function ericfft(n0,numper,N) % ERICFFT(n0,numper,N) defines sound data taken by Eric % Brewe and calculates a naive Fourier approximation of % order N over the intervals stretching from the n0-th local % maximum to the (n0+numper)-th local maximum %Default values if nargin < 3, N=20; end; if nargin < 2, numper=2; end; if nargin < 1, n0=1; end; % % First define the data -- this is pasted in from EXCEL % mydata=[0,2.494; 0.00017,2.472; 0.00033,2.46; 0.0005,2.494; 0.00067,2.511; 0.00083,2.511; 0.001,2.464; 0.00117,2.444; 0.00133,2.467; 0.0015,2.481; 0.00167,2.442; 0.00183,2.37; 0.002,2.461; 0.00217,2.666; 0.00233,2.824; 0.0025,2.686; 0.00267,2.479; 0.00283,2.38; 0.003,2.464; 0.00317,2.594; 0.00333,2.567; 0.0035,2.515; 0.00367,2.503; 0.00383,2.595; 0.004,2.575; 0.00417,2.482; 0.00433,2.394; 0.0045,2.481; 0.00467,2.625; 0.00483,2.668; 0.005,2.577; 0.00517,2.454; 0.00533,2.451; 0.0055,2.499; 0.00567,2.507; 0.00583,2.467; 0.006,2.49; 0.00617,2.563; 0.00633,2.63; 0.0065,2.595; 0.00667,2.511; 0.00683,2.491; 0.007,2.516; 0.00717,2.549; 0.00733,2.537; 0.0075,2.535; 0.00767,2.537; 0.00783,2.55; 0.008,2.519; 0.00817,2.486; 0.00833,2.486; 0.0085,2.523; 0.00867,2.549; 0.00883,2.529; 0.009,2.503; 0.00917,2.477; 0.00933,2.489; 0.0095,2.479; 0.00967,2.475; 0.00983,2.474; 0.01,2.49; 0.01017,2.501; 0.01033,2.492; 0.0105,2.481; 0.01067,2.472; 0.01083,2.469; 0.011,2.476; 0.01117,2.472; 0.01133,2.449; 0.0115,2.386; 0.01167,2.523; 0.01183,2.646; 0.012,2.777; 0.01217,2.636; 0.01233,2.497; 0.0125,2.421; 0.01267,2.481; 0.01283,2.571; 0.013,2.54; 0.01317,2.536; 0.01333,2.531; 0.0135,2.575; 0.01367,2.543; 0.01383,2.476; 0.014,2.436; 0.01417,2.513; 0.01433,2.604; 0.0145,2.629; 0.01467,2.559; 0.01483,2.482; 0.015,2.467; 0.01517,2.486; 0.01533,2.505; 0.0155,2.492; 0.01567,2.543; 0.01583,2.601; 0.016,2.612; 0.01617,2.551; 0.01633,2.494; 0.0165,2.492; 0.01667,2.519; 0.01683,2.549; 0.017,2.529; 0.01717,2.531; 0.01733,2.534; 0.0175,2.535; 0.01767,2.504; 0.01783,2.49; 0.018,2.505; 0.01817,2.539; 0.01833,2.549; 0.0185,2.517; 0.01867,2.48; 0.01883,2.469; 0.019,2.487; 0.01917,2.49; 0.01933,2.489; 0.0195,2.477; 0.01967,2.491; 0.01983,2.489; 0.02,2.497; 0.02017,2.494; 0.02033,2.461; 0.0205,2.482; 0.02067,2.477; 0.02083,2.465; 0.021,2.422; 0.02117,2.432; 0.02133,2.592; 0.0215,2.741; 0.02167,2.714; 0.02183,2.554; 0.022,2.431; 0.02217,2.44; 0.02233,2.544; 0.0225,2.564; 0.02267,2.539; 0.02283,2.515; 0.023,2.571; 0.02317,2.567; 0.02333,2.516; 0.0235,2.435; 0.02367,2.459; 0.02383,2.572; 0.024,2.64; 0.02417,2.601; 0.02433,2.495; 0.0245,2.469; 0.02467,2.48; 0.02483,2.533; 0.025,2.514; 0.02517,2.504; 0.02533,2.525; 0.0255,2.592; 0.02567,2.614; 0.02583,2.555; 0.026,2.494; 0.02617,2.47; 0.02633,2.526; 0.0265,2.557; 0.02667,2.547; 0.02683,2.513; 0.027,2.506; 0.02717,2.525; 0.02733,2.524; 0.0275,2.503; 0.02767,2.49; 0.02783,2.513; 0.028,2.535; 0.02817,2.525; 0.02833,2.486; 0.0285,2.466; 0.02867,2.472; 0.02883,2.49; 0.029,2.484; 0.02917,2.486; 0.02933,2.487; 0.0295,2.511; 0.02967,2.503; 0.02983,2.477; 0.03,2.452; 0.03017,2.438; 0.03033,2.439; 0.0305,2.431; 0.03067,2.58; 0.03083,2.68; 0.031,2.729; 0.03117,2.59; 0.03133,2.475; 0.0315,2.445; 0.03167,2.513; 0.03183,2.559; 0.032,2.541; 0.03217,2.537; 0.03233,2.549; 0.0325,2.559; 0.03267,2.515; 0.03283,2.461; 0.033,2.474; 0.03317,2.556; 0.03333,2.606; 0.0335,2.597; 0.03367,2.53; 0.03383,2.501; 0.034,2.487; 0.03417,2.492; 0.03433,2.497; 0.0345,2.517; 0.03467,2.569; 0.03483,2.604; 0.035,2.582; 0.03517,2.52; 0.03533,2.503; 0.0355,2.517; 0.03567,2.545; 0.03583,2.546; 0.036,2.521; 0.03617,2.524; 0.03633,2.52; 0.0365,2.523; 0.03667,2.503; 0.03683,2.503; 0.037,2.521; 0.03717,2.54; 0.03733,2.525; 0.0375,2.484; 0.03767,2.474; 0.03783,2.489; 0.038,2.497; 0.03817,2.484; 0.03833,2.471; 0.0385,2.479; 0.03867,2.506; 0.03883,2.517; 0.039,2.482; 0.03917,2.445; 0.03933,2.459; 0.0395,2.48; 0.03967,2.465; 0.03983,2.411; 0.04,2.513; 0.04017,2.645; 0.04033,2.765; 0.0405,2.628; 0.04067,2.5; 0.04083,2.421; 0.041,2.509; 0.04117,2.574; 0.04133,2.547; 0.0415,2.509; 0.04167,2.515; 0.04183,2.579; 0.042,2.559; 0.04217,2.49; 0.04233,2.442; 0.0425,2.513; 0.04267,2.607; 0.04283,2.634; 0.043,2.537; 0.04317,2.481; 0.04333,2.474; 0.0435,2.519; 0.04367,2.511; 0.04383,2.509; 0.044,2.534; 0.04417,2.563; 0.04433,2.585; 0.0445,2.561; 0.04467,2.547; 0.04483,2.517; 0.045,2.524; 0.04517,2.523; 0.04533,2.541; 0.0455,2.536; 0.04567,2.524; 0.04583,2.507; 0.046,2.51; 0.04617,2.521; 0.04633,2.523; 0.0465,2.519; 0.04667,2.503; 0.04683,2.505; 0.047,2.503; 0.04717,2.5; 0.04733,2.481; 0.0475,2.472; 0.04767,2.474; 0.04783,2.482; 0.048,2.489; 0.04817,2.489; 0.04833,2.494; 0.0485,2.486; 0.04867,2.487; 0.04883,2.45; 0.049,2.431; 0.04917,2.395; 0.04933,2.534; 0.0495,2.651; 0.04967,2.757; 0.04983,2.632; 0.05,2.503; 0.05017,2.434; 0.05033,2.485; 0.0505,2.565; 0.05067,2.543; 0.05083,2.545; 0.051,2.54; 0.05117,2.574; 0.05133,2.529; 0.0515,2.472; 0.05167,2.445; 0.05183,2.526; 0.052,2.6; 0.05217,2.621; 0.05233,2.543; 0.0525,2.495; 0.05267,2.476; 0.05283,2.492; 0.053,2.496; 0.05317,2.491; 0.05333,2.534; 0.0535,2.569; 0.05367,2.591; 0.05383,2.577; 0.054,2.564; 0.05417,2.534; 0.05433,2.503; 0.0545,2.503; 0.05467,2.524; 0.05483,2.555; 0.055,2.553; 0.05517,2.519; 0.05533,2.5; 0.0555,2.503; 0.05567,2.516; 0.05583,2.514; 0.056,2.507; 0.05617,2.514; 0.05633,2.519; 0.0565,2.504; 0.05667,2.474; 0.05683,2.457; 0.057,2.469; 0.05717,2.494; 0.05733,2.503; 0.0575,2.496; 0.05767,2.487; 0.05783,2.507; 0.058,2.474; 0.05817,2.442; 0.05833,2.414; 0.0585,2.429; 0.05867,2.457; 0.05883,2.595; 0.059,2.721; 0.05917,2.694; 0.05933,2.584; 0.0595,2.452; 0.05967,2.438; 0.05983,2.524; 0.06,2.563; 0.06017,2.561; 0.06033,2.533; 0.0605,2.555; 0.06067,2.541; 0.06083,2.497; 0.061,2.461; 0.06117,2.471; 0.06133,2.565; 0.0615,2.625; 0.06167,2.602; 0.06183,2.517; 0.062,2.469; 0.06217,2.467; 0.06233,2.489; 0.0625,2.494; 0.06267,2.513; 0.06283,2.546; 0.063,2.591; 0.06317,2.596; 0.06333,2.547; 0.0635,2.486; 0.06367,2.494; 0.06383,2.533; 0.064,2.567; 0.06417,2.556; 0.06433,2.533; 0.0645,2.523; 0.06467,2.521; 0.06483,2.509; 0.065,2.499; 0.06517,2.51; 0.06533,2.536; 0.0655,2.549; 0.06567,2.525; 0.06583,2.481; 0.066,2.462; 0.06617,2.469; 0.06633,2.491; 0.0665,2.511; 0.06667,2.506; 0.06683,2.494; 0.067,2.471; 0.06717,2.471; 0.06733,2.484; 0.0675,2.481; 0.06767,2.479; 0.06783,2.451; 0.068,2.449; 0.06817,2.419; 0.06833,2.486; 0.0685,2.625; 0.06867,2.753; 0.06883,2.658; 0.069,2.526; 0.06917,2.434; 0.06933,2.455; 0.0695,2.563; 0.06967,2.551; 0.06983,2.55; 0.07,2.523; 0.07017,2.564; 0.07033,2.537; 0.0705,2.484; 0.07067,2.45; 0.07083,2.497; 0.071,2.599; 0.07117,2.625; 0.07133,2.574; 0.0715,2.486; 0.07167,2.464; 0.07183,2.48; 0.072,2.503; 0.07217,2.501; 0.07233,2.52; 0.0725,2.556; 0.07267,2.586; 0.07283,2.574; 0.073,2.521; 0.07317,2.496; 0.07333,2.516; 0.0735,2.557; 0.07367,2.579; 0.07383,2.553; 0.074,2.521; 0.07417,2.501; 0.07433,2.505; 0.0745,2.511; 0.07467,2.524; 0.07483,2.536; 0.075,2.537; 0.07517,2.529; 0.07533,2.5; 0.0755,2.469; 0.07567,2.465; 0.07583,2.485; 0.076,2.515; 0.07617,2.516; 0.07633,2.494; 0.0765,2.45; 0.07667,2.452; 0.07683,2.496; 0.077,2.52; 0.07717,2.49; 0.07733,2.452; 0.0775,2.428; 0.07767,2.434; 0.07783,2.416; 0.078,2.563; 0.07817,2.664; 0.07833,2.742; 0.0785,2.615; 0.07867,2.477; 0.07883,2.436; 0.079,2.489; 0.07917,2.566; 0.07933,2.557; 0.0795,2.533; 0.07967,2.541; 0.07983,2.553; 0.08,2.527; 0.08017,2.462; 0.08033,2.446; 0.0805,2.535; 0.08067,2.607; 0.08083,2.624; 0.081,2.535; 0.08117,2.481; 0.08133,2.465; 0.0815,2.484; 0.08167,2.497; 0.08183,2.494; 0.082,2.541; 0.08217,2.569; 0.08233,2.595; 0.0825,2.564; 0.08267,2.513; 0.08283,2.494; 0.083,2.497; 0.08317,2.546; 0.08333,2.564; 0.0835,2.56; 0.08367,2.535; 0.08383,2.513; 0.084,2.513; 0.08417,2.511; 0.08433,2.519; 0.0845,2.527; 0.08467,2.535; 0.08483,2.534; 0.085,2.511; 0.08517,2.484; 0.08533,2.46; 0.0855,2.477; 0.08567,2.504; 0.08583,2.516; 0.086,2.505; 0.08617,2.485; 0.08633,2.475; 0.0865,2.479; 0.08667,2.477; 0.08683,2.476; 0.087,2.486; 0.08717,2.484; 0.08733,2.455; 0.0875,2.421; 0.08767,2.42; 0.08783,2.591; 0.088,2.74; 0.08817,2.709; 0.08833,2.554; 0.0885,2.432; 0.08867,2.442; 0.08883,2.55; 0.089,2.556; 0.08917,2.536; 0.08933,2.506; 0.0895,2.574; 0.08967,2.57; 0.08983,2.514; 0.09,2.444; 0.09017,2.461; 0.09033,2.577; 0.0905,2.63; 0.09067,2.597; 0.09083,2.504; 0.091,2.472; 0.09117,2.487; 0.09133,2.507; 0.0915,2.484; 0.09167,2.492; 0.09183,2.535; 0.092,2.592; 0.09217,2.58; 0.09233,2.541; 0.0925,2.496; 0.09267,2.507; 0.09283,2.553; 0.093,2.56; 0.09317,2.55; 0.09333,2.533; 0.0935,2.556; 0.09367,2.551; 0.09383,2.524; 0.094,2.49; 0.09417,2.503; 0.09433,2.537; 0.0945,2.559; 0.09467,2.52; 0.09483,2.487; 0.095,2.476; 0.09517,2.49; 0.09533,2.497; 0.0955,2.495; 0.09567,2.491; 0.09583,2.494; 0.096,2.492; 0.09617,2.48; 0.09633,2.472; 0.0965,2.474; 0.09667,2.486; 0.09683,2.465; 0.097,2.46; 0.09717,2.442; 0.09733,2.415; 0.0975,2.51; 0.09767,2.644; 0.09783,2.757; 0.098,2.642; 0.09817,2.506; 0.09833,2.43; 0.0985,2.492; 0.09867,2.575; 0.09883,2.555; 0.099,2.519; 0.09917,2.526; 0.09933,2.576; 0.0995,2.555; 0.09967,2.486; 0.09983,2.447; 0.1,2.51; 0.10017,2.609; 0.10033,2.619; 0.1005,2.546; 0.10067,2.485; 0.10083,2.481; 0.101,2.499; 0.10117,2.495; 0.10133,2.476; 0.1015,2.506; 0.10167,2.565; 0.10183,2.601; 0.102,2.564; 0.10217,2.507; 0.10233,2.48; 0.1025,2.531; 0.10267,2.585; 0.10283,2.582; 0.103,2.536; 0.10317,2.511; 0.10333,2.523; 0.1035,2.527; 0.10367,2.52; 0.10383,2.51; 0.104,2.535; 0.10417,2.553; 0.10433,2.541; 0.1045,2.49; 0.10467,2.467; 0.10483,2.48; 0.105,2.509; 0.10517,2.511; 0.10533,2.492; 0.1055,2.487; 0.10567,2.486; 0.10583,2.481; 0.106,2.479; 0.10617,2.477; 0.10633,2.486; 0.1065,2.479; 0.10667,2.472; 0.10683,2.462; 0.107,2.434; 0.10717,2.432; 0.10733,2.595; 0.1075,2.71; 0.10767,2.709; 0.10783,2.566; 0.108,2.446; 0.10817,2.455; 0.10833,2.54; 0.1085,2.563; 0.10867,2.541; 0.10883,2.519; 0.109,2.561; 0.10917,2.561; 0.10933,2.52; 0.1095,2.465; 0.10967,2.475; 0.10983,2.572; 0.11,2.606; 0.11017,2.591; 0.11033,2.51; 0.1105,2.482; 0.11067,2.495; 0.11083,2.51; 0.111,2.507; 0.11117,2.504; 0.11133,2.557; 0.1115,2.584; 0.11167,2.569; 0.11183,2.505; 0.112,2.495; 0.11217,2.539; 0.11233,2.576; 0.1125,2.55; 0.11267,2.515; 0.11283,2.517; 0.113,2.537; 0.11317,2.54; 0.11333,2.501; 0.1135,2.497; 0.11367,2.523; 0.11383,2.564; 0.114,2.54; 0.11417,2.496; 0.11433,2.461; 0.1145,2.48; 0.11467,2.504; 0.11483,2.504; 0.115,2.494; 0.11517,2.491; 0.11533,2.494; 0.1155,2.484; 0.11567,2.486; 0.11583,2.474; 0.116,2.476; 0.11617,2.465; 0.11633,2.465; 0.1165,2.454; 0.11667,2.428; 0.11683,2.504; 0.117,2.648; 0.11717,2.749; 0.11733,2.635; 0.1175,2.5; 0.11767,2.43; 0.11783,2.482; 0.118,2.572; 0.11817,2.56; 0.11833,2.54; 0.1185,2.529; 0.11867,2.566; 0.11883,2.536; 0.119,2.487; 0.11917,2.445; 0.11933,2.515; 0.1195,2.611; 0.11967,2.63; 0.11983,2.557; 0.12,2.474; 0.12017,2.462; 0.12033,2.484; 0.1205,2.511; 0.12067,2.494; 0.12083,2.511; 0.121,2.571; 0.12117,2.61; 0.12133,2.571; 0.1215,2.49; 0.12167,2.486; 0.12183,2.529; 0.122,2.565; 0.12217,2.553; 0.12233,2.52; 0.1225,2.524; 0.12267,2.533; 0.12283,2.521; 0.123,2.497; 0.12317,2.492; 0.12333,2.529; 0.1235,2.551; 0.12367,2.541; 0.12383,2.485; 0.124,2.459; 0.12417,2.474; 0.12433,2.495; 0.1245,2.504; 0.12467,2.479; 0.12483,2.475; 0.125,2.48; 0.12517,2.507; 0.12533,2.499; 0.1255,2.464; 0.12567,2.455; 0.12583,2.464; 0.126,2.465; 0.12617,2.426; 0.12633,2.48; 0.1265,2.616; 0.12667,2.757; 0.12683,2.662; 0.127,2.526; 0.12717,2.416; 0.12733,2.46; 0.1275,2.567; 0.12767,2.565; 0.12783,2.545; 0.128,2.521; 0.12817,2.563; 0.12833,2.547; 0.1285,2.496; 0.12867,2.442; 0.12883,2.497; 0.129,2.587; 0.12917,2.628; 0.12933,2.567; 0.1295,2.489; 0.12967,2.466; 0.12983,2.486; 0.13,2.5; 0.13017,2.497; 0.13033,2.509; 0.1305,2.544; 0.13067,2.591; 0.13083,2.585; 0.131,2.557; 0.13117,2.504; 0.13133,2.511; 0.1315,2.523; 0.13167,2.539; 0.13183,2.553; 0.132,2.531; 0.13217,2.535; 0.13233,2.505; 0.1325,2.507; 0.13267,2.497; 0.13283,2.523; 0.133,2.529; 0.13317,2.529; 0.13333,2.505; 0.1335,2.479; 0.13367,2.475; 0.13383,2.475; 0.134,2.48; 0.13417,2.486; 0.13433,2.49; 0.1345,2.487; 0.13467,2.492; 0.13483,2.479; 0.135,2.482; 0.13517,2.455; 0.13533,2.466; 0.1355,2.456; 0.13567,2.429; 0.13583,2.517; 0.136,2.628; 0.13617,2.742; 0.13633,2.641; 0.1365,2.495; 0.13667,2.424; 0.13683,2.484; 0.137,2.581; 0.13717,2.563; 0.13733,2.523; 0.1375,2.521; 0.13767,2.567; 0.13783,2.557; 0.138,2.487; 0.13817,2.436; 0.13833,2.503; 0.1385,2.61; 0.13867,2.636; 0.13883,2.549; 0.139,2.472; 0.13917,2.469; 0.13933,2.504; 0.1395,2.515; 0.13967,2.514; 0.13983,2.524; 0.14,2.549; 0.14017,2.577; 0.14033,2.56; 0.1405,2.537; 0.14067,2.509; 0.14083,2.516; 0.141,2.529; 0.14117,2.543; 0.14133,2.533; 0.1415,2.521; 0.14167,2.521; 0.14183,2.517; 0.142,2.516; 0.14217,2.51; 0.14233,2.516; 0.1425,2.521; 0.14267,2.515; 0.14283,2.492; 0.143,2.48; 0.14317,2.484; 0.14333,2.501; 0.1435,2.492; 0.14367,2.482; 0.14383,2.462; 0.144,2.484; 0.14417,2.49; 0.14433,2.503; 0.1445,2.484; 0.14467,2.467; 0.14483,2.447; 0.145,2.424; 0.14517,2.396; 0.14533,2.576; 0.1455,2.722; 0.14567,2.739; 0.14583,2.58; 0.146,2.444; 0.14617,2.436; 0.14633,2.526; 0.1465,2.569; 0.14667,2.54; 0.14683,2.53; 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0.20567,2.499; 0.20583,2.51; 0.206,2.575; 0.20617,2.607; 0.20633,2.575; 0.2065,2.52; 0.20667,2.5; 0.20683,2.515; 0.207,2.549; 0.20717,2.533; 0.20733,2.529; 0.2075,2.514; 0.20767,2.525; 0.20783,2.507; 0.208,2.501; 0.20817,2.5; 0.20833,2.517; 0.2085,2.533; 0.20867,2.511; 0.20883,2.494; 0.209,2.474; 0.20917,2.475; 0.20933,2.469; 0.2095,2.477; 0.20967,2.489; 0.20983,2.505; 0.21,2.509; 0.21017,2.475; 0.21033,2.469; 0.2105,2.454; 0.21067,2.479; 0.21083,2.452; 0.211,2.43; 0.21117,2.549; 0.21133,2.66; 0.2115,2.711; 0.21167,2.602; 0.21183,2.487; 0.212,2.45; 0.21217,2.524; 0.21233,2.56; 0.2125,2.546; 0.21267,2.539; 0.21283,2.555; 0.213,2.549; 0.21317,2.521; 0.21333,2.466; 0.2135,2.475; 0.21367,2.55; 0.21383,2.592; 0.214,2.595; 0.21417,2.527; 0.21433,2.5; 0.2145,2.479; 0.21467,2.5; 0.21483,2.517; 0.215,2.523; 0.21517,2.547; 0.21533,2.569; 0.2155,2.585; 0.21567,2.554; 0.21583,2.523; 0.216,2.509; 0.21617,2.529; 0.21633,2.543; 0.2165,2.539; 0.21667,2.526; 0.21683,2.526; 0.217,2.524; 0.21717,2.51; 0.21733,2.496; 0.2175,2.497; 0.21767,2.515; 0.21783,2.524; 0.218,2.514; 0.21817,2.5; 0.21833,2.476; 0.2185,2.47; 0.21867,2.467; 0.21883,2.489; 0.219,2.503; 0.21917,2.499; 0.21933,2.482; 0.2195,2.46; 0.21967,2.479; 0.21983,2.465; 0.22,2.469; 0.22017,2.434; 0.22033,2.506; 0.2205,2.599; 0.22067,2.704; 0.22083,2.645; 0.221,2.54; 0.22117,2.469; 0.22133,2.485; 0.2215,2.56; 0.22167,2.546; 0.22183,2.55; 0.222,2.533; 0.22217,2.559; 0.22233,2.547; 0.2225,2.496; 0.22267,2.465; 0.22283,2.509; 0.223,2.575; 0.22317,2.601; 0.22333,2.561; 0.2235,2.503; 0.22367,2.475; 0.22383,2.486; 0.224,2.505; 0.22417,2.534; 0.22433,2.547; 0.2245,2.555; 0.22467,2.565; 0.22483,2.559; 0.225,2.544; 0.22517,2.53; 0.22533,2.52; 0.2255,2.536; 0.22567,2.537; 0.22583,2.537; 0.226,2.515; 0.22617,2.511; 0.22633,2.513; 0.2265,2.516; 0.22667,2.52; 0.22683,2.504; 0.227,2.505; 0.22717,2.504; 0.22733,2.505; 0.2275,2.495; 0.22767,2.474; 0.22783,2.464; 0.228,2.475; 0.22817,2.501; 0.22833,2.509; 0.2285,2.49; 0.22867,2.459; 0.22883,2.449; 0.229,2.461; 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0.24083,2.523; 0.241,2.475; 0.24117,2.487; 0.24133,2.553; 0.2415,2.587; 0.24167,2.581; 0.24183,2.514; 0.242,2.49; 0.24217,2.482; 0.24233,2.496; 0.2425,2.501; 0.24267,2.501; 0.24283,2.546; 0.243,2.599; 0.24317,2.59; 0.24333,2.55; 0.2435,2.481; 0.24367,2.506; 0.24383,2.55; 0.244,2.577; 0.24417,2.551; 0.24433,2.507; 0.2445,2.517; 0.24467,2.52; 0.24483,2.525; 0.245,2.503; 0.24517,2.506; 0.24533,2.529; 0.2455,2.539; 0.24567,2.501; 0.24583,2.461; 0.246,2.457; 0.24617,2.486; 0.24633,2.505; 0.2465,2.491; 0.24667,2.479; 0.24683,2.484; 0.247,2.497; 0.24717,2.475; 0.24733,2.46; 0.2475,2.444; 0.24767,2.467; 0.24783,2.429; 0.248,2.47; 0.24817,2.581; 0.24833,2.73; 0.2485,2.668; 0.24867,2.554; 0.24883,2.449; 0.249,2.457; 0.24917,2.565; 0.24933,2.571; 0.2495,2.543; 0.24967,2.505; 0.24983,2.561; 0.25,2.551; 0.25017,2.527; 0.25033,2.456; 0.2505,2.49; 0.25067,2.56; 0.25083,2.622; 0.251,2.581; 0.25117,2.495; 0.25133,2.474; 0.2515,2.481; 0.25167,2.51; 0.25183,2.494; 0.252,2.524; 0.25217,2.554; 0.25233,2.6; 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0.38083,2.551; 0.381,2.485; 0.38117,2.457; 0.38133,2.482; 0.3815,2.497; 0.38167,2.504; 0.38183,2.547; 0.382,2.602; 0.38217,2.617; 0.38233,2.561; 0.3825,2.506; 0.38267,2.482; 0.38283,2.513; 0.383,2.553; 0.38317,2.546; 0.38333,2.541; 0.3835,2.517; 0.38367,2.52; 0.38383,2.496; 0.384,2.492; 0.38417,2.499; 0.38433,2.529; 0.3845,2.544; 0.38467,2.519; 0.38483,2.479; 0.385,2.46; 0.38517,2.466; 0.38533,2.471; 0.3855,2.487; 0.38567,2.492; 0.38583,2.506; 0.386,2.492; 0.38617,2.469; 0.38633,2.464; 0.3865,2.466; 0.38667,2.467; 0.38683,2.439; 0.387,2.469; 0.38717,2.575; 0.38733,2.707; 0.3875,2.669; 0.38767,2.565; 0.38783,2.449; 0.388,2.476; 0.38817,2.553; 0.38833,2.575; 0.3885,2.54; 0.38867,2.523; 0.38883,2.544; 0.389,2.555; 0.38917,2.519; 0.38933,2.462; 0.3895,2.486; 0.38967,2.567; 0.38983,2.626; 0.39,2.58; 0.39017,2.507; 0.39033,2.454; 0.3905,2.486; 0.39067,2.506; 0.39083,2.526; 0.391,2.531; 0.39117,2.556; 0.39133,2.582; 0.3915,2.571; 0.39167,2.539; 0.39183,2.491; 0.392,2.509; 0.39217,2.534; 0.39233,2.559; 0.3925,2.536; 0.39267,2.519; 0.39283,2.515; 0.393,2.517; 0.39317,2.513; 0.39333,2.504; 0.3935,2.515; 0.39367,2.523; 0.39383,2.517; 0.394,2.497; 0.39417,2.485; 0.39433,2.469; 0.3945,2.482; 0.39467,2.482; 0.39483,2.501; 0.395,2.494; 0.39517,2.491; 0.39533,2.475; 0.3955,2.474; 0.39567,2.469; 0.39583,2.469; 0.396,2.45; 0.39617,2.422; 0.39633,2.523; 0.3965,2.634; 0.39667,2.709; 0.39683,2.617; 0.397,2.52; 0.39717,2.472; 0.39733,2.519; 0.3975,2.561; 0.39767,2.549; 0.39783,2.515; 0.398,2.541; 0.39817,2.565; 0.39833,2.55; 0.3985,2.486; 0.39867,2.455; 0.39883,2.533; 0.399,2.604; 0.39917,2.61; 0.39933,2.535; 0.3995,2.486; 0.39967,2.479; 0.39983,2.494; 0.4,2.509; 0.40017,2.511; 0.40033,2.536; 0.4005,2.576; 0.40067,2.589; 0.40083,2.563; 0.401,2.516; 0.40117,2.495; 0.40133,2.517; 0.4015,2.543; 0.40167,2.554; 0.40183,2.53; 0.402,2.519; 0.40217,2.505; 0.40233,2.509; 0.4025,2.507; 0.40267,2.511; 0.40283,2.52; 0.403,2.52; 0.40317,2.511; 0.40333,2.485; 0.4035,2.48; 0.40367,2.476; 0.40383,2.482; 0.404,2.489; 0.40417,2.497; 0.40433,2.497; 0.4045,2.496; 0.40467,2.484; 0.40483,2.47; 0.405,2.46; 0.40517,2.465; 0.40533,2.469; 0.4055,2.44; 0.40567,2.536; 0.40583,2.631; 0.406,2.685; 0.40617,2.614; 0.40633,2.529; 0.4065,2.485; 0.40667,2.513; 0.40683,2.551; 0.407,2.54; 0.40717,2.535; 0.40733,2.544; 0.4075,2.557; 0.40767,2.52; 0.40783,2.489; 0.408,2.476; 0.40817,2.545; 0.40833,2.582; 0.4085,2.595; 0.40867,2.525; 0.40883,2.495; 0.409,2.474; 0.40917,2.486; 0.40933,2.516; 0.4095,2.527; 0.40967,2.559; 0.40983,2.556; 0.41,2.564; 0.41017,2.545; 0.41033,2.537; 0.4105,2.524; 0.41067,2.517; 0.41083,2.529; 0.411,2.531; 0.41117,2.525; 0.41133,2.52; 0.4115,2.514; 0.41167,2.515; 0.41183,2.515; 0.412,2.511; 0.41217,2.513; 0.41233,2.509; 0.4125,2.509; 0.41267,2.495; 0.41283,2.489; 0.413,2.479; 0.41317,2.475; 0.41333,2.484; 0.4135,2.503; 0.41367,2.506; 0.41383,2.496; 0.414,2.482; 0.41417,2.474; 0.41433,2.476; 0.4145,2.454; 0.41467,2.429; 0.41483,2.441; 0.415,2.549; 0.41517,2.668; 0.41533,2.694; 0.4155,2.6; 0.41567,2.494; 0.41583,2.477; 0.416,2.526; 0.41617,2.566; 0.41633,2.54; 0.4165,2.527; 0.41667,2.545; 0.41683,2.561; 0.417,2.524; 0.41717,2.462; 0.41733,2.469; 0.4175,2.563; 0.41767,2.617; 0.41783,2.595; 0.418,2.513; 0.41817,2.472; 0.41833,2.489; 0.4185,2.515; 0.41867,2.507; 0.41883,2.5; 0.419,2.541; 0.41917,2.584; 0.41933,2.595; 0.4195,2.549; 0.41967,2.509; 0.41983,2.51; 0.42,2.533; 0.42017,2.541; 0.42033,2.524; 0.4205,2.516; 0.42067,2.519; 0.42083,2.526; 0.421,2.511; 0.42117,2.495; 0.42133,2.505; 0.4215,2.521; 0.42167,2.517; 0.42183,2.501; 0.422,2.487; 0.42217,2.485; 0.42233,2.48; 0.4225,2.467; 0.42267,2.481; 0.42283,2.511; 0.423,2.509; 0.42317,2.496; 0.42333,2.467; 0.4235,2.472; 0.42367,2.485; 0.42383,2.476; 0.424,2.451; 0.42417,2.447; 0.42433,2.569; 0.4245,2.674; 0.42467,2.68; 0.42483,2.569; 0.425,2.476; 0.42517,2.481; 0.42533,2.545; 0.4255,2.564; 0.42567,2.543; 0.42583,2.526; 0.426,2.55; 0.42617,2.557; 0.42633,2.51; 0.4265,2.472; 0.42667,2.494; 0.42683,2.576; 0.427,2.614; 0.42717,2.574; 0.42733,2.494; 0.4275,2.472; 0.42767,2.506; 0.42783,2.52; 0.428,2.509; 0.42817,2.507; 0.42833,2.549; 0.4285,2.589; 0.42867,2.587; 0.42883,2.53; 0.429,2.497; 0.42917,2.507; 0.42933,2.536; 0.4295,2.541; 0.42967,2.531; 0.42983,2.515; 0.43,2.52; 0.43017,2.516; 0.43033,2.504; 0.4305,2.491; 0.43067,2.503; 0.43083,2.52; 0.431,2.525; 0.43117,2.505; 0.43133,2.485; 0.4315,2.479; 0.43167,2.471; 0.43183,2.479; 0.432,2.497; 0.43217,2.504; 0.43233,2.507; 0.4325,2.484; 0.43267,2.469; 0.43283,2.472; 0.433,2.479; 0.43317,2.454; 0.43333,2.435; 0.4335,2.521; 0.43367,2.631; 0.43383,2.681; 0.434,2.615; 0.43417,2.523; 0.43433,2.496; 0.4345,2.527; 0.43467,2.547; 0.43483,2.54; 0.435,2.523; 0.43517,2.554; 0.43533,2.555; 0.4355,2.54; 0.43567,2.49; 0.43583,2.479; 0.436,2.529; 0.43617,2.6; 0.43633,2.594; 0.4365,2.534; 0.43667,2.476; 0.43683,2.499; 0.437,2.517; 0.43717,2.52; 0.43733,2.496; 0.4375,2.527; 0.43767,2.577; 0.43783,2.597; 0.438,2.555; 0.43817,2.511; 0.43833,2.506; 0.4385,2.53; 0.43867,2.545; 0.43883,2.533; 0.439,2.524; 0.43917,2.519; 0.43933,2.523; 0.4395,2.504; 0.43967,2.504; 0.43983,2.503; 0.44,2.523; 0.44017,2.523; 0.44033,2.507; 0.4405,2.486; 0.44067,2.482; 0.44083,2.477; 0.441,2.485; 0.44117,2.507; 0.44133,2.504; 0.4415,2.496; 0.44167,2.465; 0.44183,2.471; 0.442,2.487; 0.44217,2.494; 0.44233,2.457; 0.4425,2.439; 0.44267,2.477; 0.44283,2.596; 0.443,2.684; 0.44317,2.638; 0.44333,2.547; 0.4435,2.474; 0.44367,2.501; 0.44383,2.545; 0.444,2.547; 0.44417,2.537; 0.44433,2.534; 0.4445,2.567; 0.44467,2.555; 0.44483,2.511; 0.445,2.474; 0.44517,2.51; 0.44533,2.581; 0.4455,2.606; 0.44567,2.555; 0.44583,2.5; 0.446,2.487; 0.44617,2.509; 0.44633,2.509; 0.4465,2.506; 0.44667,2.534; 0.44683,2.565; 0.447,2.589; 0.44717,2.547; 0.44733,2.523; 0.4475,2.503; 0.44767,2.526; 0.44783,2.531; 0.448,2.529; 0.44817,2.524; 0.44833,2.527; 0.4485,2.527; 0.44867,2.506; 0.44883,2.495; 0.449,2.494; 0.44917,2.515; 0.44933,2.523; 0.4495,2.515; 0.44967,2.491; 0.44983,2.484; 0.45,2.476; 0.45017,2.475; 0.45033,2.484; 0.4505,2.497; 0.45067,2.509; 0.45083,2.5; 0.451,2.48; 0.45117,2.46; 0.45133,2.467; 0.4515,2.471; 0.45167,2.455; 0.45183,2.441; 0.452,2.544; 0.45217,2.662; 0.45233,2.682; 0.4525,2.589; 0.45267,2.477; 0.45283,2.475; 0.453,2.546; 0.45317,2.572; 0.45333,2.543; 0.4535,2.513; 0.45367,2.54; 0.45383,2.57; 0.454,2.536; 0.45417,2.481; 0.45433,2.471; 0.4545,2.555; 0.45467,2.612; 0.45483,2.592; 0.455,2.516; 0.45517,2.482; 0.45533,2.495; 0.4555,2.507; 0.45567,2.507; 0.45583,2.513; 0.456,2.554; 0.45617,2.585; 0.45633,2.576; 0.4565,2.526; 0.45667,2.505; 0.45683,2.507; 0.457,2.53; 0.45717,2.533; 0.45733,2.529; 0.4575,2.52; 0.45767,2.521; 0.45783,2.513; 0.458,2.501; 0.45817,2.492; 0.45833,2.507; 0.4585,2.517; 0.45867,2.521; 0.45883,2.5; 0.459,2.482; 0.45917,2.477; 0.45933,2.476; 0.4595,2.481; 0.45967,2.49; 0.45983,2.51; 0.46,2.506; 0.46017,2.472; 0.46033,2.465; 0.4605,2.467; 0.46067,2.474; 0.46083,2.451; 0.461,2.456; 0.46117,2.572; 0.46133,2.692; 0.4615,2.665; 0.46167,2.57; 0.46183,2.457; 0.462,2.486; 0.46217,2.551; 0.46233,2.563; 0.4625,2.543; 0.46267,2.515; 0.46283,2.561; 0.463,2.553; 0.46317,2.515; 0.46333,2.467; 0.4635,2.5; 0.46367,2.582; 0.46383,2.61; 0.464,2.569; 0.46417,2.486; 0.46433,2.479; 0.4645,2.509; 0.46467,2.526; 0.46483,2.503; 0.465,2.507; 0.46517,2.547; 0.46533,2.604; 0.4655,2.58; 0.46567,2.527; 0.46583,2.486; 0.466,2.511; 0.46617,2.537; 0.46633,2.54; 0.4665,2.521; 0.46667,2.511; 0.46683,2.527; 0.467,2.521; 0.46717,2.501; 0.46733,2.484; 0.4675,2.499; 0.46767,2.516; 0.46783,2.523; 0.468,2.497; 0.46817,2.479; 0.46833,2.464; 0.4685,2.466; 0.46867,2.481; 0.46883,2.494; 0.469,2.506; 0.46917,2.499; 0.46933,2.49; 0.4695,2.452; 0.46967,2.454; 0.46983,2.438; 0.47,2.447; 0.47017,2.534; 0.47033,2.652; 0.4705,2.67; 0.47067,2.595; 0.47083,2.513; 0.471,2.476; 0.47117,2.519; 0.47133,2.559; 0.4715,2.563; 0.47167,2.541; 0.47183,2.546; 0.472,2.534; 0.47217,2.517; 0.47233,2.484; 0.4725,2.491; 0.47267,2.54; 0.47283,2.597; 0.473,2.591; 0.47317,2.536; 0.47333,2.479; 0.4735,2.457; 0.47367,2.51; 0.47383,2.524; 0.474,2.53; 0.47417,2.52; 0.47433,2.557; 0.4745,2.576; 0.47467,2.564; 0.47483,2.513; 0.475,2.494; 0.47517,2.526; 0.47533,2.556; 0.4755,2.544; 0.47567,2.514; 0.47583,2.503; 0.476,2.521; 0.47617,2.531; 0.47633,2.507; 0.4765,2.495; 0.47667,2.496; 0.47683,2.523; 0.477,2.514; 0.47717,2.494; 0.47733,2.466; 0.4775,2.467; 0.47767,2.482; 0.47783,2.5; 0.478,2.495; 0.47817,2.472; 0.47833,2.471; 0.4785,2.481; 0.47867,2.482; 0.47883,2.461; 0.479,2.415; 0.47917,2.509; 0.47933,2.605; 0.4795,2.699; 0.47967,2.622; 0.47983,2.534; 0.48,2.472; 0.48017,2.513; 0.48033,2.556; 0.4805,2.549; 0.48067,2.53; 0.48083,2.544; 0.481,2.56; 0.48117,2.546; 0.48133,2.494; 0.4815,2.457; 0.48167,2.521; 0.48183,2.595; 0.482,2.615; 0.48217,2.543; 0.48233,2.482; 0.4825,2.464; 0.48267,2.497; 0.48283,2.526; 0.483,2.535; 0.48317,2.535; 0.48333,2.541; 0.4835,2.566; 0.48367,2.557; 0.48383,2.539; 0.484,2.514; 0.48417,2.513; 0.48433,2.54; 0.4845,2.547; 0.48467,2.54; 0.48483,2.506; 0.485,2.504; 0.48517,2.514; 0.48533,2.533; 0.4855,2.519; 0.48567,2.506; 0.48583,2.494; 0.486,2.497; 0.48617,2.497; 0.48633,2.485; 0.4865,2.472; 0.48667,2.469; 0.48683,2.482; 0.487,2.482; 0.48717,2.496; 0.48733,2.485; 0.4875,2.471; 0.48767,2.462; 0.48783,2.464; 0.488,2.441; 0.48817,2.46; 0.48833,2.569; 0.4885,2.688; 0.48867,2.652; 0.48883,2.56; 0.489,2.469; 0.48917,2.484; 0.48933,2.566; 0.4895,2.556; 0.48967,2.539; 0.48983,2.511; 0.49,2.561; 0.49017,2.55; 0.49033,2.515; 0.4905,2.457; 0.49067,2.487; 0.49083,2.584; 0.491,2.609; 0.49117,2.575; 0.49133,2.492; 0.4915,2.472; 0.49167,2.482; 0.49183,2.503; 0.492,2.533; 0.49217,2.534; 0.49233,2.554; 0.4925,2.554; 0.49267,2.554; 0.49283,2.525; 0.493,2.521; 0.49317,2.529; 0.49333,2.543; 0.4935,2.55; 0.49367,2.535; 0.49383,2.513; 0.494,2.51; 0.49417,2.513; 0.49433,2.519; 0.4945,2.517; 0.49467,2.519; 0.49483,2.519; 0.495,2.499; 0.49517,2.484; 0.49533,2.475; 0.4955,2.489; 0.49567,2.497; 0.49583,2.492; 0.496,2.476; 0.49617,2.479; 0.49633,2.489; 0.4965,2.489; 0.49667,2.471; 0.49683,2.461; 0.497,2.475; 0.49717,2.446; 0.49733,2.439; 0.4975,2.549; 0.49767,2.669; 0.49783,2.684; 0.498,2.595; 0.49817,2.47; 0.49833,2.47; 0.4985,2.55; 0.49867,2.576; 0.49883,2.543; 0.499,2.505; 0.49917,2.549; 0.49933,2.565; 0.4995,2.534; 0.49967,2.464; 0.49983,2.47; 0.5,2.563]; % % separate time and voltage measurements % tt=mydata(:,1); vv=mydata(:,2); t0=tt(1) nn=size(tt,1) dt=(tt(nn)-tt(1))/(nn-1) echo off size(mydata) % %take a look at the measured data % hold off plot(tt,vv) hold on % % the following is naive, yet tricky. it simply % serves to identify the underlying period by % identifying the time lag between the distinct % max value. On an advanced level more sophisticated % methods will be used. Here the charm is the simplicity % % Find the first "peak" % pause [a,b]=max(vv(1:50)); % % then look for a peak in each window of length myguess % % vmax holds the local max values, and % imax holds the indices when these occur % imax=b; vmax=a; myguess=57; for i=1:nn/myguess-1 [a,b]=max(vv(b+2:b+2+myguess)); % % the 2 instead of the 1 helps skip the rare cases where % two successive measurements have the same max value % b=imax(size(imax,2))+b+1; imax=[imax,b]; vmax=[vmax,a]; end; dmax=imax(2:size(imax,2))-imax(1:size(imax,2)-1) hold off plot(tt(imax),vv(imax),'ro') % display('It appears that the period is slowly decreasing') display('Nonetheless all further analysis will be based on') display('an average PERIOD') % p=mean(dmax) % % taking a smaller window, adapted to the underlying period % % numper is the number or periods in the window % mydata=mydata(imax(n0):imax(n0+numper),:); tt=mydata(:,1); vv=mydata(:,2); t0=tt(1); nn=size(tt,1); dt=(tt(nn)-tt(1))/(nn-1); p=(tt(nn)-tt(1))/numper/dt; echo off size(mydata) % % Order of Fourier approximation % % Generate the values of the sines and cosines % of the first N frequencies, % NNc=[0:N]; NNs=[1:N]; ttt=tt-t0*ones(size(tt)); cc=cos(2*pi*ttt*NNc/(p*dt)); ss=sin(2*pi*ttt*NNs/(p*dt)); % % multiply the measured values -- all in big array % A=[cc,ss]; integrand=vv*ones(1,2*N+1).*A; % % and integrate (trapezoidal sums) % FC=sum((1/2)*(integrand(1:nn-1,:)+integrand(2:nn,:))... *dt); % .*((tt(2:nn)-tt(1:nn-1))*ones(1,2*N+1))); % % To obtain the Fourier coefficients multiply by the % nomalization factor (2/p)*(number of periods...) except % for the first which has to absorb an additional (1/2) % FC=FC*2/(tt(nn)-tt(1)); FC(1)=FC(1)/2 % % Calculate the summands in the Fourier expansion, and % plot them right away % hold off % win=[1:min([300,nn])]; win=[1:nn]; app=FC(1).*A(:,1); plot(tt(win),vv(win),'b-') hold on plot(tt(win),app(win),'r-') for k=1:N hold off app=app+FC(1+k).*A(:,1+k)+FC(1+k+N).*A(:,1+k+N); plot(tt(win),vv(win),'b-') hold on plot(tt(win),app(win),'r-') pause end