2
$\begingroup$

enter image description hereI applied the LowpassFilter to my data and it shifted the result. Why is it? How can I filter high frequency oscillations without the shift?

  t = Transpose@
       Join[{Transpose[dat][[1]]}, { 
         LowpassFilter[Transpose[dat][[2]], 0.4]}];
    ListLogPlot[{dat, t}, Joined -> True, ImageSize -> 800]

   dat={{0., 1.}, {0.001, 0.998759}, {0.002, 0.997516}, {0.003, 
      0.996268}, {0.004, 0.995011}, {0.005, 0.993742}, {0.006, 
      0.992457}, {0.007, 0.991152}, {0.008, 0.989824}, {0.009, 
      0.988466}, {0.01, 0.987075}, {0.011, 0.985644}, {0.012, 
      0.984167}, {0.013, 0.982637}, {0.014, 0.981046}, {0.015, 
      0.979383}, {0.016, 0.977638}, {0.017, 0.975797}, {0.018, 
      0.973843}, {0.019, 0.971757}, {0.02, 0.969513}, {0.021, 
      0.967081}, {0.022, 0.964421}, {0.023, 0.96148}, {0.024, 
      0.958187}, {0.025, 0.954446}, {0.026, 0.950115}, {0.027, 
      0.944986}, {0.028, 0.938726}, {0.029, 0.930769}, {0.03, 
      0.920047}, {0.031, 0.904209}, {0.032, 0.876587}, {0.033, 
      0.804836}, {0.034, 0.500818}, {0.035, 0.308999}, {0.036, 
      0.217665}, {0.037, 0.164207}, {0.038, 0.130845}, {0.039, 
      0.106335}, {0.04, 0.0861833}, {0.041, 0.0731473}, {0.042, 
      0.0631012}, {0.043, 0.0519342}, {0.044, 0.0453451}, {0.045, 
      0.0410456}, {0.046, 0.0363328}, {0.047, 0.0314015}, {0.048, 
      0.0271143}, {0.049, 0.023765}, {0.05, 0.0211957}, {0.051, 
      0.0191451}, {0.052, 0.0174149}, {0.053, 0.0158905}, {0.054, 
      0.0145144}, {0.055, 0.0132581}, {0.056, 0.0121059}, {0.057, 
      0.011048}, {0.058, 0.0100777}, {0.059, 0.00919198}, {0.06, 
      0.00839146}, {0.061, 0.00768054}, {0.062, 0.00706556}, {0.063, 
      0.00655166}, {0.064, 0.00613841}, {0.065, 0.00581535}, {0.066, 
      0.0055593}, {0.067, 0.00533546}, {0.068, 0.00510361}, {0.069, 
      0.00482888}, {0.07, 0.00449424}, {0.071, 0.00410968}, {0.072, 
      0.00371266}, {0.073, 0.0033568}, {0.074, 0.00309091}, {0.075, 
      0.00293616}, {0.076, 0.00287259}, {0.077, 0.0028441}, {0.078, 
      0.00278275}, {0.079, 0.00264226}, {0.08, 0.00242324}, {0.081, 
      0.00217458}, {0.082, 0.00196699}, {0.083, 0.00185171}, {0.084, 
      0.00182855}, {0.085, 0.00184469}, {0.086, 0.00182743}, {0.087, 
      0.00173134}, {0.088, 0.00156851}, {0.089, 0.00139996}, {0.09, 
      0.0012924}, {0.091, 0.0012701}, {0.092, 0.00129737}, {0.093, 
      0.00130563}, {0.094, 0.00124575}, {0.095, 0.00112537}, {0.096, 
      0.00100165}, {0.097, 0.000934566}, {0.098, 0.000938175}, {0.099, 
      0.00097006}, {0.1, 0.00096793}, {0.101, 0.000902526}, {0.102, 
      0.00080152}, {0.103, 0.000723851}, {0.104, 0.000707156}, {0.105, 
      0.000735033}, {0.106, 0.000753353}, {0.107, 0.000720309}, {0.108, 
      0.000644056}, {0.109, 0.000573425}, {0.11, 0.000551034}, {0.111, 
      0.000573425}, {0.112, 0.00059592}, {0.113, 0.000576719}, {0.114, 
      0.000516979}, {0.115, 0.000458051}, {0.116, 0.000439513}, {0.117, 
      0.000460186}, {0.118, 0.000480799}, {0.119, 0.000464639}, {0.12, 
      0.000414339}, {0.121, 0.000367668}, {0.122, 0.000357661}, {0.123, 
      0.000378891}, {0.124, 0.000394526}, {0.125, 0.000375741}, {0.126, 
      0.000331438}, {0.127, 0.000297416}, {0.128, 0.000297542}, {0.129, 
      0.000318885}, {0.13, 0.000326917}, {0.131, 0.000303306}, {0.132, 
      0.000264978}, {0.133, 0.000244425}, {0.134, 0.000253806}, {0.135, 
      0.000272458}, {0.136, 0.000270799}, {0.137, 0.000243189}, {0.138, 
      0.000213208}, {0.139, 0.000206365}, {0.14, 0.000221619}, {0.141, 
      0.000233561}, {0.142, 0.000221836}, {0.143, 0.000193838}, {0.144, 
      0.000175279}, {0.145, 0.00018034}, {0.146, 0.000195983}, {0.147, 
      0.000197852}, {0.148, 0.000178571}, {0.149, 0.000155547}, {0.15, 
      0.000149985}, {0.151, 0.000162246}, {0.152, 0.00017221}, {0.153, 
      0.000163408}, {0.154, 0.00014206}, {0.155, 0.000128952}, {0.156, 
      0.000134549}, {0.157, 0.000147087}, {0.158, 0.000147234}, {0.159, 
      0.00013118}, {0.16, 0.000114564}, {0.161, 0.000113213}, {0.162, 
      0.00012432}, {0.163, 0.000130461}, {0.164, 0.000120924}, {0.165, 
      0.00010428}, {0.166, 0.0000974084}, {0.167, 0.000104907}, {0.168, 
      0.000113993}, {0.169, 0.00011054}, {0.17, 0.000096207}, {0.171, 
      0.000085864}, {0.172, 0.0000890772}, {0.173, 0.0000986547}, {0.174, 
      0.0000999924}, {0.175, 0.0000891551}, {0.176, 0.0000773168}, {0.177,
       0.00007655}, {0.178, 0.0000849768}, {0.179, 0.0000895514}, {0.18, 
      0.000082501}, {0.181, 0.000070731}, {0.182, 0.0000667978}, {0.183, 
      0.0000731816}, {0.184, 0.0000795477}, {0.185, 0.0000759973}, {0.186,
       0.0000653548}, {0.187, 0.0000592302}, {0.188, 
      0.0000632564}, {0.189, 0.0000702506}, {0.19, 0.0000696101}, {0.191, 
      0.0000606938}, {0.192, 0.000053303}, {0.193, 0.0000550418}, {0.194, 
      0.0000618286}, {0.195, 0.0000634037}, {0.196, 0.0000564523}, {0.197,
       0.0000485654}, {0.198, 0.0000483074}, {0.199, 0.0000543524}, {0.2, 
      0.0000574702}, {0.201, 0.0000524722}, {0.202, 0.0000446702}, {0.203,
       0.0000428039}, {0.204, 0.0000478171}, {0.205, 
      0.0000518925}, {0.206, 0.0000486826}, {0.207, 0.000041365}, {0.208, 
      0.0000382956}, {0.209, 0.000042167}, {0.21, 0.0000467287}, {0.211, 
      0.0000450621}, {0.212, 0.0000384739}, {0.213, 0.0000345762}, {0.214,
       0.0000373176}, {0.215, 0.0000420095}, {0.216, 
      0.0000416134}, {0.217, 0.0000358796}, {0.218, 0.000031474}, {0.219, 
      0.0000331723}, {0.22, 0.0000377417}, {0.221, 0.0000383486}, {0.222, 
      0.0000335065}, {0.223, 0.0000288513}, {0.224, 0.0000296335}, {0.225,
       0.0000339135}, {0.226, 0.00003528}, {0.227, 0.0000313073}, {0.228, 
      0.000026601}, {0.229, 0.0000266094}, {0.23, 0.0000305004}, {0.231, 
      0.0000324165}, {0.232, 0.0000292538}, {0.233, 0.0000246411}, {0.234,
       0.0000240176}, {0.235, 0.0000274704}, {0.236, 
      0.0000297617}, {0.237, 0.000027329}, {0.238, 0.0000229097}, {0.239, 
      0.0000217866}, {0.24, 0.0000247879}, {0.241, 0.0000273143}, {0.242, 
      0.0000255229}, {0.243, 0.0000213609}, {0.244, 0.0000198557}, {0.245,
       0.0000224164}, {0.246, 0.0000250686}, {0.247, 0.000023829}, {0.248,
       0.0000199606}, {0.249, 0.000018174}, {0.25, 0.0000203207}, {0.251, 
      0.0000230158}, {0.252, 0.0000222429}, {0.253, 0.0000186833}, {0.254,
       0.0000166997}, {0.255, 0.0000184676}, {0.256, 
      0.0000211448}, {0.257, 0.0000207604}, {0.258, 0.0000175103}, {0.259,
       0.0000153982}, {0.26, 0.0000168271}, {0.261, 0.0000194433}, {0.262,
       0.0000193776}, {0.263, 0.0000164275}, {0.264, 
      0.0000142418}, {0.265, 0.000015372}, {0.266, 0.0000178983}, {0.267, 
      0.0000180903}, {0.268, 0.000015424}, {0.269, 0.0000132075}, {0.27, 
      0.0000140786}, {0.271, 0.0000164966}, {0.272, 0.0000168942}, {0.273,
       0.0000144914}, {0.274, 0.000012277}, {0.275, 0.000012926}, {0.276, 
      0.0000152257}, {0.277, 0.0000157844}, {0.278, 0.000013623}, {0.279, 
      0.0000114351}, {0.28, 0.0000118959}, {0.281, 0.0000140734}, {0.282, 
      0.0000147561}, {0.283, 0.0000128132}, {0.284, 0.0000106697}, {0.285,
       0.0000109727}, {0.286, 0.0000130283}, {0.287, 
      0.0000138042}, {0.288, 0.0000120574}, {0.289, 9.97064*10^-6}, {0.29,
       0.0000101429}, {0.291, 0.0000120801}, {0.292, 
      0.0000129237}, {0.293, 0.0000113515}, {0.294, 
      9.32968*10^-6}, {0.295, 9.39479*10^-6}, {0.296, 
      0.0000112191}, {0.297, 0.0000121097}, {0.298, 0.0000106918}, {0.299,
       8.73992*10^-6}, {0.3, 8.71847*10^-6}, {0.301, 
      0.0000104365}, {0.302, 0.0000113573}, {0.303, 0.0000100751}, {0.304,
       8.19561*10^-6}, {0.305, 8.10532*10^-6}, {0.306, 
      9.72457*10^-6}, {0.307, 0.000010662}, {0.308, 
      9.49836*10^-6}, {0.309, 7.69192*10^-6}, {0.31, 
      7.54797*10^-6}, {0.311, 9.07614*10^-6}, {0.312, 
      0.0000100195}, {0.313, 8.95891*10^-6}, {0.314, 
      7.22472*10^-6}, {0.315, 7.04007*10^-6}, {0.316, 
      8.48487*10^-6}, {0.317, 9.42544*10^-6}, {0.318, 
      8.45415*10^-6}, {0.319, 6.79047*10^-6}, {0.32, 
      6.57613*10^-6}, {0.321, 7.94506*10^-6}, {0.322, 
      8.87612*10^-6}, {0.323, 7.98167*10^-6}, {0.324, 
      6.38614*10^-6}, {0.325, 6.15142*10^-6}, {0.326, 
      7.45165*10^-6}, {0.327, 8.3679*10^-6}, {0.328, 
      7.53925*10^-6}, {0.329, 6.00907*10^-6}, {0.33, 
      5.76183*10^-6}, {0.331, 7.00009*10^-6}, {0.332, 
      7.89743*10^-6}, {0.333, 7.12478*10^-6}, {0.334, 
      5.65691*10^-6}, {0.335, 5.4038*10^-6}, {0.336, 
      6.58635*10^-6}, {0.337, 7.46162*10^-6}, {0.338, 
      6.73631*10^-6}, {0.339, 5.32763*10^-6}, {0.34, 
      5.07422*10^-6}, {0.341, 6.20681*10^-6}, {0.342, 
      7.05762*10^-6}, {0.343, 6.37201*10^-6}, {0.344, 
      5.01939*10^-6}, {0.345, 4.77036*10^-6}, {0.346, 
      5.85825*10^-6}, {0.347, 6.6828*10^-6}, {0.348, 
      6.03017*10^-6}, {0.349, 4.73056*10^-6}, {0.35, 
      4.48983*10^-6}, {0.351, 5.5378*10^-6}, {0.352, 
      6.33476*10^-6}, {0.353, 5.7092*10^-6}, {0.354, 
      4.45968*10^-6}, {0.355, 4.23055*10^-6}, {0.356, 
      5.24289*10^-6}, {0.357, 6.01129*10^-6}, {0.358, 
      5.40762*10^-6}, {0.359, 4.20542*10^-6}, {0.36, 
      3.99063*10^-6}, {0.361, 4.97123*10^-6}, {0.362, 
      5.71037*10^-6}, {0.363, 5.12404*10^-6}, {0.364, 
      3.96658*10^-6}, {0.365, 3.76846*10^-6}, {0.366, 
      4.72074*10^-6}, {0.367, 5.43015*10^-6}, {0.368, 
      4.85719*10^-6}, {0.369, 3.7421*10^-6}, {0.37, 
      3.56255*10^-6}, {0.371, 4.48959*10^-6}, {0.372, 
      5.16893*10^-6}, {0.373, 4.60586*10^-6}, {0.374, 
      3.53097*10^-6}, {0.375, 3.37162*10^-6}, {0.376, 
      4.27611*10^-6}, {0.377, 4.92517*10^-6}, {0.378, 
      4.36897*10^-6}, {0.379, 3.3323*10^-6}, {0.38, 
      3.19449*10^-6}, {0.381, 4.07881*10^-6}, {0.382, 
      4.69745*10^-6}, {0.383, 4.14549*10^-6}, {0.384, 
      3.14527*10^-6}, {0.385, 3.03013*10^-6}, {0.386, 
      3.89634*10^-6}, {0.387, 4.48448*10^-6}, {0.388, 
      3.93447*10^-6}, {0.389, 2.96913*10^-6}, {0.39, 
      2.87759*10^-6}, {0.391, 3.72749*10^-6}, {0.392, 
      4.28507*10^-6}, {0.393, 3.73504*10^-6}, {0.394, 
      2.80319*10^-6}, {0.395, 2.73604*10^-6}, {0.396, 
      3.57117*10^-6}, {0.397, 4.09815*10^-6}, {0.398, 
      3.54639*10^-6}, {0.399, 2.64682*10^-6}, {0.4, 2.6047*10^-6}, {0.401,
       3.42637*10^-6}, {0.402, 3.92272*10^-6}, {0.403, 
      3.36778*10^-6}, {0.404, 2.49945*10^-6}, {0.405, 
      2.4829*10^-6}, {0.406, 3.2922*10^-6}, {0.407, 
      3.75787*10^-6}, {0.408, 3.19851*10^-6}, {0.409, 
      2.36054*10^-6}, {0.41, 2.36999*10^-6}, {0.411, 
      3.16783*10^-6}, {0.412, 3.60278*10^-6}, {0.413, 
      3.03796*10^-6}, {0.414, 2.2296*10^-6}, {0.415, 
      2.26543*10^-6}, {0.416, 3.05254*10^-6}, {0.417, 
      3.45669*10^-6}, {0.418, 2.88553*10^-6}, {0.419, 
      2.10619*10^-6}, {0.42, 2.16868*10^-6}, {0.421, 
      2.94563*10^-6}, {0.422, 3.3189*10^-6}, {0.423, 
      2.7407*10^-6}, {0.424, 1.98989*10^-6}, {0.425, 
      2.07928*10^-6}, {0.426, 2.8465*10^-6}, {0.427, 
      3.18878*10^-6}, {0.428, 2.60296*10^-6}, {0.429, 
      1.88033*10^-6}, {0.43, 1.99681*10^-6}, {0.431, 
      2.75458*10^-6}, {0.432, 3.06575*10^-6}, {0.433, 
      2.47186*10^-6}, {0.434, 1.77716*10^-6}, {0.435, 
      1.92087*10^-6}, {0.436, 2.66938*10^-6}, {0.437, 
      2.94928*10^-6}, {0.438, 2.34697*10^-6}, {0.439, 
      1.68005*10^-6}, {0.44, 1.85111*10^-6}, {0.441, 
      2.59042*10^-6}, {0.442, 2.83889*10^-6}, {0.443, 
      2.22792*10^-6}, {0.444, 1.58873*10^-6}, {0.445, 
      1.7872*10^-6}, {0.446, 2.51729*10^-6}, {0.447, 
      2.73412*10^-6}, {0.448, 2.11435*10^-6}, {0.449, 
      1.50291*10^-6}, {0.45, 1.72887*10^-6}, {0.451, 
      2.44961*10^-6}, {0.452, 2.63458*10^-6}, {0.453, 
      2.00593*10^-6}, {0.454, 1.42235*10^-6}, {0.455, 
      1.67583*10^-6}, {0.456, 2.38703*10^-6}, {0.457, 
      2.53991*10^-6}, {0.458, 1.90237*10^-6}, {0.459, 
      1.34683*10^-6}, {0.46, 1.62786*10^-6}, {0.461, 
      2.32926*10^-6}, {0.462, 2.44977*10^-6}, {0.463, 
      1.80339*10^-6}, {0.464, 1.27615*10^-6}, {0.465, 
      1.58475*10^-6}, {0.466, 2.27602*10^-6}, {0.467, 
      2.36385*10^-6}, {0.468, 1.70874*10^-6}, {0.469, 
      1.21011*10^-6}, {0.47, 1.54632*10^-6}, {0.471, 
      2.22707*10^-6}, {0.472, 2.28191*10^-6}, {0.473, 
      1.61819*10^-6}, {0.474, 1.14856*10^-6}, {0.475, 
      1.5124*10^-6}, {0.476, 2.1822*10^-6}, {0.477, 
      2.20368*10^-6}, {0.478, 1.53154*10^-6}, {0.479, 
      1.09133*10^-6}, {0.48, 1.48287*10^-6}, {0.481, 
      2.14126*10^-6}, {0.482, 2.12897*10^-6}, {0.483, 
      1.44858*10^-6}, {0.484, 1.0383*10^-6}, {0.485, 
      1.45763*10^-6}, {0.486, 2.10411*10^-6}, {0.487, 
      2.05759*10^-6}, {0.488, 1.36915*10^-6}, {0.489, 
      9.89362*10^-7}, {0.49, 1.43661*10^-6}, {0.491, 
      2.07064*10^-6}, {0.492, 1.98939*10^-6}, {0.493, 
      1.29307*10^-6}, {0.494, 9.4441*10^-7}, {0.495, 
      1.41977*10^-6}, {0.496, 2.04081*10^-6}, {0.497, 
      1.92424*10^-6}, {0.498, 1.22022*10^-6}, {0.499, 9.0337*10^-7}, {0.5,
       1.40712*10^-6}, {0.501, 2.01461*10^-6}, {0.502, 
      1.86204*10^-6}, {0.503, 1.15044*10^-6}, {0.504, 
      8.66185*10^-7}, {0.505, 1.3987*10^-6}, {0.506, 
      1.99207*10^-6}, {0.507, 1.80274*10^-6}, {0.508, 
      1.08362*10^-6}, {0.509, 8.3282*10^-7}, {0.51, 
      1.39461*10^-6}, {0.511, 1.9733*10^-6}, {0.512, 
      1.74628*10^-6}, {0.513, 1.01965*10^-6}, {0.514, 
      8.03269*10^-7}, {0.515, 1.395*10^-6}, {0.516, 
      1.95846*10^-6}, {0.517, 1.69269*10^-6}, {0.518, 
      9.58421*10^-7}, {0.519, 7.77554*10^-7}, {0.52, 
      1.40013*10^-6}, {0.521, 1.94782*10^-6}, {0.522, 
      1.64201*10^-6}, {0.523, 8.99843*10^-7}, {0.524, 
      7.55732*10^-7}, {0.525, 1.41031*10^-6}, {0.526, 
      1.94173*10^-6}, {0.527, 1.59434*10^-6}, {0.528, 
      8.43829*10^-7}, {0.529, 7.37907*10^-7}, {0.53, 
      1.42601*10^-6}, {0.531, 1.9407*10^-6}, {0.532, 
      1.54985*10^-6}, {0.533, 7.90303*10^-7}, {0.534, 
      7.24239*10^-7}, {0.535, 1.44784*10^-6}, {0.536, 
      1.9454*10^-6}, {0.537, 1.50877*10^-6}, {0.538, 
      7.39193*10^-7}, {0.539, 7.14959*10^-7}, {0.54, 
      1.47659*10^-6}, {0.541, 1.95672*10^-6}, {0.542, 
      1.47146*10^-6}, {0.543, 6.90437*10^-7}, {0.544, 
      7.10396*10^-7}, {0.545, 1.51338*10^-6}, {0.546, 
      1.97586*10^-6}, {0.547, 1.4384*10^-6}, {0.548, 
      6.43978*10^-7}, {0.549, 7.11002*10^-7}, {0.55, 
      1.55964*10^-6}, {0.551, 2.00444*10^-6}, {0.552, 
      1.41025*10^-6}, {0.553, 5.99765*10^-7}, {0.554, 
      7.17409*10^-7}, {0.555, 1.61737*10^-6}, {0.556, 
      2.04466*10^-6}, {0.557, 1.38795*10^-6}, {0.558, 
      5.57758*10^-7}, {0.559, 7.30494*10^-7}, {0.56, 
      1.68928*10^-6}, {0.561, 2.09956*10^-6}, {0.562, 
      1.3728*10^-6}, {0.563, 5.17924*10^-7}, {0.564, 
      7.51488*10^-7}, {0.565, 1.77916*10^-6}, {0.566, 
      2.17338*10^-6}, {0.567, 1.36666*10^-6}, {0.568, 
      4.80244*10^-7}, {0.569, 7.82149*10^-7}, {0.57, 
      1.89242*10^-6}, {0.571, 2.27224*10^-6}, {0.572, 
      1.37224*10^-6}, {0.573, 4.44717*10^-7}, {0.574, 
      8.25041*10^-7}, {0.575, 2.03697*10^-6}, {0.576, 
      2.40518*10^-6}, {0.577, 1.39361*10^-6}, {0.578, 
      4.11368*10^-7}, {0.579, 8.84006*10^-7}, {0.58, 
      2.22477*10^-6}, {0.581, 2.58598*10^-6}, {0.582, 
      1.43706*10^-6}, {0.583, 3.80273*10^-7}, {0.584, 
      9.65004*10^-7}, {0.585, 2.47462*10^-6}, {0.586, 
      2.83655*10^-6}, {0.587, 1.5128*10^-6}, {0.588, 
      3.51587*10^-7}, {0.589, 1.0777*10^-6}, {0.59, 
      2.81743*10^-6}, {0.591, 3.19356*10^-6}, {0.592, 
      1.63818*10^-6}, {0.593, 3.25625*10^-7}, {0.594, 
      1.23864*10^-6}, {0.595, 3.30725*10^-6}, {0.596, 
      3.72228*10^-6}, {0.597, 1.84487*10^-6}, {0.598, 
      3.03031*10^-7}, {0.599, 1.47827*10^-6}, {0.6, 
      4.04609*10^-6}, {0.601, 4.54874*10^-6}, {0.602, 
      2.19564*10^-6}, {0.603, 2.85199*10^-7}, {0.604, 
      1.85809*10^-6}, {0.605, 5.24683*10^-6}, {0.606, 
      5.94417*10^-6}, {0.607, 2.83037*10^-6}, {0.608, 
      2.75494*10^-7}, {0.609, 2.51968*10^-6}, {0.61, 
      7.4213*10^-6}, {0.611, 8.58807*10^-6}, {0.612, 
      4.11647*10^-6}, {0.613, 2.83522*10^-7}, {0.614, 
      3.85801*10^-6}, {0.615, 0.0000120895}, {0.616, 
      0.0000146289}, {0.617, 7.30221*10^-6}, {0.618, 
      3.45669*10^-7}, {0.619, 7.3862*10^-6}, {0.62, 0.0000257201}, {0.621,
       0.0000343123}, {0.622, 0.0000192095}, {0.623, 
      7.02859*10^-7}, {0.624, 0.0000243285}, {0.625, 0.000110468}, {0.626,
       0.000205954}, {0.627, 0.00019318}, {0.628, 0.0000156217}, {0.629, 
      0.0122}, {0.63, 0.00288597}, {0.631, 0.00062195}, {0.632, 
      0.000118106}, {0.633, 1.78527*10^-6}, {0.634, 0.000021198}, {0.635, 
      0.0000486644}, {0.636, 0.0000409984}, {0.637, 0.0000151486}, {0.638,
       4.67411*10^-7}, {0.639, 4.33954*10^-6}, {0.64, 
      0.0000130141}, {0.641, 0.0000131765}, {0.642, 
      5.74749*10^-6}, {0.643, 2.68633*10^-7}, {0.644, 
      1.64356*10^-6}, {0.645, 5.74861*10^-6}, {0.646, 
      6.4176*10^-6}, {0.647, 3.08947*10^-6}, {0.648, 
      1.95866*10^-7}, {0.649, 8.09307*10^-7}, {0.65, 
      3.20192*10^-6}, {0.651, 3.83052*10^-6}, {0.652, 
      1.97964*10^-6}, {0.653, 1.57638*10^-7}, {0.654, 
      4.6958*10^-7}, {0.655, 2.05342*10^-6}, {0.656, 
      2.58684*10^-6}, {0.657, 1.40884*10^-6}, {0.658, 
      1.33321*10^-7}, {0.659, 3.09697*10^-7}, {0.66, 
      1.45288*10^-6}, {0.661, 1.89884*10^-6}, {0.662, 
      1.07347*10^-6}, {0.663, 1.16095*10^-7}, {0.664, 
      2.28254*10^-7}, {0.665, 1.1064*10^-6}, {0.666, 
      1.47937*10^-6}, {0.667, 8.57016*10^-7}, {0.668, 
      1.03136*10^-7}, {0.669, 1.85307*10^-7}, {0.67, 
      8.91773*10^-7}, {0.671, 1.20431*10^-6}, {0.672, 
      7.07129*10^-7}, {0.673, 9.30764*10^-8}, {0.674, 
      1.62855*10^-7}, {0.675, 7.51305*10^-7}, {0.676, 
      1.01323*10^-6}, {0.677, 5.97512*10^-7}, {0.678, 
      8.5172*10^-8}, {0.679, 1.51953*10^-7}, {0.68, 
      6.55132*10^-7}, {0.681, 8.74*10^-7}, {0.682, 5.13798*10^-7}, {0.683,
       7.89741*10^-8}, {0.684, 1.47819*10^-7}, {0.685, 
      5.86661*10^-7}, {0.686, 7.68378*10^-7}, {0.687, 
      4.47615*10^-7}, {0.688, 7.41891*10^-8}, {0.689, 
      1.4774*10^-7}, {0.69, 5.36145*10^-7}, {0.691, 
      6.85412*10^-7}, {0.692, 3.93817*10^-7}, {0.693, 
      7.06098*10^-8}, {0.694, 1.50104*10^-7}, {0.695, 
      4.97598*10^-7}, {0.696, 6.18242*10^-7}, {0.697, 
      3.49107*10^-7}, {0.698, 6.80795*10^-8}, {0.699, 
      1.53915*10^-7}, {0.7, 4.67207*10^-7}, {0.701, 
      5.62416*10^-7}, {0.702, 3.11288*10^-7}, {0.703, 
      6.64729*10^-8}, {0.704, 1.58536*10^-7}, {0.705, 
      4.42467*10^-7}, {0.706, 5.14953*10^-7}, {0.707, 
      2.78852*10^-7}, {0.708, 6.5685*10^-8}, {0.709, 
      1.63549*10^-7}, {0.71, 4.21693*10^-7}, {0.711, 
      4.7381*10^-7}, {0.712, 2.50735*10^-7}, {0.713, 
      6.56244*10^-8}, {0.714, 1.68671*10^-7}, {0.715, 
      4.03729*10^-7}, {0.716, 4.37553*10^-7}, {0.717, 
      2.26164*10^-7}, {0.718, 6.6209*10^-8}, {0.719, 
      1.73708*10^-7}, {0.72, 3.87766*10^-7}, {0.721, 
      4.05159*10^-7}, {0.722, 2.04569*10^-7}, {0.723, 
      6.73637*10^-8}, {0.724, 1.78522*10^-7}, {0.725, 
      3.73233*10^-7}, {0.726, 3.75884*10^-7}, {0.727, 
      1.85514*10^-7}, {0.728, 6.90188*10^-8}, {0.729, 
      1.83019*10^-7}, {0.73, 3.59724*10^-7}, {0.731, 
      3.49182*10^-7}, {0.732, 1.68665*10^-7}, {0.733, 
      7.11085*10^-8}, {0.734, 1.87128*10^-7}, {0.735, 
      3.46945*10^-7}, {0.736, 3.24644*10^-7}, {0.737, 
      1.53755*10^-7}, {0.738, 7.35705*10^-8}, {0.739, 1.908*10^-7}, {0.74,
       3.34688*10^-7}, {0.741, 3.01964*10^-7}, {0.742, 
      1.4057*10^-7}, {0.743, 7.63458*10^-8}, {0.744, 1.94*10^-7}, {0.745, 
      3.22803*10^-7}, {0.746, 2.80908*10^-7}, {0.747, 
      1.28933*10^-7}, {0.748, 7.93778*10^-8}, {0.749, 
      1.96704*10^-7}, {0.75, 3.11186*10^-7}, {0.751, 
      2.61296*10^-7}, {0.752, 1.18696*10^-7}, {0.753, 
      8.26129*10^-8}, {0.754, 1.98896*10^-7}, {0.755, 
      2.99764*10^-7}, {0.756, 2.42988*10^-7}, {0.757, 
      1.09731*10^-7}, {0.758, 8.59997*10^-8}, {0.759, 
      2.00568*10^-7}, {0.76, 2.8849*10^-7}, {0.761, 
      2.25875*10^-7}, {0.762, 1.0193*10^-7}, {0.763, 
      8.94893*10^-8}, {0.764, 2.01716*10^-7}, {0.765, 
      2.77334*10^-7}, {0.766, 2.09869*10^-7}, {0.767, 
      9.51917*10^-8}, {0.768, 9.30356*10^-8}, {0.769, 
      2.02342*10^-7}, {0.77, 2.66281*10^-7}, {0.771, 1.949*10^-7}, {0.772,
       8.94295*10^-8}, {0.773, 9.65946*10^-8}, {0.774, 
      2.0245*10^-7}, {0.775, 2.55327*10^-7}, {0.776, 
      1.8091*10^-7}, {0.777, 8.45625*10^-8}, {0.778, 
      1.00125*10^-7}, {0.779, 2.02051*10^-7}, {0.78, 
      2.44475*10^-7}, {0.781, 1.67852*10^-7}, {0.782, 
      8.05159*10^-8}, {0.783, 1.03588*10^-7}, {0.784, 
      2.01155*10^-7}, {0.785, 2.33736*10^-7}, {0.786, 
      1.55685*10^-7}, {0.787, 7.72202*10^-8}, {0.788, 
      1.06949*10^-7}, {0.789, 1.99777*10^-7}, {0.79, 
      2.23123*10^-7}, {0.791, 1.44371*10^-7}, {0.792, 
      7.461*10^-8}, {0.793, 1.10172*10^-7}, {0.794, 
      1.97935*10^-7}, {0.795, 2.12653*10^-7}, {0.796, 
      1.33881*10^-7}, {0.797, 7.26231*10^-8}, {0.798, 
      1.13229*10^-7}, {0.799, 1.95648*10^-7}, {0.8, 
      2.02346*10^-7}, {0.801, 1.24183*10^-7}, {0.802, 
      7.12004*10^-8}, {0.803, 1.1609*10^-7}, {0.804, 
      1.92937*10^-7}, {0.805, 1.92224*10^-7}, {0.806, 
      1.1525*10^-7}, {0.807, 7.02853*10^-8}, {0.808, 
      1.18731*10^-7}, {0.809, 1.89825*10^-7}, {0.81, 
      1.82306*10^-7}, {0.811, 1.07056*10^-7}, {0.812, 
      6.98237*10^-8}, {0.813, 1.2113*10^-7}, {0.814, 
      1.86337*10^-7}, {0.815, 1.72616*10^-7}, {0.816, 
      9.95736*10^-8}, {0.817, 6.97634*10^-8}, {0.818, 
      1.23267*10^-7}, {0.819, 1.82499*10^-7}, {0.82, 
      1.63174*10^-7}, {0.821, 9.2777*10^-8}, {0.822, 
      7.00546*10^-8}, {0.823, 1.25125*10^-7}, {0.824, 
      1.78338*10^-7}, {0.825, 1.54002*10^-7}, {0.826, 
      8.66399*10^-8}, {0.827, 7.06493*10^-8}, {0.828, 
      1.26691*10^-7}, {0.829, 1.73882*10^-7}, {0.83, 
      1.45119*10^-7}, {0.831, 8.11356*10^-8}, {0.832, 
      7.15013*10^-8}, {0.833, 1.27952*10^-7}, {0.834, 
      1.69161*10^-7}, {0.835, 1.36544*10^-7}, {0.836, 
      7.6237*10^-8}, {0.837, 7.25667*10^-8}, {0.838, 
      1.28902*10^-7}, {0.839, 1.64204*10^-7}, {0.84, 
      1.28294*10^-7}, {0.841, 7.19163*10^-8}, {0.842, 
      7.38034*10^-8}, {0.843, 1.29533*10^-7}, {0.844, 
      1.59041*10^-7}, {0.845, 1.20385*10^-7}, {0.846, 
      6.8145*10^-8}, {0.847, 7.51713*10^-8}, {0.848, 
      1.29843*10^-7}, {0.849, 1.53702*10^-7}, {0.85, 
      1.12831*10^-7}, {0.851, 6.48943*10^-8}, {0.852, 
      7.66324*10^-8}, {0.853, 1.29831*10^-7}, {0.854, 
      1.48217*10^-7}, {0.855, 1.05643*10^-7}, {0.856, 
      6.21345*10^-8}, {0.857, 7.81508*10^-8}, {0.858, 
      1.29498*10^-7}, {0.859, 1.42617*10^-7}, {0.86, 
      9.88319*10^-8}, {0.861, 5.98355*10^-8}, {0.862, 
      7.96927*10^-8}, {0.863, 1.28848*10^-7}, {0.864, 
      1.36932*10^-7}, {0.865, 9.24053*10^-8}, {0.866, 
      5.79668*10^-8}, {0.867, 8.12264*10^-8}, {0.868, 
      1.27888*10^-7}, {0.869, 1.3119*10^-7}, {0.87, 
      8.63693*10^-8}, {0.871, 5.64974*10^-8}, {0.872, 
      8.27227*10^-8}, {0.873, 1.26625*10^-7}, {0.874, 
      1.25422*10^-7}, {0.875, 8.07278*10^-8}, {0.876, 
      5.53963*10^-8}, {0.877, 8.41545*10^-8}, {0.878, 
      1.25069*10^-7}, {0.879, 1.19654*10^-7}, {0.88, 
      7.54827*10^-8}, {0.881, 5.46319*10^-8}, {0.882, 
      8.54968*10^-8}, {0.883, 1.23233*10^-7}, {0.884, 
      1.13914*10^-7}, {0.885, 7.06337*10^-8}, {0.886, 
      5.41732*10^-8}, {0.887, 8.67272*10^-8}, {0.888, 
      1.2113*10^-7}, {0.889, 1.08229*10^-7}, {0.89, 
      6.61786*10^-8}, {0.891, 5.39888*10^-8}, {0.892, 
      8.78255*10^-8}, {0.893, 1.18776*10^-7}, {0.894, 
      1.02622*10^-7}, {0.895, 6.21134*10^-8}, {0.896, 
      5.40477*10^-8}, {0.897, 8.87739*10^-8}, {0.898, 
      1.16185*10^-7}, {0.899, 9.71179*10^-8}, {0.9, 
      5.84318*10^-8}, {0.901, 5.43195*10^-8}, {0.902, 
      8.95568*10^-8}, {0.903, 1.13377*10^-7}, {0.904, 
      9.17387*10^-8}, {0.905, 5.51261*10^-8}, {0.906, 
      5.47741*10^-8}, {0.907, 9.01611*10^-8}, {0.908, 
      1.10369*10^-7}, {0.909, 8.65049*10^-8}, {0.91, 
      5.21866*10^-8}, {0.911, 5.5382*10^-8}, {0.912, 
      9.05757*10^-8}, {0.913, 1.07182*10^-7}, {0.914, 
      8.14358*10^-8}, {0.915, 4.9602*10^-8}, {0.916, 
      5.61146*10^-8}, {0.917, 9.0792*10^-8}, {0.918, 
      1.03836*10^-7}, {0.919, 7.65488*10^-8}, {0.92, 
      4.73597*10^-8}, {0.921, 5.69441*10^-8}, {0.922, 
      9.08034*10^-8}, {0.923, 1.0035*10^-7}, {0.924, 
      7.18597*10^-8}, {0.925, 4.54453*10^-8}, {0.926, 
      5.78439*10^-8}, {0.927, 9.06057*10^-8}, {0.928, 
      9.67475*10^-8}, {0.929, 6.73824*10^-8}, {0.93, 
      4.38434*10^-8}, {0.931, 5.87883*10^-8}, {0.932, 
      9.01964*10^-8}, {0.933, 9.30486*10^-8}, {0.934, 
      6.31293*10^-8}, {0.935, 4.25373*10^-8}, {0.936, 
      5.9753*10^-8}, {0.937, 8.95754*10^-8}, {0.938, 
      8.92751*10^-8}, {0.939, 5.91107*10^-8}, {0.94, 
      4.15094*10^-8}, {0.941, 6.07148*10^-8}, {0.942, 
      8.87441*10^-8}, {0.943, 8.54484*10^-8}, {0.944, 
      5.53352*10^-8}, {0.945, 4.07411*10^-8}, {0.946, 
      6.1652*10^-8}, {0.947, 8.77061*10^-8}, {0.948, 
      8.15897*10^-8}, {0.949, 5.18094*10^-8}, {0.95, 
      4.02132*10^-8}, {0.951, 6.25445*10^-8}, {0.952, 
      8.64663*10^-8}, {0.953, 7.77198*10^-8}, {0.954, 
      4.85384*10^-8}, {0.955, 3.99056*10^-8}, {0.956, 
      6.33736*10^-8}, {0.957, 8.50316*10^-8}, {0.958, 
      7.3859*10^-8}, {0.959, 4.55251*10^-8}, {0.96, 3.9798*10^-8}, {0.961,
       6.41223*10^-8}, {0.962, 8.34101*10^-8}, {0.963, 
      7.0027*10^-8}, {0.964, 4.27711*10^-8}, {0.965, 
      3.98696*10^-8}, {0.966, 6.4775*10^-8}, {0.967, 
      8.16113*10^-8}, {0.968, 6.62427*10^-8}, {0.969, 
      4.02758*10^-8}, {0.97, 4.00996*10^-8}, {0.971, 
      6.53181*10^-8}, {0.972, 7.96461*10^-8}, {0.973, 
      6.25243*10^-8}, {0.974, 3.80374*10^-8}, {0.975, 
      4.04671*10^-8}, {0.976, 6.57395*10^-8}, {0.977, 
      7.75264*10^-8}, {0.978, 5.88887*10^-8}, {0.979, 
      3.60522*10^-8}, {0.98, 4.09511*10^-8}, {0.981, 
      6.60287*10^-8}, {0.982, 7.5265*10^-8}, {0.983, 
      5.53521*10^-8}, {0.984, 3.43151*10^-8}, {0.985, 
      4.15311*10^-8}, {0.986, 6.61772*10^-8}, {0.987, 
      7.28757*10^-8}, {0.988, 5.19293*10^-8}, {0.989, 
      3.28195*10^-8}, {0.99, 4.21867*10^-8}, {0.991, 
      6.61779*10^-8}, {0.992, 7.03728*10^-8}, {0.993, 
      4.86342*10^-8}, {0.994, 3.15576*10^-8}, {0.995, 
      4.28982*10^-8}, {0.996, 6.60256*10^-8}, {0.997, 
      6.77713*10^-8}, {0.998, 4.54792*10^-8}, {0.999, 3.05203*10^-8}, {1.,
       4.36463*10^-8}}
$\endgroup$
3
  • $\begingroup$ Are you asking why its shifted down? I assume that's a result of the power you're removing from the signal by filtering. $\endgroup$
    – N.J.Evans
    Sep 17, 2015 at 14:12
  • $\begingroup$ I cut paste your data and code and it plots the filtered curve right through the middle of the data. $\endgroup$
    – george2079
    Sep 17, 2015 at 15:47
  • $\begingroup$ Possible version issue? This works for me with 10.1 (looks nearly the same as Kattern's median filter plot ) $\endgroup$
    – george2079
    Sep 17, 2015 at 16:09

2 Answers 2

3
$\begingroup$

For understanding the behavior of LowpassFilter[ ]:

First consider a cutoff frequency of 0 : nothing passes, the outcome is a null signal.
Then think of a cutoff frequency of Pi: everything passes, the outcome is the input.

You may experiment it for example with:

n = 30; 
Manipulate[l2 = LowpassFilter[l1 = 
                               Join[ConstantArray[0, n], ConstantArray[1, n]], freq]; 
           ListLinePlot[{l1, l2}],
           {freq, 0, Pi}]

Mathematica graphics

In v9 it gives you:

enter image description here

Edit - Hope you don't mind I'll put this here for comparison: from v10,

l1 = Join[ConstantArray[0, 30], ConstantArray[1, 30]];
Show[Table[ {
    ListLinePlot[LowpassFilter[l1, Exp[logfreq]]] }, {logfreq, -5, 0, .5}]~
       Prepend~ListLinePlot[l1, PlotStyle -> Red], PlotRange -> All]

enter image description here

$\endgroup$
8
  • $\begingroup$ did you reproduce his error? $\endgroup$
    – george2079
    Sep 17, 2015 at 15:52
  • $\begingroup$ @george2079 I haven't tried the OP code :) $\endgroup$ Sep 17, 2015 at 15:58
  • $\begingroup$ @george2079 Well, I did now. I got the same plot posted in the question.V9 here,just in case $\endgroup$ Sep 17, 2015 at 16:00
  • $\begingroup$ For your manipulator example in v10, the filtered curve always goes from {0,0} to {60,1} passing through {30,1/2}. What I would "expect", although I don't have the expertise to say what LowpassFilter is supposed to do) $\endgroup$
    – george2079
    Sep 17, 2015 at 16:53
  • $\begingroup$ @george2079 See the uploaded animation $\endgroup$ Sep 17, 2015 at 16:58
2
$\begingroup$

MovingAverage may be a possible solution.

mv = MovingAverage[dat[[All, 2]], 5];
ListLogPlot[{dat, MapThread[List, {dat[[;; Length@mv, 1]], mv}]}, 
 Joined -> True, ImageSize -> 800]

mv

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.