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["Demonstration of effect of derivative peak sharpening on perpendicular drop area measurements of two symmetrical overlapping peaks.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Tom O'Haver (toh@umd.edu), Version 3, August 2018"]
["Simulated peaks",null,"The simulated data of two Gaussian peaks are in column A and B (X and Y), rows 9 to 313.  Cells B4 - B6 control the peak width, noise, and relative height  of peak 2."]
["peak 2",0.5,null,"% error","Area 1","Area 2","Peak 1 true","Peak 2 true","Click buttons to change K1 and K2"]
["Width",313,null,"Raw",{"$f":"((SUM(B9:B134)*(A10-A9)-G4))/G4","v":-1.131484822183166E-2},{"$f":"(SUM(B135:B313)*(A10-A9)-H4)/H4","v":2.2248946982547178E-2},{"$f":"(1.0646*1*B4)","v":333.21980000000002},{"$f":"(1.0646*$B$3*B4)","v":166.60990000000001},"K1=",3265.6333333333332,null,"The smooth function is defined by the 17 red coefficients in row 5, columns K through AA."]
["Noise",0,null,"Sharp",{"$f":"((SUM(J9:J134)*(A10-A9)-G4))/G4","v":-6.8084774604151702E-4},{"$f":"((SUM(J135:J313)*(A11-A10)-H4))/H4","v":9.8090202611270821E-4},null,null,"K2=",47989624.805,null,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8]
["delta x",10,null,"Rs=",{"$f":"500/(2*B4)","v":0.79872204472843455},null,null,null,{"$f":"B4^2/30","v":3265.6333333333332},{"$f":"B4^4/200","v":47989624.805},"Smooth coefficients--->",0,0,0,0,0,0,0,1,2,1,0,0,0,0,0,0,0," "]
["Simulated data",null,"1st",null,"Smoothed","2nd","Smoothed","4th","Smoothed","Sharpened"]
["X","Y"," derivative",null,"1st deriv."," derivative"," 2nd deriv."," derivative","4th deriv.","Signal"]
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[650,{"$f":"EXP(-1*(($A74-1000)/(0.60056*$B$4))^2)+$B$3*EXP(-1*(($A74-1500)/(0.60056*$B$4))^2)+$B$5*(RAND()-RAND()+RAND()-RAND())","v":3.1215315039849891E-2},5.6822764342252222E-4,null,5.715446709411748E-4,9.8530667915784329E-6,9.8774940794372182E-6,2.4127941767587965E-10,2.382964987826958E-10,{"$f":"B74-($J$4*G74)+($J$5*I74)","v":1.0394800693163777E-2}]
[{"$f":"A74+$B$6","v":660},3.7946765936658924E-2,{"$f":"(B75-B74)/(A75-A74)","v":6.7314508968090332E-4},null,6.7669684155915078E-4,{"$f":"(E76-E74)/(A76-A74)","v":1.1223672569073069E-5},1.124491359616393E-5,2.0906195956695559E-10,2.0573086510130305E-10,1.109794829359239E-2]
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[680,5.5133344498232595E-2,9.2638831270509261E-4,null,9.3028169065777384E-4,1.4201674107934314E-5,1.4212410246709087E-5,1.0353856197205623E-10,9.9747375827140463E-11,1.3507662990798978E-2,null,"Type in (or Copy and Paste) any data you like into column A (X) and B (Y). "]
[690,6.5894150435918952E-2,1.0760805937686357E-3,null,1.0800516044813225E-3,1.5767050316036565E-5,1.5770278021489572E-5,2.8392255769027968E-11,2.4546084767809349E-11,1.5572162251447457E-2,null,"Change the smooth width by changing the 17 red coefficients in row 5, columns K through AA."]
[700,7.8310719612748214E-2,1.2416569176829262E-3,null,1.2456226969785051E-3,1.734533734595084E-5,1.7339502698577668E-5,-6.2138734438874785E-11,-6.5886151742200263E-11,1.8524409914896206E-2,null,"Extend the spreadsheet to longer columns of data by dragging the last row of columns A through H down as needed. "]
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[1250,0.25580646776615401,-1.3907118483307778E-3,null,{"$f":"(C126*$L$6+C127*$M$6+C128*$N$6+C129*$O$6+C130*$P$6+C131*$Q$6+C132*$R$6+C133*$S$6+C134*$T$6+C135*$U$6+C136*$V$6+C137*$W$6+C138*$X$6+C139*$Y$6+C140*$Z$6+C141*$AA$6+C142*$AB$6)/SUM($L$6:$AB$6)","v":-1.3910258323771977E-3},3.6645086299780946E-5,{"$f":"(F126*$L$6+F127*$M$6+F128*$N$6+F129*$O$6+F130*$P$6+F131*$Q$6+F132*$R$6+F133*$S$6+F134*$T$6+F135*$U$6+F136*$V$6+F137*$W$6+F138*$X$6+F139*$Y$6+F140*$Z$6+F141*$AA$6+F142*$AB$6)/SUM($L$6:$AB$6)","v":3.6524433297179472E-5},-1.2057953687824319E-9,-1.2049996911229892E-9,7.8703577842641675E-2,"Midpoint between the two peaks"]
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[1980,7.3646518048786917E-4,-2.2717641732319234E-5,null,-2.3032155327674661E-5,5.7276082080148228E-7,5.7884155626882596E-7,6.0985506053041591E-11,6.1159973310819942E-11,1.7812250718879116E-3]
[1990,5.596683181705906E-4,-1.7679686231727856E-5,null,-1.7938136087905867E-5,4.5729494962496213E-7,4.6250464077170579E-7,5.2297091501061274E-11,5.2494241860722958E-11,1.5684767177641689E-3]
[2000,4.2291301661210538E-4,-1.3675530155848523E-5,null,-1.3886256335175419E-5,3.6266784303541674E-7,3.6708656187501013E-7,4.4397278387727692E-11,4.4604970552447816E-11,1.3647187051843875E-3]
[2010,3.177702286393377E-4,-1.0514278797276767E-5,null,{"$f":"(C202*$L$6+C203*$M$6+C204*$N$6+C205*$O$6+C206*$P$6+C207*$Q$6+C208*$R$6+C209*$S$6+C210*$T$6+C211*$U$6+C212*$V$6+C213*$W$6+C214*$X$6+C215*$Y$6+C216*$Z$6+C217*$AA$6+C218*$AB$6)/SUM($L$6:$AB$6)","v":-1.0684779227197532E-5},2.8571561180424498E-7,2.8942739433340555E-7,3.7328233933274626E-11,3.7536828592351912E-11,1.1739848026409221E-3]
[2020,2.3741993705545696E-4,-8.0350291583880743E-6,null,-8.1719440990905195E-6,2.236105106897155E-7,2.2669952036511082E-7,3.1093568115130698E-11,3.129574466185752E-11,9.9897347101609614E-4]
[2030,1.7638554423236532E-4,-6.1034392823091643E-6,null,-6.2125690134032222E-6,1.7386144827676736E-7,1.7640907364286836E-7,2.5667608483894063E-11,2.5858113876861857E-11,8.4121937615732408E-4]
[2040,1.3030186092630048E-4,-4.6083683306064848E-6,null,-4.6947151335551724E-6,1.3430288732822333E-7,1.3638567031418353E-7,2.1003670424528614E-11,2.1179030268250977E-11,7.0128998606639522E-4]
[2050,9.5715015019314908E-5,-3.4586845906985568E-6,null,-3.5265112668387558E-6,1.030754583235201E-7,1.0476373515531015E-7,1.7041171740052613E-11,1.7199388393171697E-11,5.7898726523541045E-4]
[2060,6.9911939465800661E-5,-2.5803075553514247E-6,null,-2.6332059670847704E-6,7.8601136645977019E-8,7.9958268692457812E-8,1.371153966805294E-11,1.3851796681208231E-11,4.7354007755441455E-4]
[2070,5.0776697796423911E-5,-1.913524166937675E-6,null,-1.9544885339192153E-6,5.9555343154357123E-8,6.0637418096826649E-8,1.0942935648674431E-11,1.1065322520503133E-11,3.8377780011741917E-4]
[2080,3.6670715331923042E-5,-1.4105982464500869E-6,null,-1.4420991039976279E-6,4.4837849432615344E-8,4.5693741760665258E-8,8.6638791166107325E-12,8.7691455429980198E-12,3.0827971358248223E-4]
[2090,2.6333957770396413E-5,-1.033675756152663E-6,null,-1.0577315452669084E-6,3.3543925023073229E-8,3.4215617071148161E-8,6.8058882900961787E-12,6.8952329610630095E-12,2.4549794088676895E-4]
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[2110,1.3351655413598714E-5,-5.4525381336754904E-7,null,-5.5899616915029174E-7,1.842192815594325E-8,{"$f":"(F212*$L$6+F213*$M$6+F214*$N$6+F215*$O$6+F216*$P$6+F217*$Q$6+F218*$R$6+F219*$S$6+F220*$T$6+F221*$U$6+F222*$V$6+F223*$W$6+F224*$X$6+F225*$Y$6+F226*$Z$6+F227*$AA$6+F228*$AB$6)/SUM($L$6:$AB$6)","v":1.8826188783170488E-8},4.1042466560922342E-12,4.1663006239812217E-12,1.5181142955334728E-4]
[2120,9.426649138060234E-6,-3.9250062755384795E-7,null,-4.027820404172984E-7,1.352413001496462E-8,1.3834228531108334E-8,3.1514330362914703E-12,3.2022805309398623E-12,1.17925372506082E-4]
[2130,6.6179182061207479E-6,-2.8087309319394862E-7,null,-2.8851356885099934E-7,9.866725938560846E-9,1.0102841493562768E-8,2.4020093950842735E-12,2.4432359804073626E-12,9.087572027318471E-5]
[2140,4.6198435914982261E-6,-1.9980746146225218E-7,null,-2.0544752164608148E-7,7.1537840821647598E-9,7.3322582140509121E-9,1.8174920951694338E-12,1.8505808781408388E-12,6.9484058772372712E-5]
[2150,3.2068228868394962E-6,-1.4130207046587298E-7,null,-1.4543788720770415E-7,5.1547387533132843E-9,5.2886717726068294E-9,1.3653299271402139E-12,1.3916290517009738E-12,5.2719716116023232E-5]
[2160,2.2134234224713123E-6,-9.9339946436818389E-8,null,-1.0235274657981579E-7,3.691425501635988E-9,3.7912173020188323E-9,1.018364257354034E-12,1.0390703842399335E-12,3.9697295712750141E-5]
[2170,1.5191331926737786E-6,-6.9429022979753368E-8,null,-7.1609377174984388E-8,2.627279451490069E-9,2.7011085343724489E-9,7.5422309511145241E-13,7.7037694045780172E-13,2.9668403456869694E-5]
[2180,1.0367380296376542E-6,-4.823951630361244E-8,null,-4.980715755001441E-8,1.8584497328736699E-9,1.9126890047706463E-9,5.5469731425426793E-13,5.6718782491960261E-13,2.2009727971214233E-5]
[2190,7.0353228350686009E-7,-3.3320574613079411E-8,null,-3.4440382517510991E-8,1.3065771018451767E-9,1.346148400870551E-9,4.0513357605842218E-13,4.1470787920882672E-13,1.6209180720919478E-5]
[2200,4.7472363810413319E-7,-2.2880864540272691E-8,null,-2.3675615513110877E-8,9.1298966691818079E-10,9.4166122739382451E-10,2.9386705046419454E-13,3.0114387605095128E-13,1.1851384969227858E-5]
[2210,3.1852205451594604E-7,-1.5620158358818715E-8,null,-1.6180589179147375E-8,6.3408847389375952E-10,6.5472087410277586E-10,2.1170782721699383E-13,2.1719262766924333E-13,8.6034364562758335E-6]
[2220,2.1251029992915228E-7,-1.0601175458679377E-8,null,-1.0993846035235687E-8,4.3771688170540398E-10,4.5246365169852474E-10,1.5148780577879118E-13,1.5558826452215474E-13,6.2015523553000251E-6]
[2230,1.4098155128149943E-7,-7.1528748647652842E-9,null,-7.4262515450392942E-9,3.0033236948953143E-10,3.1080155160579009E-10,1.0766961931404273E-13,1.1071063688097059E-13,4.4389795701462847E-6]
[2240,9.3000741362027123E-8,-4.7980809919472308E-9,null,-4.9871986454450579E-9,2.0482458573869356E-10,2.1220729923867253E-10,7.6015503117005714E-14,7.8253073471862884E-14,3.1553451471443751E-6]
[2250,6.1003164030822265E-8,-3.1997577331204857E-9,null,-3.3297598302654226E-9,1.3884765598777151E-10,1.4401924811835726E-10,5.331166833939735E-14,5.4945311503350106E-14,2.2274939905735331E-6]
[2260,3.9788735402087379E-8,-2.1214428628734885E-9,null,-2.2102455256896276E-9,9.3557094759192441E-11,9.7155864333800924E-11,3.7142406217600019E-14,3.832601314044678E-14,1.5617642971863566E-6]
[2270,2.5805348963176904E-8,-1.3983386438910474E-9,null,-1.4586179350815735E-9,6.2661611829047313E-11,6.5149443036284598E-11,2.5707571787189707E-14,2.6558652592173776E-14,1.0875909293605449E-6]
[2280,1.6641833066469793E-8,-9.1635158967071108E-10,null,-9.5701328910868142E-10,4.1717453727851313E-11,4.3426050453644156E-11,1.7677060576715675E-14,1.8284477487177571E-14,7.5229348953515518E-7]
[2290,1.0671719734447228E-8,-5.9701133320225647E-10,null,-6.2426886052454733E-10,2.7607682529826681E-11,2.8773482101689983E-11,1.2076217008089239E-14,1.2506537946249402E-14,5.1689214111710247E-7]
[2300,6.8047078742175768E-9,-3.8670118602296514E-10,null,{"$f":"(C231*$L$6+C232*$M$6+C233*$N$6+C234*$O$6+C235*$P$6+C236*$Q$6+C237*$R$6+C238*$S$6+C239*$T$6+C240*$U$6+C241*$V$6+C242*$W$6+C243*$X$6+C244*$Y$6+C245*$Z$6+C246*$AA$6+C296*$AB$6)/SUM($L$6:$AB$6)","v":-4.0485963851214774E-10},1.8161109619255265E-11,{"$f":"(F231*$L$6+F232*$M$6+F233*$N$6+F234*$O$6+F235*$P$6+F236*$Q$6+F237*$R$6+F238*$S$6+F239*$T$6+F240*$U$6+F241*$V$6+F242*$W$6+F243*$X$6+F244*$Y$6+F245*$Z$6+F246*$AA$6+F296*$AB$6)/SUM($L$6:$AB$6)","v":1.8951400552971506E-11},8.196657192103458E-15,{"$f":"(H231*$L$6+H232*$M$6+H233*$N$6+H234*$O$6+H235*$P$6+H236*$Q$6+H237*$R$6+H238*$S$6+H239*$T$6+H240*$U$6+H241*$V$6+H242*$W$6+H243*$X$6+H244*$Y$6+H245*$Z$6+H246*$AA$6+H296*$AB$6)/SUM($L$6:$AB$6)","v":8.4992938988343627E-15},3.5279430782756874E-7]
[2310,4.3144593862135344E-9,-2.4902484880040425E-10,null,{"$f":"(C232*$L$6+C233*$M$6+C234*$N$6+C235*$O$6+C236*$P$6+C237*$Q$6+C238*$R$6+C239*$S$6+C240*$T$6+C241*$U$6+C242*$V$6+C243*$W$6+C244*$X$6+C245*$Y$6+C246*$Z$6+C296*$AA$6+C297*$AB$6)/SUM($L$6:$AB$6)","v":-2.6104666813944203E-10},1.1875700443548809E-11,{"$f":"(F232*$L$6+F233*$M$6+F234*$N$6+F235*$O$6+F236*$P$6+F237*$Q$6+F238*$R$6+F239*$S$6+F240*$T$6+F241*$U$6+F242*$V$6+F243*$W$6+F244*$X$6+F245*$Y$6+F246*$Z$6+F296*$AA$6+F297*$AB$6)/SUM($L$6:$AB$6)","v":1.2407981881094413E-11},5.5276442030412987E-15,{"$f":"(H232*$L$6+H233*$M$6+H234*$N$6+H235*$O$6+H236*$P$6+H237*$Q$6+H238*$R$6+H239*$S$6+H240*$T$6+H241*$U$6+H242*$V$6+H243*$W$6+H244*$X$6+H245*$Y$6+H246*$Z$6+H296*$AA$6+H297*$AB$6)/SUM($L$6:$AB$6)","v":5.7389472765601069E-15},2.3920446673371172E-7]
[2320,2.72010149687359E-9,-1.5943578893399444E-10,null,{"$f":"(C233*$L$6+C234*$M$6+C235*$N$6+C236*$O$6+C237*$P$6+C238*$Q$6+C239*$R$6+C240*$S$6+C241*$T$6+C242*$U$6+C243*$V$6+C244*$W$6+C245*$X$6+C246*$Y$6+C296*$Z$6+C297*$AA$6+C298*$AB$6)/SUM($L$6:$AB$6)","v":-1.6734562964117155E-10},7.7194170180247693E-12,{"$f":"(F233*$L$6+F234*$M$6+F235*$N$6+F236*$O$6+F237*$P$6+F238*$Q$6+F239*$R$6+F240*$S$6+F241*$T$6+F242*$U$6+F243*$V$6+F244*$W$6+F245*$X$6+F246*$Y$6+F296*$Z$6+F297*$AA$6+F298*$AB$6)/SUM($L$6:$AB$6)","v":8.0756208904338388E-12},3.7038435080543724E-15,{"$f":"(H233*$L$6+H234*$M$6+H235*$N$6+H236*$O$6+H237*$P$6+H238*$Q$6+H239*$R$6+H240*$S$6+H241*$T$6+H242*$U$6+H243*$V$6+H244*$W$6+H245*$X$6+H246*$Y$6+H296*$Z$6+H297*$AA$6+H298*$AB$6)/SUM($L$6:$AB$6)","v":3.8503222074884099E-15},1.6112360284543798E-7]
[2330,1.7052405779106587E-9,-1.0148609189629313E-10,null,{"$f":"(C234*$L$6+C235*$M$6+C236*$N$6+C237*$O$6+C238*$P$6+C239*$Q$6+C240*$R$6+C241*$S$6+C242*$T$6+C243*$U$6+C244*$V$6+C245*$W$6+C246*$X$6+C296*$Y$6+C297*$Z$6+C298*$AA$6+C299*$AB$6)/SUM($L$6:$AB$6)","v":-1.0665832777894665E-10},4.9879490821370062E-12,{"$f":"(F234*$L$6+F235*$M$6+F236*$N$6+F237*$O$6+F238*$P$6+F239*$Q$6+F240*$R$6+F241*$S$6+F242*$T$6+F243*$U$6+F244*$V$6+F245*$W$6+F246*$X$6+F296*$Y$6+F297*$Z$6+F298*$AA$6+F299*$AB$6)/SUM($L$6:$AB$6)","v":5.2247973029950136E-12},2.465957610803596E-15,{"$f":"(H234*$L$6+H235*$M$6+H236*$N$6+H237*$O$6+H238*$P$6+H239*$Q$6+H240*$R$6+H241*$S$6+H242*$T$6+H243*$U$6+H244*$V$6+H245*$W$6+H246*$X$6+H296*$Y$6+H297*$Z$6+H298*$AA$6+H299*$AB$6)/SUM($L$6:$AB$6)","v":2.5667795298230754E-15},1.0782175493870373E-7]
[2340,1.0629871940185999E-9,-6.4225338389205879E-11,null,{"$f":"(C235*$L$6+C236*$M$6+C237*$N$6+C238*$O$6+C239*$P$6+C240*$Q$6+C241*$R$6+C242*$S$6+C243*$T$6+C244*$U$6+C245*$V$6+C246*$W$6+C296*$X$6+C297*$Y$6+C298*$Z$6+C299*$AA$6+C300*$AB$6)/SUM($L$6:$AB$6)","v":-6.7586647998431433E-11},3.2038740296812732E-12,{"$f":"(F235*$L$6+F236*$M$6+F237*$N$6+F238*$O$6+F239*$P$6+F240*$Q$6+F241*$R$6+F242*$S$6+F243*$T$6+F244*$U$6+F245*$V$6+F246*$W$6+F296*$X$6+F297*$Y$6+F298*$Z$6+F299*$AA$6+F300*$AB$6)/SUM($L$6:$AB$6)","v":3.3603567598776268E-12},1.6313593896307372E-15,{"$f":"(H235*$L$6+H236*$M$6+H237*$N$6+H238*$O$6+H239*$P$6+H240*$Q$6+H241*$R$6+H242*$S$6+H243*$T$6+H244*$U$6+H245*$V$6+H246*$W$6+H296*$X$6+H297*$Y$6+H298*$Z$6+H299*$AA$6+H300*$AB$6)/SUM($L$6:$AB$6)","v":1.7002678964587528E-15},7.1684512566112366E-8]
[2350,6.5888896082839151E-10,-4.0409823319020841E-11,null,{"$f":"(C236*$L$6+C237*$M$6+C238*$N$6+C239*$O$6+C240*$P$6+C241*$Q$6+C242*$R$6+C243*$S$6+C244*$T$6+C245*$U$6+C246*$V$6+C296*$W$6+C297*$X$6+C298*$Y$6+C299*$Z$6+C300*$AA$6+C301*$AB$6)/SUM($L$6:$AB$6)","v":-4.2580847185321183E-11},2.0457298980109545E-12,{"$f":"(F236*$L$6+F237*$M$6+F238*$N$6+F239*$O$6+F240*$P$6+F241*$Q$6+F242*$R$6+F243*$S$6+F244*$T$6+F245*$U$6+F246*$V$6+F296*$W$6+F297*$X$6+F298*$Y$6+F299*$Z$6+F300*$AA$6+F301*$AB$6)/SUM($L$6:$AB$6)","v":2.1484599726125349E-12},1.0723951957699404E-15,{"$f":"(H236*$L$6+H237*$M$6+H238*$N$6+H239*$O$6+H240*$P$6+H241*$Q$6+H242*$R$6+H243*$S$6+H244*$T$6+H245*$U$6+H246*$V$6+H296*$W$6+H297*$X$6+H298*$Y$6+H299*$Z$6+H300*$AA$6+H301*$AB$6)/SUM($L$6:$AB$6)","v":1.119163546102936E-15},4.7351045131845697E-8]
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