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MathGroup Archive 1997

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Re: Sinusoidal Nonlinear Fit

  • To: mathgroup at smc.vnet.net
  • Subject: [mg7887] Re: Sinusoidal Nonlinear Fit
  • From: Mark Evans <evans at gte.net>
  • Date: Thu, 17 Jul 1997 15:35:48 -0400
  • Organization: None
  • Sender: owner-wri-mathgroup at wolfram.com

Mark Evans wrote:
> 
> I am foiled by NonlinearFit....


I found the magic command for getting a good fit based on trigonometric
functions:

<<NumericalMath`TrigFit`
fit = Chop[TrigFit[Flatten[Take[Transpose[passive4],{2}]], 5, {t, 3.45,
13.45}]]


The book says that this TrigFit uses Fourier components directly, which
is essentially what I wanted.  I can use the trig function with the
largest coefficient as the best-fit sinusoid.

I am still puzzled why NonlinearFit could not do this job.  Here again
is the data if you missed it in the first message.

Is this considered a "bug" in NonlinearFit?  Or is NonlinearFit not
supposed to handle periodic functions?


-- Mark


passive4 = 
{{3.45, 634.765625}, 
{3.5, 622.5585937}, 
{3.55, 639.6484375}, 
{3.5999999, 603.0273437}, 
{3.6500001, 649.4140625}, 
{3.7, 654.296875}, 
{3.75, 690.9179687}, 
{3.8, 678.7109375}, 
{3.8499999, 712.890625}, 
{3.9000001, 751.953125}, 
{3.95, 839.84375}, 
{4., 849.609375}, 
{4.0500002, 949.7070312}, 
{4.0999999, 917.96875}, 
{4.1500001, 1022.949219}, 
{4.1999998, 974.1210937}, 
{4.25, 1076.660156}, 
{4.3000002, 1003.417969}, 
{4.3499999, 1096.191406}, 
{4.4000001, 1064.453125}, 
{4.4499998, 1105.957031}, 
{4.5, 1088.867188}, 
{4.5500002, 1101.074219}, 
{4.5999999, 1105.957031}, 
{4.6500001, 1098.632813}, 
{4.6999998, 1120.605469}, 
{4.75, 1091.308594}, 
{4.8000002, 1127.929688}, 
{4.8499999, 1096.191406}, 
{4.9000001, 1123.046875}, 
{4.9499998, 1081.542969}, 
{5., 1118.164063}, 
{5.0500002, 1081.542969}, 
{5.0999999, 1127.929688}, 
{5.1500001, 1086.425781}, 
{5.1999998, 1130.371094}, 
{5.25, 1076.660156}, 
{5.3000002, 1132.8125}, 
{5.3499999, 1083.984375}, 
{5.4000001, 1147.460938}, 
{5.4499998, 1066.894531}, 
{5.5, 1118.164063}, 
{5.5500002, 998.5351562}, 
{5.5999999, 1047.363281}, 
{5.6500001, 949.7070312}, 
{5.6999998, 1000.976563}, 
{5.75, 910.6445312}, 
{5.8000002, 947.265625}, 
{5.8499999, 883.7890625}, 
{5.9000001, 908.203125}, 
{5.9499998, 852.0507812}, 
{6., 866.6992187}, 
{6.0500002, 793.4570312}, 
{6.0999999, 781.25}, 
{6.1500001, 717.7734375}, 
{6.1999998, 690.9179687}, 
{6.25, 651.8554687}, 
{6.3000002, 620.1171875}, 
{6.3499999, 563.9648437}, 
{6.4000001, 537.109375}, 
{6.4499998, 502.9296875}, 
{6.5, 461.4257812}, 
{6.5500002, 446.7773437}, 
{6.5999999, 397.9492187}, 
{6.6500001, 397.9492187}, 
{6.6999998, 351.5625}, 
{6.75, 334.4726562}, 
{6.8000002, 305.1757812}, 
{6.8499999, 283.203125}, 
{6.9000001, 285.6445312}, 
{6.9499998, 278.3203125}, 
{7., 261.2304687}, 
{7.0500002, 246.5820312}, 
{7.0999999, 178.2226562}, 
{7.1500001, 200.1953125}, 
{7.1999998, 190.4296875}, 
{7.25, 153.8085937}, 
{7.3000002, 180.6640625}, 
{7.3499999, 197.7539062}, 
{7.4000001, 183.1054687}, 
{7.4499998, 166.015625}, 
{7.5, 197.7539062}, 
{7.5500002, 153.8085937}, 
{7.5999999, 168.4570312}, 
{7.6500001, 200.1953125}, 
{7.6999998, 200.1953125}, 
{7.75, 190.4296875}, 
{7.8000002, 190.4296875}, 
{7.8499999, 251.4648437}, 
{7.9000001, 207.5195312}, 
{7.9499998, 270.9960937}, 
{8., 241.6992187}, 
{8.0500002, 275.8789062}, 
{8.1000004, 341.796875}, 
{8.1499996, 400.390625}, 
{8.1999998, 434.5703125}, 
{8.25, 478.515625}, 
{8.3000002, 515.1367187}, 
{8.3500004, 527.34375}, 
{8.3999996, 573.7304687}, 
{8.4499998, 603.0273437}, 
{8.5, 649.4140625}, 
{8.5500002, 649.4140625}, 
{8.6000004, 708.0078125}, 
{8.6499996, 705.5664062}, 
{8.6999998, 771.484375}, 
{8.75, 756.8359375}, 
{8.8000002, 827.6367187}, 
{8.8500004, 803.2226562}, 
{8.8999996, 883.7890625}, 
{8.9499998, 852.0507812}, 
{9., 944.8242187}, 
{9.0500002, 903.3203125}, 
{9.1000004, 988.7695312}, 
{9.1499996, 952.1484375}, 
{9.1999998, 1022.949219}, 
{9.25, 1000.976563}, 
{9.3000002, 1059.570313}, 
{9.3500004, 1037.597656}, 
{9.3999996, 1049.804688}, 
{9.4499998, 1071.777344}, 
{9.5, 1032.714844}, 
{9.5500002, 1059.570313}, 
{9.6000004, 1052.246094}, 
{9.6499996, 1066.894531}, 
{9.6999998, 1013.183594}, 
{9.75, 1074.21875}, 
{9.8000002, 1015.625}, 
{9.8500004, 1054.6875}, 
{9.8999996, 996.09375}, 
{9.9499998, 1059.570313}, 
{10., 996.09375}, 
{10.0500002, 1054.6875}, 
{10.1000004, 966.796875}, 
{10.1499996, 1010.742188}, 
{10.1999998, 908.203125}, 
{10.25, 937.5}, 
{10.3000002, 849.609375}, 
{10.3500004, 900.8789062}, 
{10.3999996, 817.8710937}, 
{10.4499998, 864.2578125}, 
{10.5, 783.6914062}, 
{10.5500002, 803.2226562}, 
{10.6000004, 732.421875}, 
{10.6499996, 751.953125}, 
{10.6999998, 690.9179687}, 
{10.75, 683.59375}, 
{10.8000002, 627.4414062}, 
{10.8500004, 622.5585937}, 
{10.8999996, 568.8476562}, 
{10.9499998, 551.7578125}, 
{11., 529.7851562}, 
{11.0500002, 500.4882812}, 
{11.1000004, 468.75}, 
{11.1499996, 446.7773437}, 
{11.1999998, 424.8046875}, 
{11.25, 383.3007812}, 
{11.3000002, 390.625}, 
{11.3500004, 341.796875}, 
{11.3999996, 334.4726562}, 
{11.4499998, 314.9414062}, 
{11.5, 302.734375}, 
{11.5500002, 273.4375}, 
{11.6000004, 256.3476562}, 
{11.6499996, 246.5820312}, 
{11.6999998, 251.4648437}, 
{11.75, 224.609375}, 
{11.8000002, 224.609375}, 
{11.8500004, 195.3125}, 
{11.8999996, 163.5742187}, 
{11.9499998, 141.6015625}, 
{12., 151.3671875}, 
{12.0500002, 178.2226562}, 
{12.1000004, 190.4296875}, 
{12.1499996, 173.3398437}, 
{12.1999998, 175.78125}, 
{12.25, 139.1601562}, 
{12.3000002, 195.3125}, 
{12.3500004, 156.25}, 
{12.3999996, 217.2851562}, 
{12.4499998, 222.1679687}, 
{12.5, 256.3476562}, 
{12.5500002, 244.140625}, 
{12.6000004, 258.7890625}, 
{12.6499996, 273.4375}, 
{12.6999998, 346.6796875}, 
{12.75, 375.9765625}, 
{12.8000002, 400.390625}, 
{12.8500004, 429.6875}, 
{12.8999996, 441.8945312}, 
{12.9499998, 490.7226562}, 
{13., 490.7226562}, 
{13.0500002, 517.578125}, 
{13.1000004, 505.3710937}, 
{13.1499996, 541.9921875}, 
{13.1999998, 527.34375}, 
{13.25, 546.875}, 
{13.3000002, 527.34375}, 
{13.3500004, 556.640625}, 
{13.3999996, 515.1367187}, 
{13.4499998, 559.0820312}};



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