%!
% A modified efficient digital sinewave algorithm
% =====================================
% Don Lancaster and Synergetics www.tinaja.com
% Some ultra compact low end digital sinewave generators
% were described in Column 10 of https://www.tinaja.com/glib/hackar1.pdf
% It appears that better performance and lower distortion can be
% had by making the initial triangle approximation look more like
% a true cosine wave. This can be done by adding adjustments to a
% simple clipping. At a penalty of only a few bytes extra.
% This example creates a 55 amplitue 44 frequency 8 modified triangle
% height sinewave usable by a low end microprocessor. Verified.
% This file is http://www.tinaja.com/psutils/nusine53.psl It is normally
% run by sending the file to Distiller by way of command line //acrodist /F.
% It should also be GhostScript or Google Drive compatible.
% The companion demo is http://www.tinaja.com/psutils/nusine53.pdf
% It appears that dozens of similar low distortion sinewaves of
% different amplitudes are possible.
% Development services available via don@tinaja.com.
% ///////// (A) WEB FRIENDLY COLOR UTILITIES /////////////
% tintmat is a self-generating list of 216 triple color values
/webtintmat [
0 1 5 { /a exch store
0 1 5 { /b exch store
0 1 5 { 5 div b 5 div a 5 div
}for
} for
} for
] def
% setwebtint accepts a color number 0 to 215 and then
% sets the PostScript color generator for later use...
/setwebtint { abs cvi 216 cvi mod % restrict range
webtintmat exch 3 mul 3 getinterval % get values from table
aload pop setrgbcolor} def % and set them
% The blocks are arranged as red to the right, green
% up in order of increasing blue.
% Some "pure color" sequences are
% red: 0 1 2 3 4 5
% orange: 0 7 8 15 16 23 (sort of)
% yellow: 0 7 14 21 28 35
% green: 0 6 12 18 24 30
% aqua: 0 42 84 126 168 210
% blue: 0 36 72 108 144 180
% magenta: 0 37 74 111 148 185
% purple 0 73 73 110 147 183 (sort of)
% gray 0 43 86 129 172 215
% ////////////// GONZO EXCERPTS //////////////////
/setgrid { /blocksize exch def translate % simplified
blocksize dup scale} def
% repeats [ proc distance trips] xrpt
/xrpt{gsave aload pop /trips exch def /dist exch def /rproc exch def
trips { gsave rproc grestore dist 0 translate } repeat grestore} def
/yrpt{gsave aload pop /trips exch def /dist exch def /rproc exch def
trips { gsave rproc grestore 0 dist translate } repeat grestore} def
% mergestr merges the two top stack strings into one top stack string
/mergestr {2 copy length exch length add string dup dup 4 3 roll
4 index length exch putinterval 3 1 roll exch 0 exch putinterval} def
/showgrid {gsave /vblocks exch def /hblocks exch def
thingridlines setlinewidth
[{0 0 moveto 0 vblocks rlineto stroke} 1
hblocks 1 add] xrpt
[{0 0 moveto hblocks 0 rlineto stroke} 1
vblocks 1 add] yrpt
fatterborder { gsave newpath 0 0.96 blocksize div
dtransform round idtransform
setlinewidth pop 2 setlinecap
0 0 moveto hblocks 0 rlineto 0 vblocks rlineto
hblocks neg 0 rlineto closepath stroke grestore} if
fat5 { gsave newpath 0 0.48 blocksize div dtransform round
idtransform setlinewidth pop mark {5 0 moveto 0 vblocks rlineto
stroke} 5 hblocks 5 div cvi] xrpt mark {0 5 moveto hblocks 0 rlineto
stroke} 5 vblocks 5 div cvi] yrpt grestore} if
fatter10 { gsave newpath 0 0.96 blocksize div
dtransform round idtransform setlinewidth pop
mark {10 0 moveto 0 vblocks rlineto stroke} 10
hblocks 10 div cvi] xrpt mark {0 10 moveto hblocks 0 rlineto stroke} 10
vblocks 10 div cvi] yrpt grestore} if
grestore} def
/fatterborder {true } store
/fat5 {false} store
/fatter10 { false} store
/thingridlines {0} store
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%% adjusted sinewave %%%%%%%%%%%%%
/sizegoal 55 store % height of sinewave
/steps 44 store % steps per cycle
/plothi 8 store % height of modified cosine triangle
/adjustcos { % details here will vary with other amplitudes!
{
dup 5 ge {1 sub} if
dup -5 le {1 add} if
dup 6 eq {pop 5} if
dup -6 eq {pop -5} if
} pop
dup 8 eq {pop 7} if
dup -8 eq {pop -7} if
dup 9 ge {pop 8} if
dup -9 le {pop -8} if
} store
10 250 translate
1 setlinewidth
1 setlinejoin
1 setlinecap
%%%%%%%%%%%%%%%%%%%%% cos channel %%%%%%%%%%%%%
% Calculate a 48 step low distortion digital sinewave…
/size sizegoal def % set zero to peak size
/speed 0 def % initialize speed
/cycles 6 store % number of full cycles
0 size moveto
1 1 steps cycles mul { % start a for loop
/val exch store % save position
/speed speed size 0 gt {-1}{+1} % start the algorithm
ifelse add store
/size size speed adjustcos add store % finish the algorithm
% use your sinewave here
1 0 rlineto val size lineto % for actual
% val size lineto % smoothed
} for % complete loop
212 setwebtint 1 setlinewidth stroke
%%%%%%%%%%%%%%%%%%%%%%% sin channel %%%%%%%%%%%%%%%%%%%%%%%%%
-1 0 moveto
/size sizegoal def % set zero to peak size
/speed 0 def % initialize speed
1 1 steps cycles mul { % start a for loop
/val exch store % save position
/speed speed size 0 gt {-1}{+1} % start the algorithm
ifelse add store
/size size speed adjustcos
add store % finish the algorithm
% use your sinewave here
% 1 0 rlineto val speed adjustcos lineto
val speed adjustcos lineto
} for % complete loop
30 setwebtint 1 setlinewidth stroke
%%%%%%%%%%%%%% real comparison sinewave %%%%%%%%%%%%%%%
/phase 0 store
/trim 1 store % should be one after debug
0 0 moveto
0 1 steps cycles mul {/pos exch store
pos trim mul phase add
pos 360 mul steps div sin
plothi mul neg
2 copy == ( ) print ==
lineto
} for
0 setwebtint 0 setlinewidth stroke
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
gsave 0 0 moveto
0 setlinewidth 600 0 rlineto 212 setwebtint stroke grestore % baseline
gsave 0 sizegoal moveto
0 setlinewidth 600 0 rlineto 212 setwebtint stroke grestore % baseline
gsave 0 sizegoal neg moveto
0 setlinewidth 600 0 rlineto 212 setwebtint stroke grestore % baseline
gsave 0 5 moveto
0 setlinewidth 600 0 rlineto 5 setwebtint stroke grestore % red 5
gsave 0 10 moveto
0 setlinewidth 600 0 rlineto 5 setwebtint stroke grestore % red 10
%%%%%%%%%%%%%%%%%%%%%%% grid boxes %%%%%%%%%%%%%%%%%%%%%
4 1 12 {/ruleuh exch store % upper h grid
68 ruleuh moveto 20
0 rlineto
0 setwebtint 0 setlinewidth stroke
} for
93 4 moveto % upper v grid
0 1 20 {/ruleuv exch store
68 ruleuv add 4 moveto
0 8 rlineto
0 setwebtint stroke
} for
showpage
% EOF
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Catalog:
% 23-36-4:
% filename matches amplitude
% text matches data
% no dc offset
% cos fit all green
% unity trim
% 3 cosine pair adjustment
% delta ( no previous )
% 39-40-6:
% filename matches amplitude
% text matches data
% no dc offset
% cos fit all green
% unity trim
% 3 cos pair adjustment
% delta 40-36 = 14
% 55-44-8:
% filename matches amplitude
% text matches data
% no dc offset
% cos fit all green
% unity trim
% 2 cos pair adjustment
% delta55-39 = 16
% 76-48-10:
% filename matches amplitude
% text matches data
% no dc offset
% cos fit all green
% unity trim
% 3 cos pair adjustment
% delta 76-55 = 21
% 98-52-12:
% filename matches amplitude
% text matches data
% no dc offset
% cos fit all green
% unity trim
% 2 cos pair adjustment
% delta 98-76 = 22
% 118-56-14 still has problems