.16332 0.56184 lineto
0.16518 0.56184 lineto
0.16704 0 lineto
0.1689 0.56184 lineto
0.17076 0.56184 lineto
0.17262 0.56184 lineto
0.17448 0.56183 lineto
0.17634 0.56182 lineto
0.1782 0.5618 lineto
0.18006 0.56177 lineto
0.18192 0.56173 lineto
0.18378 0.56168 lineto
0.18564 0.56161 lineto
0.1875 0.56152 lineto
0.18936 0.5614 lineto
0.19122 0.56126 lineto
0.19308 0.56108 lineto
0.19494 0.56086 lineto
0.1968 0.56059 lineto
0.19866 0.56028 lineto
0.20052 0.55991 lineto
0.20238 0.55948 lineto
0.20424 0.55898 lineto
0.2061 0.5584 lineto
0.20796 0.55774 lineto
0.20982 0.557 lineto
Mistroke
0.21168 0.55615 lineto
0.21354 0.55521 lineto
0.2154 0.55416 lineto
0.21726 0.55299 lineto
0.21912 0.5517 lineto
0.22098 0.55028 lineto
0.22284 0.54873 lineto
0.2247 0.54703 lineto
0.22656 0.54519 lineto
0.22842 0.54318 lineto
0.23028 0.54102 lineto
0.23214 0.53869 lineto
0.234 0.53618 lineto
0.23586 0.53349 lineto
0.23772 0.53062 lineto
0.23958 0.52754 lineto
0.24144 0.52426 lineto
0.2433 0.52077 lineto
0.24516 0.51706 lineto
0.24702 0.51313 lineto
0.24888 0.50895 lineto
0.25074 0.50454 lineto
0.2526 0.49987 lineto
0.25446 0.49493 lineto
0.25632 0.48972 lineto
0.25818 0.48423 lineto
0.26004 0.47844 lineto
0.2619 0.47233 lineto
0.26376 0.56185 lineto
0.26563 0.45912 lineto
0.26749 0.45199 lineto
0.26935 0.44447 lineto
0.27121 0.43655 lineto
0.27307 0.42821 lineto
0.27493 0.41941 lineto
0.27679 0.41012 lineto
0.27865 0.40031 lineto
0.28051 0.38993 lineto
0.28237 0.37894 lineto
0.28423 0.36727 lineto
0.28609 0.35485 lineto
0.28795 0.3416 lineto
0.28981 0.3274 lineto
0.29167 0.31212 lineto
0.29353 0.29557 lineto
0.29539 0.27749 lineto
0.29725 0.25754 lineto
0.29911 0.23517 lineto
0.30097 0.20948 lineto
0.30283 0.17883 lineto
Mistroke
0.30469 0.13964 lineto
0.30655 0.08423 lineto
0.30841 0.06644 lineto
0.31027 0.08171 lineto
0.31213 0.07892 lineto
0.31399 0.0635 lineto
0.31585 0.03497 lineto
0.31771 0.0012 lineto
0.31957 0.01596 lineto
0.32143 0.03058 lineto
0.32329 0.03393 lineto
0.32515 0.0315 lineto
0.32701 0.03074 lineto
0.32887 0.03767 lineto
0.33073 0.04836 lineto
0.33259 0.05738 lineto
0.33445 0.06301 lineto
0.33631 0.06504 lineto
0.33817 0.06348 lineto
0.34003 0.05816 lineto
0.34189 0.04858 lineto
0.34375 0.03418 lineto
0.34561 0.01758 lineto
0.34747 0.01546 lineto
0.34933 0.03111 lineto
0.35119 0.04637 lineto
0.35305 0.05732 lineto
0.35491 0.06467 lineto
0.35677 0.06933 lineto
0.35863 0.56185 lineto
0.36049 0.07317 lineto
0.36235 0.07342 lineto
0.36421 0.07322 lineto
0.36607 0.073 lineto
0.36793 0.07306 lineto
0.36979 0.0735 lineto
0.37165 0.07421 lineto
0.37351 0.075 lineto
0.37537 0.07568 lineto
0.37723 0.07611 lineto
0.37909 0.07626 lineto
0.38095 0.07619 lineto
0.38281 0.07599 lineto
0.38467 0.07582 lineto
0.38653 0.0758 lineto
0.38839 0.07599 lineto
0.39025 0.07643 lineto
0.39211 0.07707 lineto
0.39397 0.07786 lineto
0.39583 0.07876 lineto
Mistroke
0.39769 0.07973 lineto
0.39955 0.08073 lineto
0.40141 0.08174 lineto
0.40327 0.08267 lineto
0.40513 0.08343 lineto
0.40699 0.08387 lineto
0.40885 0.08383 lineto
0.41071 0.08313 lineto
0.41257 0.08158 lineto
0.41443 0.07895 lineto
0.41629 0.07502 lineto
0.41815 0.06949 lineto
0.42001 0.06201 lineto
0.42188 0.05216 lineto
0.42374 0.03969 lineto
0.4256 0.0259 lineto
0.42746 0.0177 lineto
0.42932 0.02287 lineto
0.43118 0.03419 lineto
0.43304 0.04418 lineto
0.4349 0.05126 lineto
0.43676 0.05547 lineto
0.43862 0.05709 lineto
0.44048 0.05628 lineto
0.44234 0.05317 lineto
0.4442 0.04805 lineto
0.44606 0.04194 lineto
0.44792 0.03775 lineto
0.44978 0.03955 lineto
0.45164 0.04746 lineto
0.4535 0.05752 lineto
0.45536 0.06688 lineto
0.45722 0.07461 lineto
0.45908 0.08056 lineto
0.46094 0.08484 lineto
0.4628 0.08754 lineto
0.46466 0.08877 lineto
0.46652 0.08856 lineto
0.46838 0.08693 lineto
0.47024 0.08385 lineto
0.4721 0.07922 lineto
0.47396 0.07292 lineto
0.47582 0.06474 lineto
0.47768 0.05451 lineto
0.47954 0.04243 lineto
0.4814 0.03041 lineto
0.48326 0.02443 lineto
0.48512 0.0291 lineto
0.48698 0.03916 lineto
0.48884 0.0492 lineto
Mistroke
0.4907 0.0577 lineto
0.49256 0.06467 lineto
0.49442 0.07037 lineto
0.49628 0.07502 lineto
0.49814 0.07878 lineto
0.5 0.08172 lineto
0.50186 0.08386 lineto
0.50372 0.08514 lineto
0.50558 0.08548 lineto
0.50744 0.08476 lineto
0.5093 0.08283 lineto
0.51116 0.07945 lineto
0.51302 0.07429 lineto
0.51488 0.06684 lineto
0.51674 0.05625 lineto
0.5186 0.041 lineto
0.52046 0.01906 lineto
0.52232 0.00011 lineto
0.52418 0.01837 lineto
0.52604 0.04175 lineto
0.5279 0.05835 lineto
0.52976 0.07013 lineto
0.53162 0.07866 lineto
0.53348 0.08478 lineto
0.53534 0.08901 lineto
0.5372 0.09165 lineto
0.53906 0.0929 lineto
0.54092 0.0929 lineto
0.54278 0.09171 lineto
0.54464 0.0894 lineto
0.5465 0.08604 lineto
0.54836 0.08168 lineto
0.55022 0.07648 lineto
0.55208 0.07071 lineto
0.55394 0.06486 lineto
0.5558 0.05973 lineto
0.55766 0.05623 lineto
0.55952 0.0549 lineto
0.56138 0.0555 lineto
0.56324 0.05721 lineto
0.5651 0.05916 lineto
0.56696 0.06075 lineto
0.56882 0.06165 lineto
0.57068 0.06168 lineto
0.57254 0.06074 lineto
0.5744 0.05878 lineto
0.57626 0.05573 lineto
0.57813 0.05159 lineto
0.57999 0.04639 lineto
0.58185 0.04044 lineto
Mistroke
0.58371 0.03459 lineto
0.58557 0.03062 lineto
0.58743 0.03057 lineto
0.58929 0.03475 lineto
0.59115 0.04128 lineto
0.59301 0.04817 lineto
0.59487 0.05429 lineto
0.59673 0.05923 lineto
0.59859 0.06287 lineto
0.60045 0.0652 lineto
0.60231 0.06625 lineto
0.60417 0.06608 lineto
0.60603 0.06479 lineto
0.60789 0.06255 lineto
0.60975 0.05966 lineto
0.61161 0.0567 lineto
0.61347 0.05443 lineto
0.61533 0.05366 lineto
0.61719 0.05465 lineto
0.61905 0.05695 lineto
0.62091 0.05967 lineto
0.62277 0.06194 lineto
0.62463 0.06316 lineto
0.62649 0.06287 lineto
0.62835 0.06068 lineto
0.63021 0.05618 lineto
0.63207 0.04884 lineto
0.63393 0.03824 lineto
0.63579 0.02595 lineto
0.63765 0.02209 lineto
0.63951 0.03489 lineto
0.64137 0.052 lineto
0.64323 0.0665 lineto
0.64509 0.07788 lineto
0.64695 0.08665 lineto
0.64881 0.09327 lineto
0.65067 0.09807 lineto
0.65253 0.10125 lineto
0.65439 0.10291 lineto
0.65625 0.10312 lineto
0.65811 0.10184 lineto
0.65997 0.099 lineto
0.66183 0.09449 lineto
0.66369 0.0881 lineto
0.66555 0.07968 lineto
0.66741 0.06946 lineto
0.66927 0.05933 lineto
0.67113 0.05484 lineto
0.67299 0.06011 lineto
0.67485 0.07032 lineto
Mistroke
0.67671 0.08029 lineto
0.67857 0.08839 lineto
0.68043 0.09447 lineto
0.68229 0.0987 lineto
0.68415 0.10127 lineto
0.68601 0.1023 lineto
0.68787 0.10185 lineto
0.68973 0.09994 lineto
0.69159 0.09651 lineto
0.69345 0.09144 lineto
0.69531 0.08452 lineto
0.69717 0.07547 lineto
0.69903 0.06395 lineto
0.70089 0.05003 lineto
0.70275 0.03641 lineto
0.70461 0.03202 lineto
0.70647 0.04011 lineto
0.70833 0.05133 lineto
0.71019 0.06069 lineto
0.71205 0.06757 lineto
0.71391 0.07229 lineto
0.71577 0.07523 lineto
0.71763 0.07671 lineto
0.71949 0.077 lineto
0.72135 0.07638 lineto
0.72321 0.07509 lineto
0.72507 0.07342 lineto
0.72693 0.07165 lineto
0.72879 0.07005 lineto
0.73065 0.06876 lineto
0.73251 0.06781 lineto
0.73438 0.06706 lineto
0.73624 0.06627 lineto
0.7381 0.06516 lineto
0.73996 0.06343 lineto
0.74182 0.06084 lineto
0.74368 0.0571 lineto
0.74554 0.05195 lineto
0.7474 0.04507 lineto
0.74926 0.03612 lineto
0.75112 0.02516 lineto
0.75298 0.01422 lineto
0.75484 0.01064 lineto
0.7567 0.0193 lineto
0.75856 0.03281 lineto
0.76042 0.04544 lineto
0.76228 0.05601 lineto
0.76414 0.06468 lineto
0.766 0.07178 lineto
0.76786 0.07756 lineto
Mistroke
0.76972 0.08224 lineto
0.77158 0.08597 lineto
0.77344 0.08884 lineto
0.7753 0.09095 lineto
0.77716 0.09233 lineto
0.77902 0.09304 lineto
0.78088 0.09312 lineto
0.78274 0.09257 lineto
0.7846 0.09143 lineto
0.78646 0.08972 lineto
0.78832 0.08747 lineto
0.79018 0.08469 lineto
0.79204 0.0814 lineto
0.7939 0.07764 lineto
0.79576 0.07342 lineto
0.79762 0.06873 lineto
0.79948 0.06355 lineto
0.80134 0.0578 lineto
0.8032 0.05136 lineto
0.80506 0.04402 lineto
0.80692 0.03548 lineto
0.80878 0.02547 lineto
0.81064 0.01414 lineto
0.8125 0.00366 lineto
0.81436 0.00063 lineto
0.81622 0.00869 lineto
0.81808 0.02136 lineto
0.81994 0.0335 lineto
0.8218 0.04388 lineto
0.82366 0.05254 lineto
0.82552 0.05975 lineto
0.82738 0.06575 lineto
0.82924 0.07075 lineto
0.8311 0.07489 lineto
0.83296 0.0783 lineto
0.83482 0.08106 lineto
0.83668 0.08326 lineto
0.83854 0.08495 lineto
0.8404 0.08617 lineto
0.84226 0.08695 lineto
0.84412 0.08734 lineto
0.84598 0.08736 lineto
0.84784 0.08706 lineto
0.8497 0.08649 lineto
0.85156 0.08575 lineto
0.85342 0.08492 lineto
0.85528 0.08413 lineto
0.85714 0.0835 lineto
0.859 0.08313 lineto
0.86086 0.08308 lineto
Mistroke
0.86272 0.08333 lineto
0.86458 0.08377 lineto
0.86644 0.08426 lineto
0.8683 0.08461 lineto
0.87016 0.08464 lineto
0.87202 0.08416 lineto
0.87388 0.08302 lineto
0.87574 0.08106 lineto
0.8776 0.07814 lineto
0.87946 0.07411 lineto
0.88132 0.06883 lineto
0.88318 0.0622 lineto
0.88504 0.05433 lineto
0.8869 0.0459 lineto
0.88876 0.03896 lineto
0.89063 0.03682 lineto
0.89249 0.04061 lineto
0.89435 0.04754 lineto
0.89621 0.05469 lineto
0.89807 0.0607 lineto
0.89993 0.06521 lineto
0.90179 0.06817 lineto
0.90365 0.06964 lineto
0.90551 0.06967 lineto
0.90737 0.06831 lineto
0.90923 0.06556 lineto
0.91109 0.06146 lineto
0.91295 0.05611 lineto
0.91481 0.04982 lineto
0.91667 0.04338 lineto
0.91853 0.03828 lineto
0.92039 0.03636 lineto
0.92225 0.03813 lineto
0.92411 0.04224 lineto
0.92597 0.04688 lineto
0.92783 0.05094 lineto
0.92969 0.05395 lineto
0.93155 0.05578 lineto
0.93341 0.05646 lineto
0.93527 0.05613 lineto
0.93713 0.05499 lineto
0.93899 0.05338 lineto
0.94085 0.05172 lineto
0.94271 0.05057 lineto
0.94457 0.05041 lineto
0.94643 0.05145 lineto
0.94829 0.05352 lineto
0.95015 0.0562 lineto
0.95201 0.05901 lineto
0.95387 0.06159 lineto
Mistroke
0.95573 0.0637 lineto
0.95759 0.06523 lineto
0.95945 0.06612 lineto
0.96131 0.06639 lineto
0.96317 0.06607 lineto
0.96503 0.06525 lineto
0.96689 0.06401 lineto
0.96875 0.0625 lineto
0.97061 0.06087 lineto
0.97247 0.0593 lineto
0.97433 0.05799 lineto
0.97619 0.05711 lineto
Mfstroke
% End of Graphics
MathPictureEnd
^*)