Re: Fitting step function

*To*: mathgroup at smc.vnet.net*Subject*: [mg122124] Re: Fitting step function*From*: premiumxy <spam at stefanabel.com>*Date*: Sat, 15 Oct 2011 06:04:05 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

Thanks for your quick and very useful replies! @Jacopo: Actually, I already started to follow the approach that you mentioned. The main problem is that my data is at some points quite noisy, and I often have single points that are far off. To not identify these points with your approach, I would have to filter them out/average the rest... it works, but is not as nice compared to a real fitting procedure, to my opinion. @Barrie: I did not fully understand your message: I see that you used a ArcTan function to fit the data. Similar to a Tanh function, this is a continuous function where I did not really encounter any problems. A main question for me was: why do the step-functions (like UnionStep...) not work with the fitting routine (at least in my case, it did not vary the parameters during the NonlinearModel fit. Could you also use a step function in your example? Also, since you asked, here is a typical dataset. There are phase steps, one at x=0 (Degrees), and the other one at approx x=-70. Please let me know if you need further infos. (The x-values correspond to angles, and do to symmetry considerations the data should be identical for x=+/-180 (Degree) shifts). Thanks! {{-100., 57.4948}, {-90., 42.6258}, {-80., -3.01049}, {-70., -53.8789}, {-60., -78.5062}, \ {-50., -96.6829}, {-40., -101.013}, {-30., -104.941}, {-20., \ -107.919}, {-10., -103.491}, {-9.18182, -103.468}, {-8.36364, \ -103.428}, {-7.54546, -105.213}, {-6.72727, -105.881}, {-5.90909, \ -106.698}, {-5.09091, -107.537}, {-4.27273, -110.424}, {-3.45455, \ -111.979}, {-2.63636, -112.266}, {-1.81818, -113.822}, {-1., \ -117.458}, {-0.916667, -117.899}, {-0.833333, -117.818}, {-0.75, \ -118.569}, {-0.666667, -120.746}, {-0.583333, -122.002}, {-0.5, \ -121.36}, {-0.416667, -123.908}, {-0.333333, -127.475}, {-0.25, \ -132.497}, {-0.166667, -142.056}, {-0.0833333, -138.18}, {0., 172.553}, {0.0833333, 95.6629}, {0.166667, 78.5605}, {0.25, 75.5235}, {0.333333, 76.3874}, {0.416667, 66.8391}, {0.5, 73.1105}, {0.583333, 75.8971}, {0.666667, 73.563}, {0.75, 73.4579}, {0.833333, 71.3489}, {0.916667, 72.4683}, {1., 73.004}, {1.81818, 72.7993}, {2.63636, 71.4382}, {3.45455, 70.4792}, {4.27273, 94.4053}, {5.09091, 91.554}, {5.90909, 90.8934}, {6.72727, 89.555}, {7.54546, 88.8319}, {8.36364, 86.212}, {9.18182, 86.6523}, {10., 84.9855}, {20., 66.2744}, {30., 63.914}, {40., 62.9344}, {50., 59.8152}, {60., 70.5103}, {70., 67.1989}, {80., 58.172}, {90., 43.9631}, {100., 0.901958}}