How to compress/ average out multiple cycles in existing data into a single cycle form?

Question

How may I seek help on how to convert a set of 30 cycles encoder data and would like to convert them into a single cycle? Do I have to manually break them down into an individual cycle and then calculate the mean?

Thanks for the help in advance.

Motorencodercycle = {0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,0., 0., 0., 0., 0., 0., 0.0337956, 0.104719, 0.174556, 0.244632, 0.318658, 0.389918, 0.459921, 0.527533, 0.599649, 0.66759, 0.737422, 0.809181, 0.875762, 0.945095, 1.01589, 1.08755, 1.16111, 1.23334, 1.30497, 1.37637, 1.4464, 1.51948, 1.58933, 1.66407, 1.73348, 1.80597, 1.87667, 1.94798, 2.01754, 2.08859, 2.15752, 2.2292, 2.29793, 2.37053, 2.34346, 2.27264, 2.2028, 2.1296, 2.05725, 1.98476,1.91536, 1.84458, 1.7738, 1.70584, 1.63485, 1.56422, 1.49401, 1.42158, 1.35187, 1.28191, 1.2126, 1.14314, 1.07186, 1.00476, 0.934155, 0.864058, 0.793671, 0.720545, 0.651723, 0.580754, 0.510848, 0.439852, 0.368106, 0.298677, 0.226856, 0.15619, 0.0822221, 0.0130682, 0.0589935, 0.127585, 0.198712, 0.268621, 0.338914, 0.408615, 0.47812, 0.548731, 0.617997, 0.686712, 0.756222, 0.82445, 0.896002, 0.966885, 1.03518, 1.10639, 1.17858, 1.25273, 1.32396, 1.39518, 1.46396, 1.53554, 1.60684, 1.67686, 1.74676, 1.81833, 1.89113, 1.96344, 2.0328, 2.10178, 2.17205, 2.248, 2.32007, 2.38956, 2.32498, 2.25439, 2.18415, 2.11511, 2.04468, 1.97513, 1.90714, 1.83452, 1.76774, 1.69734, 1.6252, 1.55428, 1.48113, 1.41293, 1.34122, 1.27307, 1.19842, 1.12688, 1.05521, 0.984419, 0.915435, 0.841024, 0.76936, 0.698637, 0.624842, 0.552464, 0.483215, 0.413364, 0.342375, 0.272552, 0.204809, 0.134016, 0.0633139, 0.0085117, 0.0786023, 0.146647, 0.221481, 0.291525, 0.363477, 0.433534, 0.504864, 0.575822, 0.647499, 0.719349, 0.789354, 0.862597, 0.933961, 1.00162, 1.07177, 1.14309, 1.21231, 1.28494, 1.35783, 1.43161, 1.50246, 1.57075, 1.64097, 1.71306, 1.78383, 1.85567, 1.92707, 1.99945, 2.06872, 2.14148, 2.21194, 2.28361, 2.35372, 2.35958, 2.28992, 2.21811, 2.14784, 2.07821, 2.00982, 1.93822, 1.86536, 1.79494, 1.72519, 1.65573, 1.58671, 1.51471, 1.44396, 1.37178, 1.30165, 1.23141, 1.15908, 1.08794, 1.01805, 0.948307, 0.876662, 0.807915, 0.738255, 0.66932, 0.599599, 0.529326, 0.461861, 0.391527, 0.320584, 0.25178, 0.182356, 0.114004, 0.0421798, 0.0283042, 0.101733, 0.170768, 0.242098, 0.31199, 0.382333, 0.454231, 0.521456, 0.592329, 0.663679, 0.733894, 0.805752, 0.878528, 0.947604, 1.01774, 1.08854, 1.16342, 1.23425, 1.30406, 1.37229, 1.44461, 1.5118, 1.58417, 1.65206, 1.71866, 1.78926, 1.86113, 1.93085, 2.00296, 2.07276, 2.14623, 2.21679, 2.28727, 2.35772, 2.35912, 2.28773, 2.21586, 2.14346, 2.07222, 1.9993, 1.9279, 1.85642, 1.78287, 1.71339, 1.64363, 1.57479, 1.50645, 1.43823, 1.3687, 1.30081, 1.23066, 1.16025, 1.08915, 1.01962, 0.948296, 0.877084, 0.806402, 0.738199, 0.670428, 0.601908, 0.530493, 0.460037, 0.391753, 0.318954, 0.247765, 0.1761, 0.106757, 0.0372425, 0.0325666, 0.104021, 0.175329, 0.243994, 0.312924, 0.384051, 0.4576, 0.528257, 0.598547, 0.669452, 0.738952, 0.811255, 0.882633, 0.954661, 1.02638, 1.09732, 1.16731, 1.23659, 1.30661, 1.37826, 1.44871, 1.52041, 1.59418, 1.66427, 1.73516, 1.80797, 1.87807, 1.94952, 2.01873, 2.0889, 2.15832, 2.22697, 2.2985, 2.36708, 2.34477, 2.27432, 2.20325, 2.13383, 2.06319, 1.99039, 1.91911, 1.8496, 1.7749, 1.70439, 1.63704, 1.56916, 1.49882, 1.4287, 1.35638, 1.287, 1.21481, 1.14252, 1.07223, 1.00069, 0.926891, 0.854073, 0.784442, 0.711297, 0.641038, 0.568887, 0.49833, 0.430966, 0.360785, 0.29102, 0.221954, 0.152536, 0.0834658, 0.0115883, 0.059732, 0.130192, 0.199177, 0.269212, 0.338935, 0.409787, 0.478198, 0.548971, 0.621314, 0.690732, 0.76261, 0.833474, 0.902546, 0.972208, 1.04477, 1.1179, 1.18667, 1.2583, 1.33091, 1.4007, 1.47069, 1.54314, 1.61489, 1.68773, 1.75774, 1.82761, 1.89766, 1.96769, 2.03859, 2.1071, 2.17651, 2.24266, 2.31527, 2.38333, 2.33264, 2.26066, 2.18759, 2.11896, 2.0481, 1.97683, 1.90525, 1.83594, 1.76698, 1.69554, 1.62411, 1.55361, 1.48362, 1.41379, 1.34338, 1.27042, 1.20258, 1.13601, 1.0651, 0.992938, 0.922422, 0.851814, 0.781536, 0.707696, 0.636817, 0.565563, 0.493732, 0.423529, 0.353791, 0.279725, 0.210597, 0.141111, 0.0716147, 0.00422172, 0.0641341, 0.136777, 0.209647, 0.281262, 0.353264, 0.426202, 0.497058, 0.566917, 0.637366, 0.710709, 0.780127, 0.8488, 0.92105, 0.992043, 1.06108, 1.13186, 1.20411, 1.27619, 1.34783, 1.41893, 1.48996, 1.56081, 1.62996, 1.70215, 1.77416, 1.84398, 1.91562, 1.98703, 2.05589, 2.12885, 2.20022, 2.2691, 2.34203, 2.37156, 2.2996, 2.22654, 2.15649, 2.08679, 2.01316, 1.94129, 1.87148, 1.79902, 1.73101, 1.66094, 1.59236, 1.52124, 1.44997, 1.37822, 1.30924, 1.23888, 1.16613, 1.09556, 1.02265, 0.953898, 0.885341, 0.815445, 0.746865, 0.677543, 0.607868, 0.537442, 0.465531, 0.396328, 0.328445, 0.257319, 0.184482, 0.113958, 0.0412947, 0.030503, 0.102526, 0.174295, 0.247648, 0.319647, 0.392037, 0.461097, 0.53212, 0.60479, 0.67691, 0.746311, 0.814288, 0.883908, 0.957325, 1.02691, 1.09732, 1.17023, 1.24242, 1.31344, 1.38777, 1.46223, 1.53915, 1.61926, 1.69379, 1.76985, 1.84768, 1.93163, 2.00732, 2.08398, 2.15978, 2.2396, 2.31881, 2.38669, 2.30817, 2.23164, 2.15482, 2.06821, 1.98989, 1.91487, 1.83882, 1.76234, 1.68746, 1.61464, 1.5442, 1.47396, 1.40611, 1.33521, 1.26573, 1.19335, 1.12547, 1.05356, 0.982641, 0.913907, 0.844764, 0.767514, 0.698243, 0.629452, 0.556704, 0.487304, 0.417169, 0.347072, 0.275019, 0.202119, 0.131809, 0.0623512, 0.00815642, 0.0788665, 0.149605, 0.218105, 0.290083, 0.359508, 0.432586, 0.502733, 0.572761, 0.640563, 0.710501, 0.779616, 0.848974, 0.919093, 0.990431, 1.05945, 1.12933, 1.20166, 1.27001, 1.33908, 1.40688, 1.47859, 1.54816, 1.61916, 1.69054, 1.7588, 1.83028, 1.8998, 1.97004, 2.03974, 2.10833, 2.1777, 2.24759, 2.31893, 2.38739, 2.32712, 2.25564, 2.18512, 2.11673, 2.04701, 1.97588, 1.90487, 1.83597, 1.76698, 1.69382, 1.62163, 1.55093, 1.47924, 1.41224, 1.34087, 1.26884, 1.19966, 1.12855, 1.05807, 0.986017, 0.914352, 0.842725, 0.773649, 0.701874, 0.629845, 0.563818, 0.493528, 0.423009, 0.354664, 0.284708, 0.213319, 0.143019, 0.0764856, 0.00574005, 0.0662113, 0.138147, 0.206071, 0.278203, 0.3467, 0.415574, 0.487515, 0.558107, 0.629931, 0.702035, 0.774895, 0.84626, 0.918296, 0.991021, 1.06293, 1.1318, 1.20383, 1.27239, 1.34565, 1.41768, 1.49043, 1.55914, 1.63117, 1.69991, 1.77197, 1.84348, 1.91192, 1.98059, 2.05212, 2.12425, 2.19596, 2.26751, 2.33831, 2.37713, 2.30959, 2.24012, 2.16899, 2.09776, 2.02839, 1.9585, 1.88691, 1.81986, 1.7479, 1.67284, 1.60326, 1.53434, 1.464, 1.39412, 1.3201, 1.2506, 1.17961, 1.10816, 1.03529, 0.963884, 0.894621, 0.827003, 0.758105, 0.687892, 0.620122, 0.550367, 0.478906, 0.408054, 0.336591, 0.265978, 0.194885, 0.122649, 0.0535349, 0.0166814, 0.0896184, 0.161053, 0.235222, 0.306813, 0.377852, 0.450035, 0.520598, 0.593604, 0.663542, 0.733679, 0.802044, 0.870685, 0.940842, 1.01045, 1.08008, 1.1526, 1.22349, 1.29254, 1.36044, 1.43222, 1.50251, 1.57092, 1.6427, 1.71327, 1.78344, 1.85555, 1.92957, 1.99871, 2.06931, 2.13897, 2.21032, 2.2796, 2.35051, 2.36234, 2.2923, 2.21986, 2.14765, 2.0779, 2.00756, 1.93573, 1.86514, 1.79539, 1.72423, 1.65631, 1.58723, 1.51601, 1.44514, 1.37546, 1.30516, 1.23723, 1.16931, 1.10026, 1.03081, 0.95723, 0.881917, 0.810691, 0.740045, 0.668695, 0.596028, 0.52455, 0.454314, 0.382638, 0.311036, 0.2407, 0.170454, 0.103188, 0.0318622, 0.0390323, 0.107828, 0.177876, 0.249778, 0.322796, 0.393596, 0.461971, 0.534179, 0.60598, 0.676117, 0.744201, 0.817128, 0.886845, 0.957163, 1.02602, 1.0965, 1.17057, 1.24211, 1.31247, 1.38433, 1.4556, 1.52585, 1.60039, 1.67186, 1.74214, 1.81238, 1.88417, 1.95486, 2.02536, 2.09469, 2.16257, 2.23351, 2.30569, 2.37558, 2.33833, 2.26735, 2.19399, 2.12317, 2.05125, 1.98342, 1.91339, 1.84077, 1.77004, 1.69934, 1.62669, 1.5547, 1.48394, 1.4144, 1.34584, 1.2744, 1.20566, 1.13639, 1.06603, 0.99536, 0.923351, 0.853357, 0.782448, 0.710049, 0.641783, 0.572249, 0.499209, 0.43054, 0.358637, 0.289471, 0.217698, 0.144986, 0.076136, 0.00679588, 0.0623864, 0.133054, 0.203204, 0.27099, 0.338134, 0.407063, 0.476002, 0.547608, 0.617237, 0.686688, 0.757683, 0.826663, 0.896895, 0.968002, 1.03864, 1.10792, 1.17896, 1.24998, 1.31942, 1.38901, 1.45863, 1.52969, 1.59765, 1.66795, 1.74046, 1.80759, 1.87924, 1.9495, 2.01989, 2.09188, 2.16355, 2.23599, 2.30556, 2.37434, 2.33839, 2.26489, 2.1964, 2.12524, 2.05764, 1.98571, 1.9129, 1.83846, 1.7707, 1.69944, 1.62929, 1.55571, 1.48309, 1.41195, 1.34014, 1.26921, 1.1995, 1.12739, 1.05735, 0.984267, 0.913872, 0.843322, 0.772272, 0.699986, 0.631118, 0.560642, 0.48972, 0.420379, 0.352332, 0.27902, 0.204896, 0.136706, 0.0660625, 0.00369704, 0.0719665, 0.144008, 0.215419, 0.284975, 0.355479, 0.42374, 0.495237, 0.564037, 0.636026, 0.707394, 0.776165, 0.845931, 0.918825, 0.988114, 1.05901, 1.13025, 1.20162, 1.273, 1.34534, 1.41446, 1.48748, 1.55982, 1.63196, 1.7044, 1.77497, 1.84567, 1.91579, 1.9881, 2.06022, 2.13225, 2.2039, 2.27232, 2.34228, 2.37366, 2.30524, 2.23333, 2.16319, 2.0917, 2.0216, 1.95047, 1.87934, 1.80829, 1.73441, 1.6622, 1.59179, 1.51939, 1.44809, 1.37958, 1.31013, 1.23684, 1.16837, 1.09602, 1.02448, 0.951367, 0.879741, 0.810806, 0.739413, 0.669519, 0.597465, 0.524833, 0.456677, 0.386109, 0.314871, 0.243298, 0.173593, 0.102778, 0.0307673, 0.0392262, 0.111262, 0.186082, 0.256004, 0.326489, 0.398526, 0.470401, 0.540761, 0.611074, 0.68014, 0.751386, 0.821939, 0.893508, 0.965382, 1.03578, 1.10347, 1.1745, 1.24469, 1.31347, 1.38463, 1.45615, 1.52689, 1.59779, 1.66765, 1.73854, 1.81068, 1.88152, 1.95338, 2.02446, 2.09486, 2.16775, 2.23998, 2.30803, 2.37621, 2.33941, 2.26901, 2.20018, 2.12854, 2.05693, 1.98827, 1.91649, 1.84502, 1.7768, 1.70586, 1.6332, 1.56272, 1.4925, 1.42061, 1.353, 1.28297, 1.21227, 1.14098, 1.07073, 1.00029, 0.930564, 0.857504, 0.785632, 0.715425, 0.644627, 0.574956, 0.506077, 0.435677, 0.36819, 0.296788, 0.22419, 0.156065, 0.0845359, 0.0128276, 0.0575036, 0.127226, 0.19857, 0.268444, 0.340976, 0.412469, 0.484634, 0.554171, 0.624111, 0.694777, 0.768411, 0.837221, 0.909999, 0.980632, 1.04926, 1.11965, 1.18843, 1.25672, 1.32662, 1.39628, 1.46902, 1.54097, 1.61203, 1.68287, 1.75365, 1.82697, 1.89539, 1.96481, 2.03442, 2.10659, 2.17648, 2.24918, 2.32015, 2.39183, 2.32233, 2.2483, 2.17673, 2.10532, 2.03421, 1.9632, 1.8913, 1.82308, 1.75113, 1.68298, 1.61262, 1.54008, 1.46796, 1.3964, 1.32591, 1.25771, 1.18866, 1.11645, 1.04775, 0.976285, 0.905703, 0.836119, 0.762812, 0.691153, 0.618322, 0.544288, 0.47592, 0.405159, 0.332113, 0.262466, 0.194558, 0.122882, 0.0486898, 0.021399, 0.09162, 0.161854, 0.233958, 0.304046, 0.37237, 0.443432, 0.51534, 0.58568, 0.658033, 0.731358, 0.803262, 0.873165, 0.943517, 1.01442, 1.0845, 1.15446, 1.22594, 1.29454, 1.36348, 1.43461, 1.50595, 1.57556, 1.64638, 1.71811, 1.78976, 1.85821, 1.92925, 2.00009, 2.06788, 2.13541, 2.20427, 2.27418, 2.34481, 2.37063, 2.2998, 2.23108, 2.1595, 2.08693, 2.01266, 1.94361, 1.87009, 1.79933, 1.72754, 1.65526, 1.5834, 1.51127, 1.44072, 1.37217, 1.3028, 1.23225, 1.16287, 1.09342, 1.02342, 0.954643, 0.882447, 0.814433, 0.745015, 0.675353, 0.603614, 0.532123, 0.462946, 0.389772, 0.318679, 0.246395, 0.17478, 0.10292, 0.0323977, 0.0387093, 0.108758, 0.18211, 0.256067, 0.327267, 0.400358, 0.469126, 0.541239, 0.61494, 0.684614, 0.753874, 0.824053, 0.894371, 0.967, 1.03688, 1.10721, 1.17843, 1.25189, 1.32156, 1.39277, 1.46392, 1.53274, 1.60176, 1.67262, 1.74296, 1.81383, 1.88562, 1.95728, 2.02769, 2.0968, 2.1694, 2.23875, 2.31023, 2.38066, 2.33536, 2.26349, 2.19084, 2.11926, 2.0474, 1.9769, 1.90539, 1.83212, 1.76333, 1.69079, 1.6213, 1.5494, 1.47911, 1.40812, 1.33729, 1.26575, 1.19584, 1.12601, 1.05639, 0.983911, 0.913369, 0.844473, 0.773936, 0.705209, 0.634624, 0.564634, 0.490127, 0.419008, 0.347892, 0.274637, 0.205369, 0.133318, 0.0639006, 0.00535766, 0.0791982, 0.150212, 0.221932, 0.293569, 0.363593, 0.43634, 0.50883, 0.578362, 0.648962, 0.718744, 0.790883, 0.860245, 0.929929, 1.0009, 1.07237, 1.14248, 1.21116, 1.2818, 1.35364, 1.42481, 1.49406, 1.56523, 1.63659, 1.70628, 1.77563, 1.8474, 1.91947, 1.99176, 2.06259, 2.13453, 2.20514, 2.27206, 2.34025, 2.37591, 2.30485, 2.23509, 2.16357, 2.09312, 2.02333, 1.95117, 1.88345, 1.81226, 1.74194, 1.67282, 1.60262, 1.53088, 1.45816, 1.38581, 1.3142, 1.24398, 1.17316, 1.10399, 1.03165, 0.96226, 0.892789, 0.824514, 0.75449, 0.679097, 0.608955, 0.53937, 0.468488, 0.398959, 0.328228, 0.258568, 0.189394, 0.116667, 0.0473417, 0.0215879, 0.092959, 0.164203, 0.238142, 0.309844, 0.382368, 0.454209, 0.52441, 0.593879, 0.66707, 0.737778, 0.809182, 0.878811, 0.951143, 1.02469, 1.09557, 1.16548, 1.23931, 1.31006, 1.37969, 1.44995, 1.52114, 1.59208, 1.66396, 1.73719, 1.80589, 1.87723, 1.95022, 2.02057, 2.09167, 2.1636, 2.23329, 2.30543, 2.37729, 2.33442, 2.26517, 2.19397, 2.12235, 2.05254, 1.98023, 1.91195, 1.84079, 1.76867, 1.69706, 1.62544, 1.55316, 1.48145, 1.41454, 1.34487, 1.27518, 1.20561, 1.13561, 1.06313, 0.995122, 0.926623, 0.856473, 0.782653, 0.711312, 0.63924, 0.568716, 0.49597, 0.425562, 0.354544, 0.281355, 0.21002, 0.141079, 0.0730673, 0.00317688, 0.0695239, 0.141057, 0.209989, 0.279813, 0.350742, 0.42354, 0.490587, 0.56207, 0.632178, 0.703003, 0.771877, 0.844533, 0.915841, 0.983809, 1.05535, 1.1251, 1.19278, 1.26268, 1.33235, 1.40579, 1.47704, 1.54808, 1.61905, 1.69048, 1.76216, 1.83094, 1.90496, 1.97792, 2.04801, 2.11865, 2.19014, 2.26062, 2.3313, 2.38216, 2.30903, 2.24002, 2.16521, 2.09484, 2.02446, 1.9546, 1.88402, 1.81396, 1.73887, 1.66739, 1.59766, 1.52934, 1.46095, 1.39101, 1.3213, 1.24951, 1.17853, 1.10886, 1.03622, 0.963613, 0.89252, 0.819895, 0.747059, 0.677072, 0.60447, 0.535448, 0.46547, 0.395207, 0.324321, 0.254542, 0.182328, 0.111158, 0.0404288, 0.0306981, 0.101337, 0.173039, 0.24359, 0.312415, 0.384405, 0.455572, 0.528088, 0.598965, 0.668443, 0.742745, 0.810378, 0.883137, 0.955942, 1.02655, 1.09636, 1.16775, 1.23628, 1.30898, 1.37966, 1.45128, 1.52189, 1.59363, 1.66482, 1.73579, 1.80769, 1.87541, 1.94233, 2.0149, 2.08489, 2.15401, 2.22444, 2.29523, 2.3669, 2.34811, 2.2778, 2.20841, 2.13619, 2.06493, 1.99349, 1.92504, 1.85056, 1.77774, 1.70594, 1.63413, 1.56376, 1.49501, 1.42451, 1.35526, 1.2865, 1.21417, 1.14401, 1.07222, 1.00138, 0.93112, 0.860787, 0.789437, 0.718944, 0.649061, 0.582631, 0.516148, 0.445598, 0.374739, 0.303918, 0.23725, 0.165909, 0.0925515, 0.0213945, 0.0518948, 0.121314, 0.191647, 0.26134, 0.332984, 0.403198, 0.47567, 0.54661, 0.618225, 0.687887, 0.757431, 0.829437, 0.900291, 0.971729, 1.04248, 1.11318, 1.18346, 1.25566, 1.32363, 1.39671, 1.46809, 1.5389, 1.60907, 1.68073, 1.75271, 1.82429, 1.89541, 1.96819, 2.03809, 2.10693, 2.17929, 2.24946, 2.31808, 2.38773, 2.32618, 2.25683, 2.18637, 2.11439, 2.04251, 1.97343, 1.90246, 1.83285, 1.764, 1.69189, 1.61955, 1.54875, 1.47715, 1.40997, 1.34285, 1.27107, 1.20167, 1.13216, 1.06232, 0.992389, 0.921218, 0.853121, 0.780321, 0.709327, 0.639291, 0.569246, 0.500774, 0.430166, 0.360336, 0.291496, 0.219471, 0.149546, 0.0785708, 0.0109595, 0.0615326, 0.132746, 0.203888, 0.27627, 0.348079, 0.419523, 0.489112, 0.561471, 0.634013, 0.70362, 0.772562, 0.843149, 0.912883, 0.983378, 1.05438, 1.12485, 1.19607, 1.26809, 1.33987, 1.41096, 1.48322, 1.55431, 1.62275, 1.69629, 1.76842, 1.84003, 1.91181, 1.98447, 2.05449, 2.12461, 2.1941, 2.26731, 2.34156, 2.37269, 2.29987, 2.23091, 2.15921, 2.08903, 2.01688, 1.94276, 1.87239, 1.80099, 1.73423, 1.66496, 1.59337, 1.52063, 1.44767, 1.37544, 1.30392, 1.22837, 1.15776, 1.08581, 1.01429, 0.942522, 0.869443, 0.797399, 0.723619, 0.654288, 0.58432, 0.518023, 0.448535, 0.379496, 0.304882, 0.23205, 0.163049, 0.0906545, 0.0179222, 0.0517203, 0.121879, 0.193869, 0.265893, 0.338677, 0.409424, 0.480199, 0.552645, 0.624149, 0.694789, 0.763974, 0.836692, 0.907951, 0.98049, 1.05204, 1.12058, 1.19599, 1.26756, 1.33939, 1.41117, 1.48015, 1.5493, 1.61858, 1.68683, 1.75817, 1.83063, 1.89956, 1.97293, 2.0418, 2.11294, 2.18326, 2.25362, 2.32424, 2.38955, 2.32127, 2.24789, 2.1782, 2.10604, 2.03461, 1.96035, 1.88968, 1.82276, 1.74956, 1.68059, 1.61018, 1.53756, 1.46321, 1.39329, 1.32286, 1.25253, 1.18079, 1.10941, 1.03795, 0.965949, 0.891758, 0.81841, 0.745121, 0.673508, 0.600745, 0.531582, 0.462173, 0.389662, 0.315992, 0.241805, 0.174209, 0.102613, 0.030634, 0.039632, 0.110035, 0.181249, 0.253677, 0.325271, 0.395962, 0.470064, 0.540084, 0.611565, 0.67961, 0.748333, 0.822598, 0.891827, 0.962778, 1.03255, 1.10602, 1.17622, 1.24679, 1.31931, 1.38739, 1.45607, 1.52749, 1.59719, 1.6682, 1.73619, 1.80455, 1.87667, 1.94584, 2.0152, 2.08532, 2.15471, 2.22495, 2.29422, 2.3687, 2.34728, 2.27609, 2.20301, 2.13536, 2.06638, 1.99522, 1.92533, 1.85422, 1.78632, 1.71596, 1.64523, 1.57406, 1.50366, 1.43209, 1.36122, 1.289, 1.21621, 1.14231, 1.07279, 0.999733, 0.93214, 0.86142, 0.790986, 0.72124, 0.652115, 0.577204, 0.506493, 0.43395, 0.362397, 0.29211, 0.21903, 0.149766, 0.0787296, 0.00799106, 0.063978, 0.132934, 0.202448, 0.269581, 0.338539, 0.409964, 0.480591, 0.548637, 0.620221, 0.693898, 0.764539, 0.833656, 0.905816, 0.978567, 1.04739, 1.11913, 1.1932, 1.26308, 1.33375, 1.40566, 1.47826, 1.5504, 1.61977, 1.68916, 1.75928, 1.82908, 1.90139, 1.97196, 2.04066, 2.10974, 2.1796, 2.25332, 2.32354, 2.38733, 2.31586, 2.24367, 2.17312, 2.09975, 2.02865, 1.95854, 1.88754, 1.81827, 1.74814, 1.67659, 1.60527, 1.53649, 1.46485, 1.39217, 1.32095, 1.25065, 1.17806, 1.10761, 1.03813, 0.970113, 0.901777, 0.832748, 0.762895, 0.693768, 0.623485, 0.552972, 0.481535, 0.410426, 0.34066, 0.270435, 0.200468, 0.129325, 0.059591, 0.0101996, 0.0822541, 0.153521, 0.225267, 0.296882, 0.365527, 0.435217, 0.503848, 0.57333, 0.644789, 0.712294, 0.785158, 0.854296, 0.925793, 0.997408, 1.06878, 1.13576, 1.20636, 1.27844, 1.34914, 1.42197, 1.49185, 1.5613, 1.6359, 1.70599, 1.77682, 1.84732, 1.9198, 1.9894, 2.06196, 2.13428, 2.207, 2.2789, 2.3484, 2.36723, 2.29833, 2.22736, 2.15516, 2.08448, 2.01243, 1.94089, 1.86941, 1.79835, 1.72443, 1.65261, 1.58079, 1.50993, 1.44056, 1.36847, 1.29668, 1.22558, 1.15824, 1.08774, 1.01412, 0.944472, 0.872196, 0.799443, 0.729537, 0.65492, 0.583621, 0.516289, 0.444457, 0.373658, 0.303394, 0.235519, 0.164342, 0.0944481, 0.022383, 0.0469471, 0.114953, 0.184859, 0.254976, 0.324024, 0.39682, 0.468356, 0.536725, 0.606112, 0.674126, 0.741423, 0.811285, 0.883676, 0.954859, 1.02535, 1.09353, 1.16696, 1.23719, 1.30729, 1.37789, 1.44493, 1.5161, 1.59079, 1.66217, 1.73465, 1.80772, 1.8764, 1.94664, 2.01682, 2.08647, 2.15834, 2.22697, 2.29786, 2.36789, 2.3445, 2.27166, 2.20245, 2.13049, 2.05886, 1.98826, 1.92072, 1.8507, 1.78074, 1.71022, 1.63846, 1.56626, 1.49876, 1.42793, 1.35775, 1.28548, 1.21523, 1.14439, 1.07461, 1.00498, 0.932618, 0.860615, 0.788838, 0.718041, 0.648264, 0.578779, 0.504997, 0.434639, 0.362868, 0.289758, 0.219055, 0.149272, 0.080435, 0.00878906}

Answer 1

I'm not sure exactly what you want but this might get you started.

First step is to find the main frequency. It has to be around 29 since that's how many peaks I count. But we can also learn that using Fourier, as below. I remove the initial 40 elements since they are not part of the cyclical behavior.

positives = Motorencodercycle[[40 ;;]];
mean = Mean[positives];

ft = Rest@Fourier[positives - mean];
MinMax[Abs[ft]]
{Length[ft], Position[Abs@ft, Max[Abs[ft]]]}

(* Out[245]= {0.000154602, 21.4385}
Out[246]= {1960, {{29}, {1932}}} *)

We can plot this data with x axis folded by the period, as follows.

per = Length[positives]/(29.0);
xvals = Mod[Range[Length@positives], per];
ListPlot[Transpose[{xvals, positives}]]

Using Manipulate as below I can get a slightly better estimate, around 29.025.

Manipulate[per = Length[positives]/(29.0 + e);
 xvals = Mod[Range[Length@positives], per];
 ListPlot[Transpose[{xvals, positives}]], {e, -.1, .2, .001}]

Answer 2

Here is an approach based on a nonlinear regression:

data = Motorencodercycle[[41 ;;]];
nlm = NonlinearModelFit[data, {(2 h/p) Abs[Mod[x - phase, p] - p/2], 
   h > 0 && p > 0}, {{h, 2.75}, {p, 67.5}, {phase, 3 \[Pi]/2}}, x]
nlm["BestFitParameters"]
(* {h -> 2.3903, p -> 67.5603, phase -> 34.516} *)
Show[ListPlot[data, AspectRatio -> 1/3], 
 Plot[nlm[x], {x, 1, Length[data]}]]

Plots of the residuals suggest that there's still some structure yet to be explained above and beyond a symmetric triangular wave. For example the signs of the residuals are opposite for the rising and falling limbs.

f = D[(2 h/p) RealAbs[Mod[x - phase, p] - p/2], x] /. nlm["BestFitParameters"];
slope = f /. x -> # & /@ Range[Length[data]];
rising = Select[Transpose[{slope, Range[Length[data]], nlm["FitResiduals"]}], #[[1]] > 0 &];
falling = Select[Transpose[{slope, Range[Length[data]], nlm["FitResiduals"]}], #[[1]] <= 0 &];
ListPlot[{rising[[All, {2, 3}]], falling[[All, {2, 3}]]}, PlotLegends -> {"Rising limb", "Falling limb"}]

Now plot the data with each cycle of data superimposed.

ListPlot[Transpose[{Mod[Range[Length[data]] - phase + p/2, p] /. nlm["BestFitParameters"], data}]]

95% single-prediction intervals can be constructed by changing Abs to RealAbs in the function fit by NonlinearModelFit:

nlm = NonlinearModelFit[data, {(2 h/p) RealAbs[Mod[x - phase, p] - p/2], h > 0 && p > 0},
   {{h, 2.75}, {p, 67.5}, {phase, 3 π/2}}, x];

spb = nlm["SinglePredictionBands"];
Show[ListPlot[Transpose[{1 + Mod[Range[Length[data]] - phase + p/2, p] /. nlm["BestFitParameters"], data}],
  PlotStyle -> PointSize[0.003]],
 Plot[spb, {x, 1, 1 + p /. nlm["BestFitParameters"]}, PlotStyle -> {{Thickness[0.003], Red}}]]

And, of course, a single prediction for a value x is found with nlm[x].

Addition: Here is an alternative but equivalent model.

f[x_, a_, p_, θ_] := a + (2 a/π) ArcSin[Sin[2 π x/p + θ]]
data = Select[Motorencodercycle, # > 0 &];
nlm2 = NonlinearModelFit[data, f[x, a, p, θ], {{a, 2.75}, {p, 67.5}, {θ, -33}}, x]
nlm2["BestFitParameters"]
Show[ListPlot[data], Plot[nlm2[x], {x, 1, Length[data]}]]

While there might seem to be a slight difference in the two figures of all of the data, the predictions are identical.