如何去除FFT图中连接正负频率的多余水平线？

我在展示观测数据趋势及对应FFT图时，FFT图里总是出现一条不需要的水平线。已知这是因为fftfreq生成的频率包含正负值，绘图时会连接最后一个负频率与第一个正频率，但我需要保留正负频率的完整展示，请问怎么去掉这条连接线？

最小可复现代码 #

import numpy as np
from scipy.fft import fft, fftfreq
import matplotlib.pyplot as plt

observations = np.array([ 3.78998207e-01,  3.05199629e-01,  2.29614343e-01,  1.86568613e-01,
                         1.83449462e-01,  1.77892746e-01,  1.66237352e-01,  1.81950778e-01,
                         9.88351226e-02,  1.29674430e-01,  7.08703360e-02,  3.64963487e-02,
                         2.75641060e-02,  6.21573753e-02,  8.51043646e-02,  5.32184940e-02,
                         6.47005530e-02, -6.41628893e-02, -1.86618020e-01, -4.08624200e-02,
                        -2.71649960e-02, -8.22041576e-03,  9.13242105e-03,  1.67080717e-01,
                        -1.37465317e-01,  2.74977101e-04,  4.47602122e-02,  8.27649668e-02,
                        -5.60661808e-02, -2.26248880e-01, -1.54768403e-01, -4.46428484e-02,
                        4.57611677e-02,  9.83215698e-02,  9.22357256e-02, -1.23436114e-01,
                      -2.76981909e-01, -1.98824586e-01, -2.33452893e-01, -2.57550630e-01,
                      -9.13919527e-02,  2.64029442e-02, -5.44394568e-02,  4.02010984e-01,
                        3.27256645e-01,  2.14259077e-01,  5.08021357e-01,  5.55141121e-01,
                        6.11203693e-01,  5.34086779e-01,  2.19652659e-01,  1.71635054e-01,
                        1.30867565e-01,  1.25133212e-01,  1.02010973e-01,  1.16727950e-02,
                        2.84545455e-02, -1.73553706e-02, -1.33998184e-01, -1.36456573e-01,
                      -1.68706794e-01, -1.28378379e-01, -1.43710423e-01, -2.02454545e-01,
                      -4.30164457e-01, -5.19982175e-01, -3.74452537e-01, -3.64076796e-01,
                      -3.20950700e-01, -2.34052515e-01, -1.37158482e-01,  2.80797054e-02,
                        7.04379682e-02,  1.13920696e-01,  1.26391389e-01,  9.31688808e-02,
                        1.46000000e-01,  1.18380338e-01,  5.18909438e-02,  1.11584791e-01,
                        6.43582617e-02, -6.36856386e-02, -9.16134931e-02, -1.02616820e-01,
                      -4.43179890e-01, -1.28223431e+00, -1.86160058e+00, -1.43772912e+00,
                      -1.21047880e+00, -7.21282278e-01, -1.65349241e-01,  4.58791266e-02,
                        2.42897190e-01,  3.26587994e-01,  3.15827382e-01, -5.29090909e-02,
                        8.97887313e-03,  2.61194000e-02, -2.24566234e-01, -9.18572710e-02])

observed_fft = fft(observations)

fs = 100
n = observations.size
fft_fre = fftfreq(n, d=1/fs)
x_time = np.arange(len(observations))

fig, axs = plt.subplots(2)
axs[0].plot(x_time, observations)
axs[1].plot(fft_fre, np.abs(observed_fft))
plt.show()

问题图示 #

两种解决方法 #

方法1：对频率排序后绘图 #

fftfreq默认输出的频率顺序是[0, 1, ..., n/2-1, -n/2, ..., -1]，直接绘图会导致最后一个负频率和第一个正频率被连接。将频率和对应的FFT幅值按频率从小到大排序后再绘制，就能避免跨零的连接线：

# 对频率和FFT幅值按频率排序
sorted_idx = np.argsort(fft_fre)
sorted_freq = fft_fre[sorted_idx]
sorted_fft_abs = np.abs(observed_fft)[sorted_idx]

# 绘制排序后的FFT图
axs[1].plot(sorted_freq, sorted_fft_abs)

方法2：分离正负频率分别绘制 #

将负频率和正频率（包含0）分成两组，分别调用plot绘制，中间自然断开：

# 分离负频率和非负频率的掩码
neg_mask = fft_fre < 0
pos_mask = fft_fre >= 0

# 分别绘制两部分
axs[1].plot(fft_fre[neg_mask], np.abs(observed_fft)[neg_mask])
axs[1].plot(fft_fre[pos_mask], np.abs(observed_fft)[pos_mask])

两种方法都能保留正负频率的完整展示，同时去掉那条多余的水平线。

内容的提问来源于stack exchange，提问作者Amina Umar