如何从Lomb Scargle周期图中提取相位？基于gatspy实现

Absolutely! You can pull phase values for each frequency from your LombScargleFast model—while it’s not as direct as grabbing phases from a discrete Fourier transform (DFT), gatspy provides tools to get this information using the fitted model parameters.

Here’s a step-by-step implementation with your existing code: #

First, after fitting your data, you can use the model_parameters() method of the LombScargleFast class to retrieve the amplitude, phase, and constant offset for any given frequency. This method directly gives you the phase term from the model's cosine-based fit (y(t) = A*cos(2πft + φ) + B, where φ is the phase we want).

import numpy as np
from gatspy.periodic import LombScargleFast
import matplotlib.pyplot as plt

# Replace with your actual t, y data
t = np.linspace(0, 10, 100)
y = 2 * np.cos(2 * np.pi * 0.5 * t + np.pi/4) + np.random.normal(0, 0.1, len(t))

# Your existing periodogram code
model = LombScargleFast().fit(t, y)
periods, power = model.periodogram_auto()
frequencies = 1 / periods

# Extract phase for each frequency
phases = []
for freq in frequencies:
    # Get amplitude, phase, and offset for the current frequency
    amplitude, phase, offset = model.model_parameters(frequency=freq)
    phases.append(phase)

# Visualize both power and phase
fig, (ax_power, ax_phase) = plt.subplots(2, 1, figsize=(10, 8))

ax_power.plot(frequencies, power)
ax_power.set_xlabel("Frequency")
ax_power.set_ylabel("Power")
ax_power.set_title("Lomb-Scargle Periodogram")

ax_phase.plot(frequencies, phases)
ax_phase.set_xlabel("Frequency")
ax_phase.set_ylabel("Phase (radians)")
ax_phase.set_title("Phase vs. Frequency")

plt.tight_layout()
plt.show()

Key Notes: #

• The phase returned is relative to a cosine function (gatspy's Lomb-Scargle implementation uses a cosine basis). If you need to align this with DFT's typical sine-based phase, you can adjust it using φ_dft = φ_lomb + π/2 (since cos(x + φ) = sin(x + φ + π/2)).
• This method works because model_parameters() fits a single-frequency cosine model to your data at the specified frequency, which aligns with what the Lomb-Scargle periodogram optimizes for when calculating power.

内容的提问来源于stack exchange，提问作者Andreas Ioannou