从Lomb-Scargle分析的数据中重建信号

Question

我想重建一个我有一些数据的信号，并使用LombScargle来获取其频率分量。

此外，我的数据还如下：

r = np.array([119.75024144, 119.77177673, 119.79671626, 119.81566188,
       119.81291201, 119.71610143, 119.24156708, 117.66932347,
       114.22145178, 109.27266933, 104.57675147, 101.63381325,
       100.42623807, 100.09436745, 100.02798438, 100.02696846,
       100.05422613, 100.12216521, 100.27569606, 100.60962812,
       101.32023289, 102.71102637, 105.01826819, 108.17052642,
       111.67848758, 114.78442424, 116.95337537, 118.19437002,
       118.84307457, 119.19571404, 119.40326818, 119.53101551,
       119.61170874, 119.66610072, 119.68315253, 119.53757829,
       118.83748609, 116.90425868, 113.32095843, 108.72465638,
       104.58292906, 101.93316248, 100.68856962, 100.22523098,
       100.08558767, 100.07194691, 100.11193397, 100.19142891,
       100.33208922, 100.5849306 , 101.04224415, 101.87565882,
       103.33985519, 105.63631456, 108.64972952, 111.86837667,
       114.67115037, 116.69548163, 117.96207449, 118.69589499,
       119.11781077, 119.36770681, 119.51566311, 119.59301667])

z = np.array ([-422.05230434, -408.98182253, -395.78387843, -382.43143962,
       -368.92341485, -355.26851343, -341.47780372, -327.56493425,
       -313.54536462, -299.43740189, -285.26768576, -271.07676026,
       -256.92098157, -242.86416227, -228.95449427, -215.207069  ,
       -201.61590575, -188.17719265, -174.89201262, -161.75452196,
       -148.74812279, -135.85126854, -123.04093538, -110.29151714,
        -97.57502515,  -84.86119278,  -72.1145478 ,  -59.2947726 ,
        -46.36450604,  -33.29821629,  -20.08471733,   -6.72030326,
          6.80047849,   20.48309726,   34.32320864,   48.30267819,
         62.393214  ,   76.56022602,   90.76260159,  104.94787451,
        119.04731699,  132.98616969,  146.71491239,  160.23436159,
        173.58582543,  186.81849059,  199.96724955,  213.05229133,
        226.08870416,  239.09310452,  252.08377421,  265.0769367 ,
        278.08234368,  291.10215472,  304.13509998,  317.18351924,
        330.25976991,  343.38777732,  356.59626164,  369.90725571,
        383.33109354,  396.87227086,  410.5309987 ,  424.2899438])
plt.plot(z,r, label='data');plt.legend()

然后，我在此数据上使用LobmbScargle：

f, a = LombScargle(z, r).autopower()
plt.plot(f, a, label='frequency components');plt.legend()

类似于傅立叶级数，我想用正弦或余弦的总和来重构信号。

我主要对查找a_i和w_i值感兴趣。

我喜欢以下内容，但是我的重建看起来不像我拥有数据的信号。

s = 0
for i in range(f.shape[0]):
    s += a[i]*np.sin(f[i]*z)
plt.plot(z, s, label='reconstructed signal');plt.legend()

在我使用Lomb-Scargle的方式上或在信号重构部分有错误，但是我还没有弄清楚是什么。