I am trying to find the local minimum of the list of data with some noise. Here is how the data looks like below image, and I want to extract the three points.
From an question by giacomo (link), I kind of get how can I approach the solution. Michael suggested to use
peakQ[{{x1_,y1_},{x2_,y2_},{x3_,y3_}}]:=y1<y2 && y2>y3
However, it will give more than 3 points of minimum because of my noisy data set; I want to find local minimum without the min points generated by the error(noise).
Here is one of the sample list. Anyone can suggest which way shall I look for?
list={0.045923, 0.0431522, 0.0482363, 0.0454668, 0.0505528, 0.0399323,
0.045022, 0.0422603, 0.0473553, 0.0446, 0.049702, 0.0469549,
0.0442125, 0.0493284, 0.0465969, 0.0517241, 0.0490052, 0.0462932,
0.0514411, 0.0487444, 0.0460562, 0.0512286, 0.0485584, 0.0458979,
0.0510991, 0.0484594, 0.0458309, 0.0432139, 0.04846, 0.0458675,
0.0511388, 0.0485726, 0.0460204, 0.0434826, 0.0488098, 0.046302,
0.04381, 0.0413343, 0.0467248, 0.0442828, 0.0418584, 0.0473013,
0.0449134, 0.0425444, 0.0401949, 0.0378653, 0.0355561, 0.0332676,
0.0310004, 0.0287548, 0.0343794, 0.0243304, 0.0300003, 0.019998,
0.0257149, 0.0236084, 0.0136793, 0.0116227, 0.00959164, 0.0075865,
0.00560771, -0.00419092, -0.0061157, -0.00801295, -0.0177285,
-0.0195693, -0.0213815, -0.0153189, -0.00922709, -0.0109513,
-0.00479991, -0.00646356, 0.00759389, 0.00599204, 0.00442172,
0.00288328, 0.00137703, 0.00774775, 0.00630671, 0.012743, 0.0113684,
0.0100275, 0.00872066, 0.00744809, 0.0062101, 0.00500694, 0.00383888,
0.0105493, 0.00945204, 0.00839062, 0.00736526, -0.00146641,
0.00542361, 0.00450775, 0.00362879, 0.00278694, -0.00585956,
0.00121527, 0.000485792, -0.00020589, -0.00870103, -0.00931655,
-0.0020527, -0.0104328, -0.0109332, -0.0113951, -0.0118183,
-0.0122027, -0.0125483, -0.0128549, -0.0131224, -0.0211909,
-0.0213801, -0.0215302, -0.0294806, -0.0295521, -0.0295844,
-0.0374165, -0.0452092, -0.0451234, -0.0606759, -0.0683501,
-0.0838232, -0.0992568, -0.114651, -0.145681, -0.160996, -0.160595,
-0.152319, -0.136166, -0.119975, -0.103746, -0.087479, -0.0790116,
-0.0626695, -0.0541267, -0.0533829, -0.0447651, -0.03611, -0.0430904,
-0.0343612, -0.0255953, -0.0246288, -0.0236258, -0.0225865,
-0.0215111, -0.0203999, -0.0114179, -0.0102358, -0.0090186,
-0.00776656, -0.00647993, -0.00515898, -0.003804, -0.00241528,
-0.00882722, 0.000462242, 0.00195043, -0.00436258, -0.0028095,
-0.00122454, 0.000391984, 0.00203973, 0.00371836, -0.0024054,
-0.000665928, -0.0067293, 0.00290212, -0.00310244, -0.00124576,
0.000639261, -0.00527978, -0.00333912, -0.0013713, 0.000623291,
-0.00518723, -0.00314018, -0.00106758, -0.014632, -0.0125093,
-0.0181931, -0.0238527, -0.0216581, -0.0272709, -0.0328609,
-0.0462586, -0.0518041, -0.0729878, -0.0784903, -0.068313,
-0.0659455, -0.0557292, -0.0454941, -0.0352408, -0.0327985,
-0.0225098, -0.0122041, -0.00971053, 0.00062775, -0.00467504,
-0.00213403, 0.0082499, 0.0108201, 0.0134042, 0.0160019, 0.0186125,
0.0212358, 0.0160438, 0.018691, 0.0213492, 0.0240183, 0.0266975,
0.02156, 0.032085, 0.0269659, 0.0296818, 0.0324055, 0.0351369,
0.0378752, 0.0327945, 0.0355458, 0.0383028, 0.041065, 0.036007,
0.0387786, 0.0415541, 0.0365084, 0.0392907, 0.0420757, 0.0370385,
0.0398276, 0.034794, 0.0375855, 0.0403777}
