0
$\begingroup$

If I have the following data:

data={{7.96774, 1.56726}, {8.135, 1.5464}, {8.302, 1.50128}, {8.469, 
  1.48137}, {8.631, 1.70807}, {8.793, 1.95927}, {8.956, 
  2.12076}, {9.121, 2.18059}, {9.291, 2.01987}, {9.462, 
  1.80644}, {9.634, 1.57076}, {9.806, 1.33481}, {9.977, 
  1.12396}, {10.147, 0.928622}, {10.318, 0.751031}, {10.488, 
  0.589379}, {10.658, 0.437464}, {10.827, 0.311543}, {10.996, 
  0.197116}, {11.165, 0.0954133}, {11.333, 
  0.00229275}, {11.502, -0.0729584}, {11.67, -0.139729}, {11.838, \
-0.197912}, {12.005, -0.250487}, {12.173, -0.293136}, {12.34, \
-0.329747}, {12.508, -0.362385}, {12.675, -0.390908}, {12.842, \
-0.414867}, {13.009, -0.435075}, {13.176, -0.452986}, {13.343, \
-0.469488}, {13.51, -0.48198}, {13.677, -0.493373}, {13.844, \
-0.503265}, {14.011, -0.513132}, {14.178, -0.519815}, {14.345, \
-0.525868}, {14.511, -0.531485}, {14.678, -0.536355}, {14.845, \
-0.540827}, {15.012, -0.5453}, {15.179, -0.549184}, {15.345, \
-0.5528}, {15.512, -0.554133}, {15.679, -0.556115}, {15.845, \
-0.558311}, {16.012, -0.560484}, {16.179, -0.562462}, {16.346, \
-0.564472}, {16.512, -0.566367}, {16.679, -0.568136}, {16.846, \
-0.569721}, {17.012, -0.571179}, {17.179, -0.57258}, {17.346, \
-0.573914}, {17.513, -0.575043}, {17.679, -0.576335}, {17.846, \
-0.577633}, {18.013, -0.578875}, {18.179, -0.580188}, {18.346, \
-0.581351}, {18.513, -0.582421}, {18.68, -0.583426}, {18.846, \
-0.584218}, {19.013, -0.585184}, {19.18, -0.586136}, {19.346, \
-0.587095}, {19.513, -0.587872}, {19.68, -0.588636}, {19.846, \
-0.589461}, {20.013, -0.590312}, {20.18, -0.590885}, {20.346, \
-0.591489}, {20.513, -0.592108}, {20.68, -0.592725}, {20.847, \
-0.593118}, {21.013, -0.593568}, {21.18, -0.594134}, {21.347, \
-0.594723}, {21.513, -0.595303}, {21.68, -0.595876}, {21.847, \
-0.596392}, {22.013, -0.596852}, {22.18, -0.59754}, {22.347, \
-0.59816}, {22.513, -0.598651}, {22.68, -0.599116}, {22.847, \
-0.599463}, {23.014, -0.599827}, {23.18, -0.600176}, {23.347, \
-0.600484}, {23.514, -0.600702}, {23.68, -0.600953}, {23.847, \
-0.601148}, {24.014, -0.601342}, {24.18, -0.601613}, {24.347, \
-0.601853}, {24.514, -0.602033}, {24.68, -0.602217}, {24.847, \
-0.602353}, {25.014, -0.602501}, {25.18, -0.602686}, {25.347, \
-0.602844}, {25.514, -0.603073}, {25.681, -0.603369}, {25.847, \
-0.603674}, {26.014, -0.603931}, {26.181, -0.604298}, {26.347, \
-0.60456}, {26.514, -0.604722}, {26.681, -0.604833}, {26.847, \
-0.604767}, {27.014, -0.604874}, {27.181, -0.604976}, {27.347, \
-0.60502}, {27.514, -0.605058}, {27.681, -0.605066}, {27.847, \
-0.605084}, {28.014, -0.605096}, {28.181, -0.60503}, {28.347, \
-0.60502}, {28.514, -0.60502}, {28.681, -0.605039}, {28.847, \
-0.605074}, {29.014, -0.605204}, {29.181, -0.605306}, {29.348, \
-0.60545}, {29.514, -0.605637}, {29.681, -0.605699}, {29.848, \
-0.605807}, {30.014, -0.606053}, {30.181, -0.606138}, {30.348, \
-0.606147}, {30.514, -0.60618}, {30.681, -0.606272}, {30.848, \
-0.606108}, {31.014, -0.606031}, {31.181, -0.606013}, {31.348, \
-0.60598}, {31.514, -0.605902}, {31.681, -0.605936}, {31.848, \
-0.605997}, {32.014, -0.606072}, {32.181, -0.606327}, {32.348, \
-0.606351}, {32.514, -0.606276}, {32.681, -0.606226}, {32.848, \
-0.605964}, {33.015, -0.605738}, {33.181, -0.605506}, {33.348, \
-0.605236}, {33.515, -0.60476}, {33.681, -0.604431}, {33.848, \
-0.60414}, {34.015, -0.603862}, {34.181, -0.603599}, {34.348, \
-0.603327}, {34.515, -0.60305}, {34.681, -0.602719}, {34.848, \
-0.602565}, {35.015, -0.602495}, {35.181, -0.602398}, {35.348, \
-0.602309}, {35.515, -0.602281}, {35.681, -0.602162}, {35.848, \
-0.602023}, {36.015, -0.601898}, {36.181, -0.601475}, {36.348, \
-0.601105}, {36.515, -0.600692}, {36.681, -0.600351}, {36.848, \
-0.599836}, {37.015, -0.599475}, {37.181, -0.599255}, {37.348, \
-0.599028}, {37.515, -0.598888}, {37.681, -0.598731}, {37.848, \
-0.598552}, {38.015, -0.598311}, {38.181, -0.598059}, {38.348, \
-0.597773}, {38.515, -0.597423}, {38.681, -0.597049}, {38.848, \
-0.596591}, {39.015, -0.596251}, {39.181, -0.595913}, {39.348, \
-0.595509}, {39.515, -0.595196}, {39.681, -0.59492}, {39.848, \
-0.5947}, {40.015, -0.594539}, {40.181, -0.594312}, {40.348, \
-0.594081}, {40.515, -0.593753}, {40.681, -0.593377}, {40.848, \
-0.592924}, {41.015, -0.592517}, {41.181, -0.592192}, {41.348, \
-0.5919}, {41.515, -0.591724}, {41.682, -0.591522}, {41.848, \
-0.591297}, {42.015, -0.591051}, {42.182, -0.590863}, {42.348, \
-0.590617}, {42.515, -0.590331}, {42.682, -0.590027}, {42.848, \
-0.589566}, {43.015, -0.589177}, {43.182, -0.58879}, {43.348, \
-0.588402}, {43.515, -0.587871}, {43.682, -0.58738}, {43.848, \
-0.586918}, {44.015, -0.586488}, {44.182, -0.585995}, {44.348, \
-0.585604}, {44.515, -0.585279}, {44.682, -0.584964}, {44.848, \
-0.584649}, {45.015, -0.584284}, {45.182, -0.583918}, {45.348, \
-0.583518}, {45.515, -0.582852}, {45.682, -0.582295}, {45.848, \
-0.581756}, {46.015, -0.58121}, {46.182, -0.580592}, {46.348, \
-0.580079}, {46.515, -0.579607}, {46.682, -0.579119}, {46.848, \
-0.57872}, {47.015, -0.578336}, {47.182, -0.577935}, {47.348, \
-0.577503}, {47.515, -0.576997}, {47.682, -0.57654}, {47.848, \
-0.576063}, {48.015, -0.575598}, {48.182, -0.575137}, {48.348, \
-0.574748}, {48.515, -0.57433}, {48.682, -0.573862}, {48.848, \
-0.573473}, {49.015, -0.573086}, {49.182, -0.57269}, {49.348, \
-0.572278}, {49.515, -0.571792}, {49.682, -0.571332}, {49.848, \
-0.570937}, {50.015, -0.570629}, {50.182, -0.570324}, {50.348, \
-0.569964}, {50.515, -0.56952}, {50.682, -0.569036}, {50.848, \
-0.568532}, {51.015, -0.567985}, {51.182, -0.567396}, {51.348, \
-0.566792}, {51.515, -0.566179}, {51.682, -0.565589}, {51.848, \
-0.565}, {52.015, -0.564412}, {52.182, -0.563903}, {52.348, \
-0.563229}, {52.515, -0.562493}, {52.682, -0.561707}, {52.848, \
-0.560841}, {53.015, -0.560048}, {53.182, -0.559269}, {53.348, \
-0.558481}, {53.515, -0.557784}, {53.682, -0.557025}, {53.848, \
-0.556204}, {54.015, -0.555307}, {54.182, -0.554469}, {54.348, \
-0.553661}, {54.515, -0.552836}, {54.681, -0.551979}, {54.848, \
-0.551237}, {55.015, -0.550454}, {55.181, -0.549659}, {55.348, \
-0.548882}, {55.515, -0.548084}, {55.681, -0.547209}, {55.848, \
-0.5463}, {56.015, -0.54531}, {56.181, -0.544287}, {56.348, \
-0.543327}, {56.515, -0.542344}, {56.681, -0.541325}, {56.848, \
-0.540258}, {57.015, -0.539077}, {57.181, -0.537932}, {57.348, \
-0.536788}, {57.515, -0.535376}, {57.681, -0.533994}, {57.848, \
-0.532621}, {58.015, -0.531276}, {58.181, -0.529846}, {58.348, \
-0.5284}, {58.514, -0.526927}, {58.681, -0.525388}, {58.848, \
-0.523733}, {59.014, -0.522078}, {59.181, -0.520365}, {59.348, \
-0.518596}, {59.514, -0.516641}, {59.681, -0.51474}, {59.847, \
-0.512765}, {60.014, -0.510794}, {60.181, -0.508724}, {60.347, \
-0.50666}, {60.514, -0.504548}, {60.681, -0.502374}, {60.847, \
-0.500135}, {61.014, -0.497802}, {61.18, -0.495308}, {61.347, \
-0.492812}, {61.514, -0.489924}, {61.68, -0.487058}, {61.847, \
-0.484101}, {62.013, -0.481123}, {62.18, -0.477741}, {62.347, \
-0.474428}, {62.513, -0.471069}, {62.68, -0.467665}, {62.846, \
-0.463933}, {63.013, -0.460164}, {63.179, -0.456292}, {63.346, \
-0.452003}, {63.513, -0.44743}, {63.679, -0.442982}, {63.846, \
-0.438375}, {64.012, -0.433582}, {64.179, -0.428323}, {64.345, \
-0.423092}, {64.512, -0.417727}, {64.678, -0.41222}, {64.845, \
-0.406054}, {65.011, -0.399997}, {65.178, -0.393814}, {65.344, \
-0.387497}, {65.511, -0.380519}, {65.677, -0.373662}, {65.844, \
-0.366692}, {66.01, -0.359231}, {66.177, -0.351331}, {66.343, \
-0.343502}, {66.51, -0.335524}, {66.676, -0.32738}, {66.842, \
-0.318816}, {67.009, -0.310346}, {67.175, -0.301801}, {67.342, \
-0.293172}, {67.508, -0.284347}, {67.675, -0.275607}, {67.841, \
-0.266868}, {68.007, -0.258133}, {68.174, -0.24947}, {68.34, \
-0.240872}, {68.507, -0.232346}, {68.673, -0.223895}, {68.84, \
-0.215818}, {69.006, -0.207777}, {69.172, -0.199948}, {69.339, \
-0.192293}, {69.505, -0.185224}, {69.672, -0.177854}, {69.838, \
-0.171028}, {70.005, -0.16521}, {70.171, -0.160071}, {70.338, \
-0.154877}, {70.504, -0.150639}, {70.671, -0.1471}, {70.838, \
-0.144246}, {71.004, -0.141337}, {71.171, -0.139207}, {71.337, \
-0.137564}, {71.504, -0.137787}, {71.671, -0.137724}, {71.837, \
-0.13802}, {72.004, -0.138688}, {72.171, -0.140468}, {72.337, \
-0.14218}, {72.504, -0.14421}, {72.671, -0.146476}, {72.838, \
-0.14986}, {73.005, -0.153233}, {73.171, -0.156506}, {73.338, \
-0.15985}, {73.505, -0.163613}, {73.672, -0.167102}, {73.838, \
-0.170444}, {74.005, -0.173696}, {74.172, -0.176653}, {74.339, \
-0.179492}, {74.505, -0.182101}, {74.672, -0.184524}, {74.839, \
-0.186456}, {75.006, -0.188589}, {75.172, -0.190549}, {75.339, \
-0.192324}, {75.506, -0.193653}, {75.672, -0.194985}, {75.839, \
-0.196205}, {76.006, -0.197348}, {76.173, -0.197963}, {76.339, \
-0.198745}, {76.506, -0.199434}, {76.673, -0.200046}, {76.839, \
-0.200399}, {77.006, -0.200728}, {77.173, -0.200978}, {77.339, \
-0.201176}, {77.506, -0.20113}, {77.673, -0.201187}, {77.839, \
-0.201292}, {78.006, -0.201484}, {78.173, -0.201872}, {78.339, \
-0.202183}, {78.506, -0.202464}, {78.673, -0.202759}, {78.839, \
-0.203127}, {79.006, -0.203282}, {79.173, -0.203404}, {79.339, \
-0.203574}, {79.506, -0.203292}, {79.673, -0.203095}, {79.839, \
-0.20295}, {80.006, -0.202848}, {80.173, -0.202596}, {80.339, \
-0.202421}, {80.506, -0.202254}, {80.673, -0.202119}, {80.839, \
-0.202066}, {81.006, -0.20202}, {81.173, -0.201953}, {81.339, \
-0.201876}, {81.506, -0.201804}, {81.673, -0.201761}, {81.84, \
-0.201765}, {82.006, -0.201758}, {82.173, -0.201739}, {82.34, \
-0.201773}, {82.506, -0.201785}, {82.673, -0.201728}, {82.84, \
-0.201631}, {83.006, -0.201539}, {83.173, -0.201393}, {83.34, \
-0.201213}, {83.506, -0.200869}, {83.673, -0.200648}, {83.84, \
-0.200468}, {84.006, -0.200313}, {84.173, -0.200043}, {84.34, \
-0.199789}, {84.506, -0.199548}, {84.673, -0.199318}, {84.84, \
-0.199003}, {85.006, -0.198857}, {85.173, -0.198756}, {85.34, \
-0.198618}, {85.506, -0.198503}, {85.673, -0.198315}, {85.84, \
-0.198102}, {86.006, -0.197854}, {86.173, -0.197428}, {86.339, \
-0.197051}, {86.506, -0.196711}, {86.673, -0.196389}, {86.839, \
-0.19602}, {87.006, -0.195708}, {87.173, -0.195422}, {87.339, \
-0.195171}, {87.506, -0.194906}, {87.673, -0.194636}, {87.839, \
-0.19441}, {88.006, -0.194146}, {88.173, -0.193767}, {88.339, \
-0.193419}, {88.506, -0.19307}, {88.673, -0.192756}, {88.839, \
-0.192465}, {89.006, -0.192252}, {89.173, -0.192063}, {89.339, \
-0.191836}, {89.506, -0.191648}, {89.673, -0.191416}, {89.839, \
-0.191232}, {90.006, -0.19105}, {90.173, -0.190693}, {90.339, \
-0.190372}, {90.506, -0.190043}, {90.673, -0.189726}, {90.839, \
-0.189441}, {91.006, -0.189198}, {91.173, -0.189069}, {91.339, \
-0.189035}, {91.506, -0.189091}, {91.673, -0.18905}, {91.839, \
-0.189031}, {92.006, -0.189143}, {92.173, -0.18921}, {92.339, \
-0.18926}, {92.506, -0.189836}, {92.673, -0.191524}, {92.84, \
-0.194287}, {93.006, -0.193717}, {93.173, -0.19187}, {93.339, \
-0.189806}, {93.506, -0.187984}, {93.673, -0.18646}, {93.839, \
-0.185048}, {94.006, -0.183745}, {94.173, -0.183}, {94.339, \
-0.18212}, {94.506, -0.181331}, {94.673, -0.180589}, {94.839, \
-0.180059}, {95.006, -0.17945}, {95.172, -0.178897}, {95.339, \
-0.178433}, {95.506, -0.1781}, {95.672, -0.177813}, {95.839, \
-0.177548}, {96.006, -0.177288}, {96.172, -0.177164}, {96.339, \
-0.176959}, {96.506, -0.176694}, {96.672, -0.176434}, {96.839, \
-0.176044}, {97.006, -0.175679}, {97.172, -0.175322}, {97.339, \
-0.175014}, {97.506, -0.174796}, {97.672, -0.174649}, {97.839, \
-0.174519}, {98.006, -0.174338}, {98.172, -0.174389}, {98.339, \
-0.174305}, {98.506, -0.174113}, {98.672, -0.173865}, {98.839, \
-0.173536}, {99.006, -0.173253}, {99.172, -0.172948}, {99.339, \
-0.172632}, {99.506, -0.172378}, {99.672, -0.172128}, {99.839, \
-0.17183}, {100.006, -0.171526}, {100.172, -0.171247}, {100.339, \
-0.170966}, {100.506, -0.170713}, {100.672, -0.1705}, {100.839, \
-0.170334}, {101.006, -0.170237}, {101.172, -0.1701}, {101.339, \
-0.169865}, {101.506, -0.169764}, {101.672, -0.16957}, {101.839, \
-0.169297}, {102.006, -0.168997}, {102.172, -0.168589}, {102.339, \
-0.168215}, {102.506, -0.167789}, {102.672, -0.167288}, {102.839, \
-0.171012}, {103.006, -0.172892}, {103.172, -0.172753}, {103.339, \
-0.171707}, {103.506, -0.1707}, {103.672, -0.170053}, {103.839, \
-0.169348}, {104.006, -0.168645}, {104.172, -0.168057}, {104.339, \
-0.167494}, {104.506, -0.166991}, {104.672, -0.16653}, {104.839, \
-0.166237}, {105.006, -0.16586}, {105.172, -0.165496}, {105.339, \
-0.165154}, {105.506, -0.164937}, {105.672, -0.164806}, {105.839, \
-0.164675}, {106.006, -0.164509}, {106.172, -0.164371}, {106.339, \
-0.164071}, {106.506, -0.163779}, {106.672, -0.163508}, {106.839, \
-0.162947}, {107.006, -0.162416}, {107.172, -0.162379}, {107.339, \
-0.162437}, {107.505, -0.161247}, {107.671, -0.140996}, {107.836, \
-0.0900667}}

Which plotted like this: ListLinePlot[data, PlotRange -> {{30, 90}, {-0.7, 0}}] gives:

enter image description here

Questions:

  1. How can I get the first derivative curve of that data?
  2. How can I get the onset of the peak and the endset of the peak based on the first derivative of the data?. Here's a picture of a paper where they take the onset and endset of several curves based on the first derivative. Since I realized that onset is a little bit trickier, it would be enough just to find the endset point (see the two images below)

enter image description here

For the case of this exercise, using the suggestion of MarcoB (int = Interpolation[data]; Plot[int'[x], {x, 30, 90}, PlotRange -> All]), I get:

enter image description here

where the endset point is shown in the image and can be defined as "the value of the x-axis where you get the lowest point in the y-axis at the end of the peak".

EDIT OF WHAT I AM USING TO TRY TO FIND THE ENDSET POINT:

I am using the following to find the endset point: FindMinimum[{int'[x], 40 <= x <= 80}, {x, 40}]. However, it gives me {0.00229078, {x -> 46.9328}} in which obviously the x value of 46.9328 is wrong. Visually inspection shows that the endset point is around 73. How can I fix this?

$\endgroup$
5
  • 2
    $\begingroup$ For the first question you might want to look at InterpolatingFunction $\endgroup$ – mattiav27 Feb 15 at 18:04
  • 4
    $\begingroup$ What is your definition for onset and endset? $\endgroup$ – Bob Hanlon Feb 15 at 18:35
  • 1
    $\begingroup$ For the first part, int = Interpolation[data]; Plot[int'[x], {x, 30, 90}, PlotRange -> All]. For the second part, it depends on how you define those points. $\endgroup$ – MarcoB Feb 15 at 19:15
  • $\begingroup$ @BobHanlon I added a figure to show the onset and endset points of several similar plots. I think finding only the endpoint should be fine for my case. Thanks. $\endgroup$ – John Feb 15 at 19:21
  • $\begingroup$ @BobHanlon I think the endset point can be defined as "the value of the x-axis where you get the lowest point in the y-axis at the end of the peak" (see the extra image I added) $\endgroup$ – John Feb 15 at 19:33

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