python实现L-S谱分析

L-S谱分析是一种非参数估计方法，用于估计信号的功率谱密度。下面是一个简单的Python实现：

import numpy as np
import matplotlib.pyplot as plt

def ls_spectrum(signal, window_size):
    n = len(signal)
    padded_signal = np.zeros(n + 2 * window_size)
    padded_signal[window_size:n+window_size] = signal
    spectrum = np.zeros(n)
    for i in range(n):
        window = np.zeros(n + 2 * window_size)
        window[i:i+2*window_size] = np.hamming(2*window_size)
        padded_signal_windowed = padded_signal * window
        padded_signal_windowed_fft = np.fft.fft(padded_signal_windowed)
        spectrum[i] = np.abs(padded_signal_windowed_fft[window_size])**2
    return spectrum

# Generate a test signal
n = 1000
t = np.linspace(0, 10, n)
signal = np.sin(2 * np.pi * 5 * t) + np.sin(2 * np.pi * 10 * t)

# Compute the L-S spectrum
window_size = 50
spectrum = ls_spectrum(signal, window_size)

# Plot the signal and spectrum
fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(8, 6))
ax1.plot(t, signal)
ax1.set_xlabel('Time (s)')
ax1.set_ylabel('Amplitude')
ax2.plot(np.arange(n), spectrum)
ax2.set_xlabel('Frequency (Hz)')
ax2.set_ylabel('Power')
plt.show()

这个实现使用汉明窗对信号进行加窗，然后计算每个窗口的傅里叶变换，最后取傅里叶变换的幅值平方作为该频率上的功率谱密度。可以看到，我们使用L-S谱分析成功地估计出了信号的频率成分。