From 6ffe2c92bc8ad8f62b2dbb62a704720722c0a79c Mon Sep 17 00:00:00 2001 From: caes Date: Sat, 13 Aug 2016 22:45:00 -0400 Subject: [PATCH] finalized tophat fft program --- pres/img/tophat_freqdomain.pdf | Bin 29256 -> 32808 bytes scripts/templates/tophat_freqdomain.gp | 10 ++-- scripts/templates/tophat_timedomain.gp | 4 +- scripts/tophat_fft.pl | 72 ++++++++++++++----------- 4 files changed, 48 insertions(+), 38 deletions(-) diff --git a/pres/img/tophat_freqdomain.pdf b/pres/img/tophat_freqdomain.pdf index 1760a0c73de9814a8291a49c26a5854b02811840..dbff5dbbcd5ee90743b2c455fb98b3d2f4909815 100644 GIT binary patch delta 31413 zcmV)CK*GPsIF0+399mAy-^Han7?H_u=34dp>?CGX_a@C7j7f$W+IJ!nWJLBc89 zU4mig-}_C*S}THis%!6qMx#E)*_pg%Fc^$@-ha97U(f&jAOGvGfBVn(umAktuKTO~ z`u{%C|Lybt|MmL!|Mctrx_|x0t9;F0|NF0h`IYvc|LOUkocgbS|M1tVjIY`9uQbM2 zt?Socf7SHWT9V+mU;pQ?e|P=eCu{pkb%saF=h^39=d;$tzy0T5|Kp#pbbs~U*UDSw zr8Gb7F7>PRRcHS7=f7V6_CNjU{?q4Ae*O7BUH|4!<^CW3{9mvC`On_pf7qAwHP?I^ zw7x#Cm*6LT(WAA0e3d)>QUAD 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zhj?4Hini4d%GvY!FPAZo^6Kzp)^>tK6W3Gei3?zLq9t6QV;p@Ww8EY|L6rT%#)j5L zu!H7iD$>&h=U-Ki};ekIa@YGrZ_Y@5vlwG*)_Yk=ak?gpwVa8Ye1$-Y)ZS5N3+ zp^l33W#KCmRGdYE?9`m}vm^++WvY|rQTRu_ z#)gm-FDUcFwYr^9=Sb`E)Fe!Jp2S~bs(_7GMN>zUH&V%P$=lpxhz&zzB;0;L1nKO9 z^-uEMt=pXGuf#T&o`MT#*BlDl?;5t3^Yu_CyQ@SENzhIW;$gW^PFihaCkyu`(+~k$ zIB%#+WRIMGFS2mc&hltS7vWQ$S-DdhkP%J8^m@iMrUPe=_T9DGnQqma#cd#VF0{TU z8qmZ}S*kvm4=h;k@oE?!{F9agKU-Ybj-t(GQQta^2`;W5X7u`JvI*ka2{$1WroM7O z4|e+obdPp;Pc<3tO8%87E+eN?K8y^%|25kFivfxKXqB1j-pFX`CMJzPuCgXb(L$QH)LCFH%(tv_fFe_5ek=Fh)5xuo; z5VeG~n%7P}O6&!!$gaCIg?J$G^HbAaWwPg|KG5_ui%XQ-+j^KwD%dy60k-Pi%o#rI zC5v$cg4qlemTJR#X^sBx#k`b?u}d2hgS^9a6RRXPNqa}NO>!3v56U%ZaSB+^HDSm( zv8&E)xZ)Cj4?vMe)zpb9O+*$L>$$&a$rHiu__oEjPO{_>Zvn(iGX<%8`y0!7de#qa zemxz44xt;D#J?hd`1NN^ElUo@sqc+4##Ne04ym6I1MrUQ0r&In zX$l*R$-UVSE^1RRwf`hvmb>DFuto1dH`N3&r+2wdnJ#s%t?{2gkbYG~s}TEiq3;;O6vJ))N^q&bQ;nO^qfWBYq}9B;xlinvals($xmin,$xmax); - # Output time-domain tophat - open $tophattab, '>', "analyses/tables/tophat${$_}.tab"; - for ($i=0; $i < $xbins; $i++) { - my $x_coord = ($xmax-$xmin)*($i/$xbins) + $xmin; - say $tophattab "$x_coord $th_list[$i]"; - } - close $tophattab; + # Output x-domain tophat + wcols $x_coords,$u,"analyses/tables/tophat${tophat_count}.tab"; - # Transform z(x) to Z(1/x) = U(1/x) + iV(1/x) + # Transform z(x) to Z(x⁻¹) = U(x⁻¹) + iV(x⁻¹) my $U = $u; my $V = $v; fft($U,$V); + # Determine frequency coordinates my $num_elements = nelem($U); say "Found $num_elements elements."; - $f = $U->xlinvals(-($num_elements/2-1)/$num_elements/$xres,1/2/$xres)->rotate(-($num_elements/2 -1)); - say "$f[1]"; + if ($num_elements % 2 == 0) { + # even number of bins + $f = $U->xlinvals( + -(${num_elements}/2-1)/${num_elements}/${xres}, 1/2/${xres} + )->rotate(-(${num_elements}/2 -1)); + } + else { + #odd number of bins + $f = $U->xlinvals( + -(${num_elements}/2-0.5)/${num_elements}/${xres}, + (${num_elements}/2-0.5)/${num_elements}/${xres} + )->rotate(-(${num_elements}-1)/2); + } + + # Calculate x offset my $φdiff = atan2($V,$U); - my $timelag = $φdiff/($twoPI*$f); + my $offset = $φdiff/($_2π*$f); - wcols $f,$timelag,"analyses/tables/tophat_fft${$_}.tab"; + wcols $f,$offset,"analyses/tables/tophat_fft${tophat_count}.tab"; } @@ -62,10 +73,9 @@ sub tophat { (my $mean,my $width) = @_; my $halfwidth = $width/2; my @vals = (); - for ($i=0; $i < $xbins; $i++) { - my $x_coord = ($xmax-$xmin)*($i/$xbins) + $xmin; - if ($x_coord >= ($mean - $halfwidth ) && $x_coord <= ($mean + $halfwidth)) { push @vals, 1/$width; } - else { push @vals, 0; } + for (my $x_coord = $xmin; $x_coord <= $xmax; $x_coord += $xres) { + push @vals, ($x_coord >= ($mean - $halfwidth) && + $x_coord <= ($mean + $halfwidth)) ? 1/$width : 0; } return @vals; } \ No newline at end of file