### HHT (Hilbert-Huang Transform) Python 实现代码示例 对于希尔伯特-黄变换（HHT），其核心在于经验模态分解（EMD）和随后的希尔伯特谱分析。以下是基于这些原理的一个简单Python实现： #### 安装依赖库 为了执行HHT，通常需要安装`PyEMD`库来完成经验模态分解部分的工作。 ```bash pip install EMD-signal numpy scipy matplotlib ``` #### 导入必要的模块并定义函数 下面展示了如何编写一个简单的程序来进行HHT处理[^1]。 ```python import numpy as np from PyEMD import EMD from scipy.signal import hilbert def hht(data, time=None): """Perform Hilbert Huang Transformation on input signal.""" # Initialize the EMD object and perform decomposition. emd = EMD() imfs = emd.emd(data) # Apply Hilbert transform to each IMF component obtained from EMD. analytic_signal = [] instantaneous_frequency = [] for i in range(len(imfs)): amp_envelope = np.abs(hilbert(imfs[i])) inst_phase = np.unwrap(np.angle(hilbert(imfs[i]))) if time is not None: inst_freq = (np.diff(inst_phase) / (2.0 * np.pi)) / np.mean(np.diff(time)) else: inst_freq = (np.diff(inst_phase) / (2.0 * np.pi)) analytic_signal.append(amp_envelope) instantaneous_frequency.append(inst_freq) return imfs, analytic_signal[:-1], instantaneous_frequency[:-1] if __name__ == "__main__": # Example usage with synthetic data. t = np.linspace(0, 1, 400) s = np.sin(2 * np.pi * 7 * t) + np.sin(2 * np.pi * 2 * t) imfs, amps, freqs = hht(s, t) print("IMFs shape:", [i.shape for i in imfs]) print("Amp envelopes shapes:", [a.shape for a in amps]) print("Instantaneous frequencies shapes:", [f.shape for f in freqs]) ``` 此段代码实现了完整的HHT流程，包括通过EMD获取固有模态函数(IMF)，接着利用希尔伯特变换得到各IMF分量对应的瞬时幅度包络线及瞬时频率[^2]。