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["Demonstration of effect of 1st symmetricalization and 2nd derivative sharpening on perpendicular drop area measurements of two overlapping exponentially modified Gaussian (EMG) peaks."]
["Simulated peaks",null,"Cells B4 - B6 control the peak width, noise, and relative height  of peak 2 of the simulated data set. Cells  J4 and J5 control the first and second derivatve weighting factors.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Automatically calculated x and y values for peaks and valleys"]
["peak 2",0.3,"AmpT","% error","Area 1","Area 2","True area 1","True area 2","Click buttons to change K1 (1st derivative) and K2 (2nd derivative) weighting factors.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Raw","y value","x","row#","sharp","y value","x","row#"]
["sigma",55.55,0.01,"Raw",{"$f":"(AD7-G4)/G4","v":2.0306122229890387E-2},{"$f":"(AD8-H4)/H4","v":-4.367932062759726E-2},{"$f":"SUM(AO10:AO314)*(A10-A9)","v":139.2432006557564},{"$f":"$B$3*G4","v":41.77296019672692},"K1=",3.3,null,"The smooth function is defined by the 17 red coefficients in row 5, columns K through AA.",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"peak1",{"$f":"INDIRECT(\"B\"&AF4)","v":0.98738575383342397},{"$f":"INDIRECT(\"A\"&AF4)","v":995},{"$f":"MATCH(1,U11:U351,0)+7","v":208},"peak1",{"$f":"INDIRECT(\"j\"&AJ4)","v":0.99713674624988347},{"$f":"INDIRECT(\"A\"&AJ4)","v":995},{"$f":"MATCH(1,AB11:AB351,0)+9","v":208}]
["Noise",0,"SlopeT","Sharp",{"$f":"(AH7-G4)/G4","v":1.8465535174924136E-2},{"$f":"(AH8-H4)/H4","v":-3.7913997085076714E-2},"total area",{"$f":"SUM(J9:J313)*(A10-A9)","v":181.01616101697795},"K2=",0,null,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,"peak2",{"$f":"INDIRECT(\"B\"&AF5)","v":0.29461083435645008},{"$f":"INDIRECT(\"A\"&AF5)","v":1190},{"$f":"MATCH(2,U11:U351,0)+7","v":247},"peak2",{"$f":"INDIRECT(\"j\"&AJ5)","v":0.2975714737695298},{"$f":"INDIRECT(\"A\"&AJ5)","v":1190},{"$f":"MATCH(2,AB12:AB352,0)+9","v":247}]
["lambda",0.3,9.9999999999999995E-7,"Rs=",{"$f":"200/(4*B4)","v":0.90009000900090008},{"$f":"AJ8","v":0.66365254433554444},"dip between sharpened peaks",null,null,null,"Smooth coefficients--->",1,2,3,4,5,6,7,8,9,8,7,6,5,4,3,2,1,"valley",{"$f":"MIN(INDIRECT(\"B\"&AF4):INDIRECT(\"B\"&AF5))","v":0.20057498604004712},{"$f":"INDIRECT(\"A\"&MATCH(AD6,INDIRECT(\"B\"&AF4):INDIRECT(\"B\"&AF5),0)+AF4-1)","v":1130},{"$f":"MATCH(AD6,INDIRECT(\"B\"&AF4):INDIRECT(\"B\"&AF5),0)+AF4-1","v":235},"valley",{"$f":"MIN(INDIRECT(\"j\"&AJ4):INDIRECT(\"j\"&AJ5))","v":0.19748406568882618},{"$f":"INDIRECT(\"A\"&MATCH(AH6,INDIRECT(\"j\"&AJ4):INDIRECT(\"j\"&AJ5),0)+AJ4-1)","v":1125},{"$f":"MATCH(AH6,INDIRECT(\"j\"&AJ4):INDIRECT(\"j\"&AJ5),0)+AJ4-1","v":234}]
["Simulated data",null,"1st",null,"Smoothed","2nd","Smoothed",null,null,"Sharpened",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Area 1",{"$f":"SUM(B9:INDIRECT(\"B\"&AF6))*(A10-A9)","v":142.07069010795334},"shift",{"$f":"AF4-109","v":99},"Area 1",{"$f":"SUM(J9:INDIRECT(\"j\"&AJ6))*(A10-A9)","v":141.81440087533429},"shift",{"$f":"AJ4-109","v":99}]
["X","Y"," derivative",null,"1st deriv."," derivative"," 2nd deriv.",null,null,"Signal","d/dt sharpened signal","smoothed",null,null,null,null,null,null,null,"Peak detection matrix",null,null,null,null,null,null,null,null,"Area 2",{"$f":"SUM(INDIRECT(\"B\"&AF6):B349)*(A11-A10)","v":39.948345674730227},"% dip",{"$f":"AD6/AD5","v":0.68081333966615476},"Area 2",{"$f":"SUM(INDIRECT(\"j\"&AJ6):J347)*(A10-A9)","v":40.18918030559319},"% dip",{"$f":"AH6/AH5","v":0.66365254433554444}]
[0,{"$f":"(($B$4*$B$6*SQRT(PI()/2)*EXP(0.5*($B$4*$B$6)^2-$B$6*(A9-1000))*ERFC((1/SQRT(2))*($B$4*$B$6-((A9-1000)/$B$4))))+$B$3*($B$4*$B$6*SQRT(PI()/2)*EXP(0.5*($B$4*$B$6)^2-$B$6*(A9-1200))*ERFC((1/SQRT(2))*($B$4*$B$6-((A9-1200)/$B$4)))))+$B$5*(RAND()-RAND()+RAND()-RAND())","v":2.049989398313179E-71},0,null,0,null,0,null,null,{"$f":"B9-($J$5*G9)+($J$4*E9)","v":2.049989398313179E-71},null,null,null,null,null,null,{"$f":"MAX(U11:U349)","v":2},"peaks in raw data",null,null,null,null,{"$f":"MAX(AB11:AB349)","v":2},"peaks in sharpened data",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"single EMG"]
[5,{"$f":"(($B$4*$B$6*SQRT(PI()/2)*EXP(0.5*($B$4*$B$6)^2-$B$6*(A10-1000))*ERFC((1/SQRT(2))*($B$4*$B$6-((A10-1000)/$B$4))))+$B$3*($B$4*$B$6*SQRT(PI()/2)*EXP(0.5*($B$4*$B$6)^2-$B$6*(A10-1200))*ERFC((1/SQRT(2))*($B$4*$B$6-((A10-1200)/$B$4)))))+$B$5*(RAND()-RAND()+RAND()-RAND())","v":1.0347069300568565E-70},{"$f":"(B10-B9)/(A10-A9)","v":1.6594159804510773E-71},null,0,{"$f":"(E11-E9)/(A11-A9)","v":0},0,null,null,{"$f":"B10-($J$5*G10)+($J$4*E10)","v":1.0347069300568565E-70},{"$f":"(J10-J9)/(A10-A9)","v":1.6594159804510773E-71},null,null,null,null,"Signal greater than amplitude threshold?","Down zero crossing in first derivative?","Crossing slope greater than slope threshold?","All three conditions met? Peak detected!","# of peaks so far","#",null,"Signal greater than amplitude threshold?","Down zero crossing in first derivative?","Crossing slope greater than slope threshold?","All three conditions met? Peak detected!","# of peaks so far","#",null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"(($B$4*$B$6*SQRT(PI()/2)*EXP(0.5*($B$4*$B$6)^2-$B$6*(A9-1000))*ERFC((1/SQRT(2))*($B$4*$B$6-((A9-1000)/$B$4)))))","v":2.049989398313179E-71}]
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