Computes the Lomb Scargle Periodogram and returns the information needed for computing the DFC and HP. A plot visualizing the Harmonic Frequencies presence in the spectrum is possible. The function is inspired from the Lomb library in a great part, with modifications to fit the requirements of harmonic powers and computation of the DFC. This function is inspired by the lsp function from the lomb package and adapted to add different colors for harmonic and non harmonic frequencies in the signal. For more information about lomb::lsp, please refer to: https://cran.r-project.org/web/packages/lomb/
lomb_scargle_periodogram.RdComputes the Lomb Scargle Periodogram and returns the information needed for computing the DFC and HP. A plot visualizing the Harmonic Frequencies presence in the spectrum is possible. The function is inspired from the Lomb library in a great part, with modifications to fit the requirements of harmonic powers and computation of the DFC. This function is inspired by the lsp function from the lomb package and adapted to add different colors for harmonic and non harmonic frequencies in the signal. For more information about lomb::lsp, please refer to: https://cran.r-project.org/web/packages/lomb/
Usage
lomb_scargle_periodogram(
data,
alpha = 0.01,
harm_cutoff = 12,
sampling = 15,
plot = TRUE,
extra_info_plot = TRUE
)Arguments
- data
a digiRhythm friendly dataframe of only two columns
- alpha
the statistical significance for the false alarm
- harm_cutoff
the order of the highest harmonic needed to be considered. An integer equal to 1, 2, 3, ... Default is 12.
- sampling
the sampling period in minutes. default = 15 min.
- plot
if TRUE, the LSP will be plotted
- extra_info_plot
if True, extra information will be shown on the plot
Value
a list that contains a dataframe (detailed below), the significance level and significance (for the record). The dataframe contains the power the frequency, the frequency in HZ, the p values according to Baluev 2008, the period that corresponds to the frequency in seconds and in hours and finally, a boolean to tell whether the frequency is harmonic or not.
Examples
data("df516b_2", package = "digiRhythm")
data <- df516b_2[1:672, c(1, 2)]
lomb_scargle_periodogram(data, alpha = 0.01, harm_cutof = 12, plot = TRUE)
#> v Correct time format: First column has a POSIXct Format
#> v Number of days good for DFC: 8 days >= 2 days
#> v Correct numeric format - Column 2 ==> Motion.Index
#> The data is digiRhythm friendly
#> $lsp_data
#> power frequency_hz p_values period_seconds period_hours
#> 1 1.949738e-02 1.655903e-06 7.067284e-01 603900.000 167.7500000
#> 2 5.863859e-02 3.311807e-06 2.620367e-06 301950.000 83.8750000
#> 3 1.973503e-02 4.967710e-06 6.795805e-01 201300.000 55.9166667
#> 4 2.639932e-03 6.623613e-06 1.000000e+00 150975.000 41.9375000
#> 5 4.699498e-03 8.279516e-06 1.000000e+00 120780.000 33.5500000
#> 6 1.147349e-02 9.935420e-06 9.999994e-01 100650.000 27.9583333
#> 7 1.258023e-02 1.157407e-05 9.999668e-01 86400.000 24.0000000
#> 8 6.120115e-04 1.324723e-05 1.000000e+00 75487.500 20.9687500
#> 9 2.035247e-03 1.490313e-05 1.000000e+00 67100.000 18.6388889
#> 10 5.228099e-03 1.655903e-05 1.000000e+00 60390.000 16.7750000
#> 11 6.112617e-04 1.821494e-05 1.000000e+00 54900.000 15.2500000
#> 12 8.423956e-03 1.987084e-05 1.000000e+00 50325.000 13.9791667
#> 13 3.440709e-03 2.152674e-05 1.000000e+00 46453.846 12.9038462
#> 14 5.382327e-02 2.314815e-05 1.379963e-05 43200.000 12.0000000
#> 15 8.871460e-03 2.483855e-05 1.000000e+00 40260.000 11.1833333
#> 16 4.847841e-03 2.649445e-05 1.000000e+00 37743.750 10.4843750
#> 17 2.438776e-03 2.815036e-05 1.000000e+00 35523.529 9.8676471
#> 18 6.076683e-03 2.980626e-05 1.000000e+00 33550.000 9.3194444
#> 19 1.670693e-03 3.146216e-05 1.000000e+00 31784.211 8.8289474
#> 20 7.192570e-03 3.311807e-05 1.000000e+00 30195.000 8.3875000
#> 21 1.410451e-03 3.472222e-05 1.000000e+00 28800.000 8.0000000
#> 22 2.973471e-03 3.642987e-05 1.000000e+00 27450.000 7.6250000
#> 23 5.457799e-03 3.808578e-05 1.000000e+00 26256.522 7.2934783
#> 24 6.162212e-03 3.974168e-05 1.000000e+00 25162.500 6.9895833
#> 25 2.065631e-03 4.139758e-05 1.000000e+00 24156.000 6.7100000
#> 26 7.820111e-04 4.305349e-05 1.000000e+00 23226.923 6.4519231
#> 27 1.162568e-06 4.470939e-05 9.999996e-01 22366.667 6.2129630
#> 28 1.782713e-02 4.629630e-05 8.739420e-01 21600.000 6.0000000
#> 29 1.054697e-02 4.802120e-05 1.000000e+00 20824.138 5.7844828
#> 30 7.282269e-05 4.967710e-05 1.000000e+00 20130.000 5.5916667
#> 31 9.957376e-03 5.133300e-05 1.000000e+00 19480.645 5.4112903
#> 32 9.230637e-04 5.298891e-05 1.000000e+00 18871.875 5.2421875
#> 33 4.418211e-03 5.464481e-05 1.000000e+00 18300.000 5.0833333
#> 34 7.859956e-03 5.630071e-05 1.000000e+00 17761.765 4.9338235
#> 35 1.244740e-02 5.787037e-05 9.999781e-01 17280.000 4.8000000
#> 36 1.180961e-02 5.961252e-05 9.999977e-01 16775.000 4.6597222
#> 37 5.660723e-04 6.126842e-05 1.000000e+00 16321.622 4.5337838
#> 38 1.402384e-03 6.292433e-05 1.000000e+00 15892.105 4.4144737
#> 39 3.898606e-04 6.458023e-05 1.000000e+00 15484.615 4.3012821
#> 40 1.102459e-03 6.623613e-05 1.000000e+00 15097.500 4.1937500
#> 41 4.489148e-03 6.789204e-05 1.000000e+00 14729.268 4.0914634
#> 42 7.176985e-03 6.944444e-05 1.000000e+00 14400.000 4.0000000
#> 43 1.853826e-02 7.120384e-05 8.094945e-01 14044.186 3.9011628
#> 44 4.338406e-03 7.285974e-05 1.000000e+00 13725.000 3.8125000
#> 45 1.746961e-03 7.451565e-05 1.000000e+00 13420.000 3.7277778
#> 46 1.635276e-03 7.617155e-05 1.000000e+00 13128.261 3.6467391
#> 47 1.110743e-03 7.782745e-05 1.000000e+00 12848.936 3.5691489
#> 48 1.257094e-02 7.948336e-05 9.999678e-01 12581.250 3.4947917
#> 49 1.317377e-02 8.101852e-05 9.998220e-01 12342.857 3.4285714
#> 50 2.026576e-02 8.279516e-05 6.180537e-01 12078.000 3.3550000
#> 51 1.311187e-03 8.445107e-05 1.000000e+00 11841.176 3.2892157
#> 52 3.973563e-03 8.610697e-05 1.000000e+00 11613.462 3.2259615
#> 53 5.152999e-04 8.776287e-05 1.000000e+00 11394.340 3.1650943
#> 54 5.374309e-04 8.941878e-05 1.000000e+00 11183.333 3.1064815
#> 55 2.400026e-03 9.107468e-05 1.000000e+00 10980.000 3.0500000
#> 56 1.808465e-03 9.259259e-05 1.000000e+00 10800.000 3.0000000
#> 57 3.929410e-03 9.438649e-05 1.000000e+00 10594.737 2.9429825
#> 58 2.521832e-03 9.604239e-05 1.000000e+00 10412.069 2.8922414
#> 59 6.225697e-04 9.769829e-05 1.000000e+00 10235.593 2.8432203
#> 60 1.269823e-03 9.935420e-05 1.000000e+00 10065.000 2.7958333
#> 61 6.215825e-05 1.010101e-04 1.000000e+00 9900.000 2.7500000
#> 62 4.773500e-03 1.026660e-04 1.000000e+00 9740.323 2.7056452
#> 63 2.571283e-03 1.041667e-04 1.000000e+00 9600.000 2.6666667
#> 64 6.267085e-03 1.059778e-04 1.000000e+00 9435.938 2.6210938
#> 65 6.154406e-04 1.076337e-04 1.000000e+00 9290.769 2.5807692
#> 66 2.898954e-03 1.092896e-04 1.000000e+00 9150.000 2.5416667
#> 67 9.206992e-04 1.109455e-04 1.000000e+00 9013.433 2.5037313
#> 68 9.422765e-04 1.126014e-04 1.000000e+00 8880.882 2.4669118
#> 69 2.470550e-03 1.142573e-04 1.000000e+00 8752.174 2.4311594
#> 70 8.588091e-03 1.157407e-04 1.000000e+00 8640.000 2.4000000
#> 71 4.472912e-03 1.175691e-04 1.000000e+00 8505.634 2.3626761
#> 72 3.161721e-03 1.192250e-04 1.000000e+00 8387.500 2.3298611
#> 73 1.377539e-03 1.208809e-04 1.000000e+00 8272.603 2.2979452
#> 74 2.725289e-03 1.225368e-04 1.000000e+00 8160.811 2.2668919
#> 75 5.945807e-04 1.241927e-04 1.000000e+00 8052.000 2.2366667
#> 76 4.864276e-03 1.258487e-04 1.000000e+00 7946.053 2.2072368
#> 77 2.181169e-02 1.273148e-04 4.452353e-01 7854.545 2.1818182
#> 78 1.778396e-02 1.291605e-04 8.774332e-01 7742.308 2.1506410
#> 79 1.120058e-02 1.308164e-04 9.999998e-01 7644.304 2.1234177
#> 80 3.670120e-03 1.324723e-04 1.000000e+00 7548.750 2.0968750
#> 81 7.633410e-03 1.341282e-04 1.000000e+00 7455.556 2.0709877
#> 82 3.172743e-03 1.357841e-04 1.000000e+00 7364.634 2.0457317
#> 83 4.720151e-04 1.374400e-04 1.000000e+00 7275.904 2.0210843
#> 84 5.527715e-04 1.388889e-04 1.000000e+00 7200.000 2.0000000
#> 85 1.087688e-04 1.407518e-04 1.000000e+00 7104.706 1.9735294
#> 86 3.359656e-05 1.424077e-04 1.000000e+00 7022.093 1.9505814
#> 87 2.118620e-03 1.440636e-04 1.000000e+00 6941.379 1.9281609
#> 88 1.306799e-03 1.457195e-04 1.000000e+00 6862.500 1.9062500
#> 89 1.251706e-03 1.473754e-04 1.000000e+00 6785.393 1.8848315
#> 90 5.631534e-03 1.490313e-04 1.000000e+00 6710.000 1.8638889
#> 91 8.089134e-03 1.506872e-04 1.000000e+00 6636.264 1.8434066
#> 92 1.257268e-02 1.523431e-04 9.999676e-01 6564.130 1.8233696
#> 93 8.610740e-03 1.539990e-04 1.000000e+00 6493.548 1.8037634
#> 94 3.262307e-04 1.556549e-04 1.000000e+00 6424.468 1.7845745
#> 95 2.574944e-03 1.573108e-04 1.000000e+00 6356.842 1.7657895
#> 96 1.266262e-03 1.589667e-04 1.000000e+00 6290.625 1.7473958
#> 97 4.156000e-03 1.606226e-04 1.000000e+00 6225.773 1.7293814
#> 98 6.300667e-04 1.622785e-04 1.000000e+00 6162.245 1.7117347
#> 99 8.629278e-03 1.639344e-04 1.000000e+00 6100.000 1.6944444
#> 100 1.639699e-03 1.655903e-04 1.000000e+00 6039.000 1.6775000
#> 101 1.812579e-03 1.672462e-04 1.000000e+00 5979.208 1.6608911
#> 102 7.433398e-04 1.689021e-04 1.000000e+00 5920.588 1.6446078
#> 103 5.697204e-04 1.705580e-04 1.000000e+00 5863.107 1.6286408
#> 104 3.377574e-04 1.722139e-04 1.000000e+00 5806.731 1.6129808
#> 105 3.882357e-03 1.738698e-04 1.000000e+00 5751.429 1.5976190
#> 106 1.882659e-03 1.755257e-04 1.000000e+00 5697.170 1.5825472
#> 107 4.349592e-03 1.771817e-04 1.000000e+00 5643.925 1.5677570
#> 108 3.198290e-03 1.788376e-04 1.000000e+00 5591.667 1.5532407
#> 109 1.813122e-02 1.804935e-04 8.479223e-01 5540.367 1.5389908
#> 110 2.565606e-04 1.821494e-04 1.000000e+00 5490.000 1.5250000
#> 111 1.517410e-02 1.838053e-04 9.909471e-01 5440.541 1.5112613
#> 112 2.296331e-04 1.854612e-04 1.000000e+00 5391.964 1.4977679
#> 113 9.501336e-03 1.871171e-04 1.000000e+00 5344.248 1.4845133
#> 114 3.326424e-03 1.887730e-04 1.000000e+00 5297.368 1.4714912
#> 115 1.358901e-03 1.904289e-04 1.000000e+00 5251.304 1.4586957
#> 116 2.389897e-03 1.920848e-04 1.000000e+00 5206.034 1.4461207
#> 117 2.219681e-03 1.937407e-04 1.000000e+00 5161.538 1.4337607
#> 118 3.238770e-04 1.953966e-04 1.000000e+00 5117.797 1.4216102
#> 119 1.675181e-04 1.970525e-04 1.000000e+00 5074.790 1.4096639
#> 120 9.513401e-04 1.987084e-04 1.000000e+00 5032.500 1.3979167
#> 121 1.095249e-04 2.003643e-04 1.000000e+00 4990.909 1.3863636
#> 122 3.713120e-03 2.020202e-04 1.000000e+00 4950.000 1.3750000
#> 123 9.314812e-03 2.036761e-04 1.000000e+00 4909.756 1.3638211
#> 124 8.898630e-04 2.053320e-04 1.000000e+00 4870.161 1.3528226
#> 125 2.397975e-03 2.069879e-04 1.000000e+00 4831.200 1.3420000
#> 126 1.726025e-03 2.086438e-04 1.000000e+00 4792.857 1.3313492
#> 127 7.449048e-03 2.102997e-04 1.000000e+00 4755.118 1.3208661
#> 128 7.070109e-04 2.119556e-04 1.000000e+00 4717.969 1.3105469
#> 129 4.371644e-03 2.136115e-04 1.000000e+00 4681.395 1.3003876
#> 130 1.416254e-03 2.152674e-04 1.000000e+00 4645.385 1.2903846
#> 131 1.026119e-03 2.169233e-04 1.000000e+00 4609.924 1.2805344
#> 132 1.852427e-03 2.185792e-04 1.000000e+00 4575.000 1.2708333
#> 133 1.475229e-05 2.202351e-04 1.000000e+00 4540.602 1.2612782
#> 134 2.068885e-03 2.218910e-04 1.000000e+00 4506.716 1.2518657
#> 135 1.452654e-03 2.235469e-04 1.000000e+00 4473.333 1.2425926
#> 136 1.598897e-03 2.252028e-04 1.000000e+00 4440.441 1.2334559
#> 137 4.554440e-04 2.268588e-04 1.000000e+00 4408.029 1.2244526
#> 138 2.308606e-04 2.285147e-04 1.000000e+00 4376.087 1.2155797
#> 139 2.772401e-03 2.301706e-04 1.000000e+00 4344.604 1.2068345
#> 140 1.977592e-04 2.318265e-04 1.000000e+00 4313.571 1.1982143
#> 141 3.988316e-03 2.334824e-04 1.000000e+00 4282.979 1.1897163
#> 142 9.414138e-04 2.351383e-04 1.000000e+00 4252.817 1.1813380
#> 143 3.871836e-03 2.367942e-04 1.000000e+00 4223.077 1.1730769
#> 144 2.219722e-03 2.384501e-04 1.000000e+00 4193.750 1.1649306
#> 145 2.456836e-04 2.401060e-04 1.000000e+00 4164.828 1.1568966
#> 146 1.663350e-04 2.417619e-04 1.000000e+00 4136.301 1.1489726
#> 147 2.058559e-04 2.434178e-04 1.000000e+00 4108.163 1.1411565
#> 148 3.647968e-04 2.450737e-04 1.000000e+00 4080.405 1.1334459
#> 149 5.678235e-04 2.467296e-04 1.000000e+00 4053.020 1.1258389
#> 150 9.799097e-05 2.483855e-04 1.000000e+00 4026.000 1.1183333
#> 151 4.077124e-06 2.500414e-04 1.000000e+00 3999.338 1.1109272
#> 152 6.882554e-04 2.516973e-04 1.000000e+00 3973.026 1.1036184
#> 153 6.678952e-04 2.533532e-04 1.000000e+00 3947.059 1.0964052
#> 154 1.525997e-03 2.550091e-04 1.000000e+00 3921.429 1.0892857
#> 155 4.310646e-04 2.566650e-04 1.000000e+00 3896.129 1.0822581
#> 156 6.285787e-04 2.583209e-04 1.000000e+00 3871.154 1.0753205
#> 157 1.104507e-03 2.599768e-04 1.000000e+00 3846.497 1.0684713
#> 158 3.058885e-03 2.616327e-04 1.000000e+00 3822.152 1.0617089
#> 159 5.886480e-04 2.632886e-04 1.000000e+00 3798.113 1.0550314
#> 160 2.725481e-03 2.649445e-04 1.000000e+00 3774.375 1.0484375
#> 161 3.278611e-04 2.666004e-04 1.000000e+00 3750.932 1.0419255
#> 162 9.983286e-04 2.682563e-04 1.000000e+00 3727.778 1.0354938
#> 163 8.076665e-04 2.699122e-04 1.000000e+00 3704.908 1.0291411
#> 164 4.992675e-03 2.715681e-04 1.000000e+00 3682.317 1.0228659
#> 165 6.078002e-04 2.732240e-04 1.000000e+00 3660.000 1.0166667
#> 166 1.911966e-03 2.748799e-04 1.000000e+00 3637.952 1.0105422
#> 167 4.835897e-04 2.765359e-04 1.000000e+00 3616.168 1.0044910
#> 168 2.195964e-04 2.781918e-04 1.000000e+00 3594.643 0.9985119
#> 169 4.952076e-04 2.798477e-04 1.000000e+00 3573.373 0.9926036
#> 170 1.833503e-03 2.815036e-04 1.000000e+00 3552.353 0.9867647
#> 171 5.796572e-04 2.831595e-04 1.000000e+00 3531.579 0.9809942
#> 172 1.493758e-03 2.848154e-04 1.000000e+00 3511.047 0.9752907
#> 173 5.487519e-04 2.864713e-04 1.000000e+00 3490.751 0.9696532
#> 174 5.867682e-04 2.881272e-04 1.000000e+00 3470.690 0.9640805
#> 175 2.485870e-04 2.897831e-04 1.000000e+00 3450.857 0.9585714
#> 176 4.003956e-04 2.914390e-04 1.000000e+00 3431.250 0.9531250
#> 177 1.389183e-03 2.930949e-04 1.000000e+00 3411.864 0.9477401
#> 178 5.272835e-03 2.947508e-04 1.000000e+00 3392.697 0.9424157
#> 179 8.422952e-04 2.964067e-04 1.000000e+00 3373.743 0.9371508
#> 180 1.012959e-03 2.980626e-04 1.000000e+00 3355.000 0.9319444
#> 181 2.365742e-03 2.997185e-04 1.000000e+00 3336.464 0.9267956
#> 182 1.434647e-03 3.013744e-04 1.000000e+00 3318.132 0.9217033
#> 183 1.632008e-03 3.030303e-04 1.000000e+00 3300.000 0.9166667
#> 184 7.287467e-03 3.046862e-04 1.000000e+00 3282.065 0.9116848
#> 185 1.395720e-04 3.063421e-04 1.000000e+00 3264.324 0.9067568
#> 186 2.166454e-03 3.079980e-04 1.000000e+00 3246.774 0.9018817
#> 187 2.647951e-04 3.096539e-04 1.000000e+00 3229.412 0.8970588
#> 188 2.779003e-03 3.113098e-04 1.000000e+00 3212.234 0.8922872
#> 189 1.211152e-03 3.129657e-04 1.000000e+00 3195.238 0.8875661
#> 190 4.166590e-03 3.146216e-04 1.000000e+00 3178.421 0.8828947
#> 191 1.951505e-04 3.162775e-04 1.000000e+00 3161.780 0.8782723
#> 192 1.493818e-03 3.179334e-04 1.000000e+00 3145.312 0.8736979
#> 193 6.340482e-04 3.195893e-04 1.000000e+00 3129.016 0.8691710
#> 194 7.807273e-04 3.212452e-04 1.000000e+00 3112.887 0.8646907
#> 195 1.851177e-06 3.229011e-04 9.999999e-01 3096.923 0.8602564
#> 196 5.429108e-04 3.245570e-04 1.000000e+00 3081.122 0.8558673
#> 197 7.349314e-04 3.262129e-04 1.000000e+00 3065.482 0.8515228
#> 198 3.875177e-03 3.278689e-04 1.000000e+00 3050.000 0.8472222
#> 199 2.250413e-04 3.295248e-04 1.000000e+00 3034.673 0.8429648
#> 200 5.878637e-04 3.311807e-04 1.000000e+00 3019.500 0.8387500
#> 201 4.898652e-05 3.328366e-04 1.000000e+00 3004.478 0.8345771
#> 202 7.695928e-04 3.344925e-04 1.000000e+00 2989.604 0.8304455
#> 203 2.872049e-03 3.361484e-04 1.000000e+00 2974.877 0.8263547
#> 204 4.240461e-03 3.378043e-04 1.000000e+00 2960.294 0.8223039
#> 205 1.007379e-04 3.394602e-04 1.000000e+00 2945.854 0.8182927
#> 206 2.668586e-04 3.411161e-04 1.000000e+00 2931.553 0.8143204
#> 207 5.748827e-04 3.427720e-04 1.000000e+00 2917.391 0.8103865
#> 208 1.366048e-03 3.444279e-04 1.000000e+00 2903.365 0.8064904
#> 209 2.744939e-04 3.460838e-04 1.000000e+00 2889.474 0.8026316
#> 210 2.171558e-03 3.477397e-04 1.000000e+00 2875.714 0.7988095
#> 211 2.679224e-04 3.493956e-04 1.000000e+00 2862.085 0.7950237
#> 212 1.983846e-03 3.510515e-04 1.000000e+00 2848.585 0.7912736
#> 213 3.497188e-03 3.527074e-04 1.000000e+00 2835.211 0.7875587
#> 214 5.625435e-05 3.543633e-04 1.000000e+00 2821.963 0.7838785
#> 215 8.259057e-04 3.560192e-04 1.000000e+00 2808.837 0.7802326
#> 216 5.787932e-05 3.576751e-04 1.000000e+00 2795.833 0.7766204
#> 217 9.150680e-05 3.593310e-04 1.000000e+00 2782.949 0.7730415
#> 218 7.332990e-04 3.609869e-04 1.000000e+00 2770.183 0.7694954
#> 219 2.795767e-04 3.626428e-04 1.000000e+00 2757.534 0.7659817
#> 220 2.525007e-03 3.642987e-04 1.000000e+00 2745.000 0.7625000
#> 221 1.366402e-03 3.659546e-04 1.000000e+00 2732.579 0.7590498
#> 222 3.442786e-03 3.676105e-04 1.000000e+00 2720.270 0.7556306
#> 223 2.895661e-03 3.692664e-04 1.000000e+00 2708.072 0.7522422
#> 224 2.593277e-03 3.709223e-04 1.000000e+00 2695.982 0.7488839
#> 225 1.603386e-03 3.725782e-04 1.000000e+00 2684.000 0.7455556
#> 226 3.346638e-03 3.742341e-04 1.000000e+00 2672.124 0.7422566
#> 227 1.211976e-03 3.758900e-04 1.000000e+00 2660.352 0.7389868
#> 228 4.541612e-05 3.775460e-04 1.000000e+00 2648.684 0.7357456
#> 229 1.084156e-03 3.792019e-04 1.000000e+00 2637.118 0.7325328
#> 230 6.641652e-04 3.808578e-04 1.000000e+00 2625.652 0.7293478
#> 231 7.188121e-04 3.825137e-04 1.000000e+00 2614.286 0.7261905
#> 232 6.688427e-04 3.841696e-04 1.000000e+00 2603.017 0.7230603
#> 233 1.070650e-03 3.858255e-04 1.000000e+00 2591.845 0.7199571
#> 234 5.330767e-04 3.874814e-04 1.000000e+00 2580.769 0.7168803
#> 235 5.325480e-05 3.891373e-04 1.000000e+00 2569.787 0.7138298
#> 236 2.001704e-03 3.907932e-04 1.000000e+00 2558.898 0.7108051
#> 237 3.302959e-04 3.924491e-04 1.000000e+00 2548.101 0.7078059
#> 238 5.403876e-03 3.941050e-04 1.000000e+00 2537.395 0.7048319
#> 239 9.324620e-04 3.957609e-04 1.000000e+00 2526.778 0.7018828
#> 240 3.116440e-04 3.974168e-04 1.000000e+00 2516.250 0.6989583
#> 241 3.277806e-03 3.990727e-04 1.000000e+00 2505.809 0.6960581
#> 242 3.831890e-03 4.007286e-04 1.000000e+00 2495.455 0.6931818
#> 243 4.135963e-03 4.023845e-04 1.000000e+00 2485.185 0.6903292
#> 244 4.639536e-03 4.040404e-04 1.000000e+00 2475.000 0.6875000
#> 245 2.439850e-03 4.056963e-04 1.000000e+00 2464.898 0.6846939
#> 246 1.103006e-03 4.073522e-04 1.000000e+00 2454.878 0.6819106
#> 247 1.060414e-03 4.090081e-04 1.000000e+00 2444.939 0.6791498
#> 248 7.062677e-04 4.106640e-04 1.000000e+00 2435.081 0.6764113
#> 249 2.710680e-03 4.123199e-04 1.000000e+00 2425.301 0.6736948
#> 250 1.069309e-03 4.139758e-04 1.000000e+00 2415.600 0.6710000
#> 251 8.629711e-04 4.156317e-04 1.000000e+00 2405.976 0.6683267
#> 252 7.290835e-04 4.172876e-04 1.000000e+00 2396.429 0.6656746
#> 253 1.916265e-04 4.189435e-04 1.000000e+00 2386.957 0.6630435
#> 254 3.974219e-04 4.205994e-04 1.000000e+00 2377.559 0.6604331
#> 255 2.292776e-03 4.222553e-04 1.000000e+00 2368.235 0.6578431
#> 256 5.637606e-03 4.239112e-04 1.000000e+00 2358.984 0.6552734
#> 257 2.928097e-03 4.255671e-04 1.000000e+00 2349.805 0.6527237
#> 258 2.604923e-03 4.272231e-04 1.000000e+00 2340.698 0.6501938
#> 259 6.112654e-04 4.288790e-04 1.000000e+00 2331.660 0.6476834
#> 260 1.310107e-03 4.305349e-04 1.000000e+00 2322.692 0.6451923
#> 261 4.424730e-04 4.321908e-04 1.000000e+00 2313.793 0.6427203
#> 262 1.450611e-03 4.338467e-04 1.000000e+00 2304.962 0.6402672
#> 263 2.021213e-03 4.355026e-04 1.000000e+00 2296.198 0.6378327
#> 264 7.816507e-04 4.371585e-04 1.000000e+00 2287.500 0.6354167
#> 265 5.064661e-04 4.388144e-04 1.000000e+00 2278.868 0.6330189
#> 266 9.598068e-05 4.404703e-04 1.000000e+00 2270.301 0.6306391
#> 267 1.051828e-04 4.421262e-04 1.000000e+00 2261.798 0.6282772
#> 268 6.808676e-04 4.437821e-04 1.000000e+00 2253.358 0.6259328
#> 269 9.448038e-04 4.454380e-04 1.000000e+00 2244.981 0.6236059
#> 270 3.978137e-04 4.470939e-04 1.000000e+00 2236.667 0.6212963
#> 271 8.826286e-04 4.487498e-04 1.000000e+00 2228.413 0.6190037
#> 272 1.569424e-03 4.504057e-04 1.000000e+00 2220.221 0.6167279
#> 273 9.149094e-04 4.520616e-04 1.000000e+00 2212.088 0.6144689
#> 274 9.196100e-04 4.537175e-04 1.000000e+00 2204.015 0.6122263
#> 275 9.454523e-04 4.553734e-04 1.000000e+00 2196.000 0.6100000
#> 276 1.898571e-03 4.570293e-04 1.000000e+00 2188.043 0.6077899
#> 277 3.045595e-03 4.586852e-04 1.000000e+00 2180.144 0.6055957
#> 278 1.565367e-03 4.603411e-04 1.000000e+00 2172.302 0.6034173
#> 279 6.035780e-04 4.619970e-04 1.000000e+00 2164.516 0.6012545
#> 280 1.067753e-03 4.636529e-04 1.000000e+00 2156.786 0.5991071
#> 281 1.235253e-03 4.653088e-04 1.000000e+00 2149.110 0.5969751
#> 282 9.421942e-04 4.669647e-04 1.000000e+00 2141.489 0.5948582
#> 283 3.584927e-04 4.686206e-04 1.000000e+00 2133.922 0.5927562
#> 284 1.966893e-03 4.702765e-04 1.000000e+00 2126.408 0.5906690
#> 285 4.384283e-05 4.719324e-04 1.000000e+00 2118.947 0.5885965
#> 286 8.818984e-04 4.735883e-04 1.000000e+00 2111.538 0.5865385
#> 287 2.140392e-03 4.752442e-04 1.000000e+00 2104.181 0.5844948
#> 288 5.863284e-04 4.769001e-04 1.000000e+00 2096.875 0.5824653
#> 289 8.423088e-04 4.785561e-04 1.000000e+00 2089.619 0.5804498
#> 290 1.209121e-03 4.802120e-04 1.000000e+00 2082.414 0.5784483
#> 291 2.022992e-03 4.818679e-04 1.000000e+00 2075.258 0.5764605
#> 292 2.037534e-03 4.835238e-04 1.000000e+00 2068.151 0.5744863
#> 293 1.483796e-04 4.851797e-04 1.000000e+00 2061.092 0.5725256
#> 294 2.140369e-03 4.868356e-04 1.000000e+00 2054.082 0.5705782
#> 295 7.303919e-04 4.884915e-04 1.000000e+00 2047.119 0.5686441
#> 296 7.028396e-05 4.901474e-04 1.000000e+00 2040.203 0.5667230
#> 297 1.068292e-03 4.918033e-04 1.000000e+00 2033.333 0.5648148
#> 298 6.928554e-04 4.934592e-04 1.000000e+00 2026.510 0.5629195
#> 299 1.193940e-03 4.951151e-04 1.000000e+00 2019.732 0.5610368
#> 300 8.310246e-04 4.967710e-04 1.000000e+00 2013.000 0.5591667
#> 301 2.347139e-03 4.984269e-04 1.000000e+00 2006.312 0.5573090
#> 302 6.081673e-04 5.000828e-04 1.000000e+00 1999.669 0.5554636
#> 303 8.162872e-04 5.017387e-04 1.000000e+00 1993.069 0.5536304
#> 304 6.569431e-04 5.033946e-04 1.000000e+00 1986.513 0.5518092
#> 305 2.193440e-04 5.050505e-04 1.000000e+00 1980.000 0.5500000
#> 306 1.832403e-03 5.067064e-04 1.000000e+00 1973.529 0.5482026
#> 307 5.930825e-04 5.083623e-04 1.000000e+00 1967.101 0.5464169
#> 308 2.253876e-04 5.100182e-04 1.000000e+00 1960.714 0.5446429
#> 309 8.712588e-04 5.116741e-04 1.000000e+00 1954.369 0.5428803
#> 310 3.708787e-04 5.133300e-04 1.000000e+00 1948.065 0.5411290
#> 311 6.551585e-05 5.149859e-04 1.000000e+00 1941.801 0.5393891
#> 312 1.108335e-03 5.166418e-04 1.000000e+00 1935.577 0.5376603
#> 313 5.921024e-05 5.182977e-04 1.000000e+00 1929.393 0.5359425
#> 314 3.034422e-03 5.199536e-04 1.000000e+00 1923.248 0.5342357
#> 315 3.806244e-03 5.216095e-04 1.000000e+00 1917.143 0.5325397
#> 316 4.730746e-03 5.232654e-04 1.000000e+00 1911.076 0.5308544
#> 317 7.382288e-04 5.249213e-04 1.000000e+00 1905.047 0.5291798
#> 318 3.381538e-04 5.265772e-04 1.000000e+00 1899.057 0.5275157
#> 319 1.413915e-03 5.282332e-04 1.000000e+00 1893.103 0.5258621
#> 320 4.793925e-03 5.298891e-04 1.000000e+00 1887.188 0.5242187
#> 321 2.487293e-03 5.315450e-04 1.000000e+00 1881.308 0.5225857
#> 322 1.594162e-03 5.332009e-04 1.000000e+00 1875.466 0.5209627
#> 323 4.009491e-03 5.348568e-04 1.000000e+00 1869.659 0.5193498
#> 324 1.105000e-04 5.365127e-04 1.000000e+00 1863.889 0.5177469
#> 325 3.744444e-04 5.381686e-04 1.000000e+00 1858.154 0.5161538
#> 326 1.099463e-04 5.398245e-04 1.000000e+00 1852.454 0.5145706
#> 327 7.163958e-04 5.414804e-04 1.000000e+00 1846.789 0.5129969
#> 328 1.185648e-03 5.431363e-04 1.000000e+00 1841.159 0.5114329
#> 329 3.446074e-03 5.447922e-04 1.000000e+00 1835.562 0.5098784
#> 330 1.419163e-03 5.464481e-04 1.000000e+00 1830.000 0.5083333
#> 331 1.405836e-03 5.481040e-04 1.000000e+00 1824.471 0.5067976
#> 332 2.068373e-04 5.497599e-04 1.000000e+00 1818.976 0.5052711
#> 333 1.672394e-03 5.514158e-04 1.000000e+00 1813.514 0.5037538
#> 334 6.217931e-03 5.530717e-04 1.000000e+00 1808.084 0.5022455
#> 335 2.756293e-03 5.547276e-04 1.000000e+00 1802.687 0.5007463
#> 336 2.756293e-03 5.563835e-04 1.000000e+00 1797.321 0.4992560
#> status_harmonic
#> 1 Non-Harmonic
#> 2 Non-Harmonic
#> 3 Non-Harmonic
#> 4 Non-Harmonic
#> 5 Non-Harmonic
#> 6 Non-Harmonic
#> 7 Harmonic
#> 8 Non-Harmonic
#> 9 Non-Harmonic
#> 10 Non-Harmonic
#> 11 Non-Harmonic
#> 12 Non-Harmonic
#> 13 Non-Harmonic
#> 14 Harmonic
#> 15 Non-Harmonic
#> 16 Non-Harmonic
#> 17 Non-Harmonic
#> 18 Non-Harmonic
#> 19 Non-Harmonic
#> 20 Non-Harmonic
#> 21 Harmonic
#> 22 Non-Harmonic
#> 23 Non-Harmonic
#> 24 Non-Harmonic
#> 25 Non-Harmonic
#> 26 Non-Harmonic
#> 27 Non-Harmonic
#> 28 Harmonic
#> 29 Non-Harmonic
#> 30 Non-Harmonic
#> 31 Non-Harmonic
#> 32 Non-Harmonic
#> 33 Non-Harmonic
#> 34 Non-Harmonic
#> 35 Harmonic
#> 36 Non-Harmonic
#> 37 Non-Harmonic
#> 38 Non-Harmonic
#> 39 Non-Harmonic
#> 40 Non-Harmonic
#> 41 Non-Harmonic
#> 42 Harmonic
#> 43 Non-Harmonic
#> 44 Non-Harmonic
#> 45 Non-Harmonic
#> 46 Non-Harmonic
#> 47 Non-Harmonic
#> 48 Non-Harmonic
#> 49 Harmonic
#> 50 Non-Harmonic
#> 51 Non-Harmonic
#> 52 Non-Harmonic
#> 53 Non-Harmonic
#> 54 Non-Harmonic
#> 55 Non-Harmonic
#> 56 Harmonic
#> 57 Non-Harmonic
#> 58 Non-Harmonic
#> 59 Non-Harmonic
#> 60 Non-Harmonic
#> 61 Non-Harmonic
#> 62 Non-Harmonic
#> 63 Harmonic
#> 64 Non-Harmonic
#> 65 Non-Harmonic
#> 66 Non-Harmonic
#> 67 Non-Harmonic
#> 68 Non-Harmonic
#> 69 Non-Harmonic
#> 70 Harmonic
#> 71 Non-Harmonic
#> 72 Non-Harmonic
#> 73 Non-Harmonic
#> 74 Non-Harmonic
#> 75 Non-Harmonic
#> 76 Non-Harmonic
#> 77 Harmonic
#> 78 Non-Harmonic
#> 79 Non-Harmonic
#> 80 Non-Harmonic
#> 81 Non-Harmonic
#> 82 Non-Harmonic
#> 83 Non-Harmonic
#> 84 Harmonic
#> 85 Non-Harmonic
#> 86 Non-Harmonic
#> 87 Non-Harmonic
#> 88 Non-Harmonic
#> 89 Non-Harmonic
#> 90 Non-Harmonic
#> 91 Non-Harmonic
#> 92 Non-Harmonic
#> 93 Non-Harmonic
#> 94 Non-Harmonic
#> 95 Non-Harmonic
#> 96 Non-Harmonic
#> 97 Non-Harmonic
#> 98 Non-Harmonic
#> 99 Non-Harmonic
#> 100 Non-Harmonic
#> 101 Non-Harmonic
#> 102 Non-Harmonic
#> 103 Non-Harmonic
#> 104 Non-Harmonic
#> 105 Non-Harmonic
#> 106 Non-Harmonic
#> 107 Non-Harmonic
#> 108 Non-Harmonic
#> 109 Non-Harmonic
#> 110 Non-Harmonic
#> 111 Non-Harmonic
#> 112 Non-Harmonic
#> 113 Non-Harmonic
#> 114 Non-Harmonic
#> 115 Non-Harmonic
#> 116 Non-Harmonic
#> 117 Non-Harmonic
#> 118 Non-Harmonic
#> 119 Non-Harmonic
#> 120 Non-Harmonic
#> 121 Non-Harmonic
#> 122 Non-Harmonic
#> 123 Non-Harmonic
#> 124 Non-Harmonic
#> 125 Non-Harmonic
#> 126 Non-Harmonic
#> 127 Non-Harmonic
#> 128 Non-Harmonic
#> 129 Non-Harmonic
#> 130 Non-Harmonic
#> 131 Non-Harmonic
#> 132 Non-Harmonic
#> 133 Non-Harmonic
#> 134 Non-Harmonic
#> 135 Non-Harmonic
#> 136 Non-Harmonic
#> 137 Non-Harmonic
#> 138 Non-Harmonic
#> 139 Non-Harmonic
#> 140 Non-Harmonic
#> 141 Non-Harmonic
#> 142 Non-Harmonic
#> 143 Non-Harmonic
#> 144 Non-Harmonic
#> 145 Non-Harmonic
#> 146 Non-Harmonic
#> 147 Non-Harmonic
#> 148 Non-Harmonic
#> 149 Non-Harmonic
#> 150 Non-Harmonic
#> 151 Non-Harmonic
#> 152 Non-Harmonic
#> 153 Non-Harmonic
#> 154 Non-Harmonic
#> 155 Non-Harmonic
#> 156 Non-Harmonic
#> 157 Non-Harmonic
#> 158 Non-Harmonic
#> 159 Non-Harmonic
#> 160 Non-Harmonic
#> 161 Non-Harmonic
#> 162 Non-Harmonic
#> 163 Non-Harmonic
#> 164 Non-Harmonic
#> 165 Non-Harmonic
#> 166 Non-Harmonic
#> 167 Non-Harmonic
#> 168 Non-Harmonic
#> 169 Non-Harmonic
#> 170 Non-Harmonic
#> 171 Non-Harmonic
#> 172 Non-Harmonic
#> 173 Non-Harmonic
#> 174 Non-Harmonic
#> 175 Non-Harmonic
#> 176 Non-Harmonic
#> 177 Non-Harmonic
#> 178 Non-Harmonic
#> 179 Non-Harmonic
#> 180 Non-Harmonic
#> 181 Non-Harmonic
#> 182 Non-Harmonic
#> 183 Non-Harmonic
#> 184 Non-Harmonic
#> 185 Non-Harmonic
#> 186 Non-Harmonic
#> 187 Non-Harmonic
#> 188 Non-Harmonic
#> 189 Non-Harmonic
#> 190 Non-Harmonic
#> 191 Non-Harmonic
#> 192 Non-Harmonic
#> 193 Non-Harmonic
#> 194 Non-Harmonic
#> 195 Non-Harmonic
#> 196 Non-Harmonic
#> 197 Non-Harmonic
#> 198 Non-Harmonic
#> 199 Non-Harmonic
#> 200 Non-Harmonic
#> 201 Non-Harmonic
#> 202 Non-Harmonic
#> 203 Non-Harmonic
#> 204 Non-Harmonic
#> 205 Non-Harmonic
#> 206 Non-Harmonic
#> 207 Non-Harmonic
#> 208 Non-Harmonic
#> 209 Non-Harmonic
#> 210 Non-Harmonic
#> 211 Non-Harmonic
#> 212 Non-Harmonic
#> 213 Non-Harmonic
#> 214 Non-Harmonic
#> 215 Non-Harmonic
#> 216 Non-Harmonic
#> 217 Non-Harmonic
#> 218 Non-Harmonic
#> 219 Non-Harmonic
#> 220 Non-Harmonic
#> 221 Non-Harmonic
#> 222 Non-Harmonic
#> 223 Non-Harmonic
#> 224 Non-Harmonic
#> 225 Non-Harmonic
#> 226 Non-Harmonic
#> 227 Non-Harmonic
#> 228 Non-Harmonic
#> 229 Non-Harmonic
#> 230 Non-Harmonic
#> 231 Non-Harmonic
#> 232 Non-Harmonic
#> 233 Non-Harmonic
#> 234 Non-Harmonic
#> 235 Non-Harmonic
#> 236 Non-Harmonic
#> 237 Non-Harmonic
#> 238 Non-Harmonic
#> 239 Non-Harmonic
#> 240 Non-Harmonic
#> 241 Non-Harmonic
#> 242 Non-Harmonic
#> 243 Non-Harmonic
#> 244 Non-Harmonic
#> 245 Non-Harmonic
#> 246 Non-Harmonic
#> 247 Non-Harmonic
#> 248 Non-Harmonic
#> 249 Non-Harmonic
#> 250 Non-Harmonic
#> 251 Non-Harmonic
#> 252 Non-Harmonic
#> 253 Non-Harmonic
#> 254 Non-Harmonic
#> 255 Non-Harmonic
#> 256 Non-Harmonic
#> 257 Non-Harmonic
#> 258 Non-Harmonic
#> 259 Non-Harmonic
#> 260 Non-Harmonic
#> 261 Non-Harmonic
#> 262 Non-Harmonic
#> 263 Non-Harmonic
#> 264 Non-Harmonic
#> 265 Non-Harmonic
#> 266 Non-Harmonic
#> 267 Non-Harmonic
#> 268 Non-Harmonic
#> 269 Non-Harmonic
#> 270 Non-Harmonic
#> 271 Non-Harmonic
#> 272 Non-Harmonic
#> 273 Non-Harmonic
#> 274 Non-Harmonic
#> 275 Non-Harmonic
#> 276 Non-Harmonic
#> 277 Non-Harmonic
#> 278 Non-Harmonic
#> 279 Non-Harmonic
#> 280 Non-Harmonic
#> 281 Non-Harmonic
#> 282 Non-Harmonic
#> 283 Non-Harmonic
#> 284 Non-Harmonic
#> 285 Non-Harmonic
#> 286 Non-Harmonic
#> 287 Non-Harmonic
#> 288 Non-Harmonic
#> 289 Non-Harmonic
#> 290 Non-Harmonic
#> 291 Non-Harmonic
#> 292 Non-Harmonic
#> 293 Non-Harmonic
#> 294 Non-Harmonic
#> 295 Non-Harmonic
#> 296 Non-Harmonic
#> 297 Non-Harmonic
#> 298 Non-Harmonic
#> 299 Non-Harmonic
#> 300 Non-Harmonic
#> 301 Non-Harmonic
#> 302 Non-Harmonic
#> 303 Non-Harmonic
#> 304 Non-Harmonic
#> 305 Non-Harmonic
#> 306 Non-Harmonic
#> 307 Non-Harmonic
#> 308 Non-Harmonic
#> 309 Non-Harmonic
#> 310 Non-Harmonic
#> 311 Non-Harmonic
#> 312 Non-Harmonic
#> 313 Non-Harmonic
#> 314 Non-Harmonic
#> 315 Non-Harmonic
#> 316 Non-Harmonic
#> 317 Non-Harmonic
#> 318 Non-Harmonic
#> 319 Non-Harmonic
#> 320 Non-Harmonic
#> 321 Non-Harmonic
#> 322 Non-Harmonic
#> 323 Non-Harmonic
#> 324 Non-Harmonic
#> 325 Non-Harmonic
#> 326 Non-Harmonic
#> 327 Non-Harmonic
#> 328 Non-Harmonic
#> 329 Non-Harmonic
#> 330 Non-Harmonic
#> 331 Non-Harmonic
#> 332 Non-Harmonic
#> 333 Non-Harmonic
#> 334 Non-Harmonic
#> 335 Non-Harmonic
#> 336 Non-Harmonic
#>
#> $sig.level.power
#> [1] 0.03431736
#>
#> $alpha
#> [1] 0.01
#>