Agent Skills
› synthetic-sciences/openscience
› spectral-analysis
spectral-analysis
GitHub用于物理信号频域分析，支持FFT、功率谱密度( Welch/periodogram)、频谱图和小波变换。适用于检测周期性、准周期或瞬态频率内容，包括滤波和相干性分析。
Trigger Scenarios
查找时间序列数据中的振荡频率
计算湍流、振动或波数据的功率谱
检测瞬态特征（如使用频谱图或小波）
对信号进行低通、带通或陷波滤波
信号间的交叉谱分析和相干性计算
Install
npx skills add synthetic-sciences/openscience --skill spectral-analysis -g -y
SKILL.md
Frontmatter
{
"name": "spectral-analysis",
"tags": [
"FFT",
"Spectral Analysis",
"PSD",
"Wavelets",
"Signal Processing",
"Frequency",
"Physics"
],
"author": "Synthetic Sciences",
"license": "MIT",
"version": "1.0.0",
"category": "physics",
"description": "Frequency-domain analysis — FFT, power spectral density (Welch\/periodogram), spectrograms, wavelet transforms, and coherence. Use for any signal with periodic, quasi-periodic, or transient frequency content in physics data.",
"dependencies": [
"scipy>=1.11.0",
"numpy>=1.24.0",
"matplotlib>=3.7.0"
]
}
Spectral Analysis
Overview
Extract frequency content from physics signals using FFT, power spectral density estimation, spectrograms, and wavelet transforms. Covers stationary and non-stationary signals.
When to Use
- Finding oscillation frequencies in time-series data
- Computing power spectra of turbulence, vibrations, or wave data
- Detecting transient features (spectrograms, wavelets)
- Filtering signals (low-pass, band-pass, notch)
- Cross-spectral analysis and coherence between signals
Core Workflows
1. FFT (Fast Fourier Transform)
import numpy as np
import matplotlib.pyplot as plt
# Signal: sum of two sinusoids + noise
dt = 0.001 # sampling interval [s]
fs = 1 / dt # sampling frequency [Hz]
t = np.arange(0, 1, dt)
signal = 1.5 * np.sin(2*np.pi*50*t) + 0.8 * np.sin(2*np.pi*120*t)
signal += 0.5 * np.random.randn(len(t))
# Compute FFT
N = len(t)
fft_vals = np.fft.rfft(signal)
freqs = np.fft.rfftfreq(N, d=dt)
amplitude = 2.0 / N * np.abs(fft_vals) # single-sided amplitude
phase = np.angle(fft_vals)
fig, axes = plt.subplots(2, 1, figsize=(10, 7))
axes[0].plot(t[:200], signal[:200], 'b-', linewidth=0.8)
axes[0].set_xlabel('Time [s]')
axes[0].set_ylabel('Amplitude')
axes[0].set_title('Time Domain Signal')
axes[0].grid(True, alpha=0.3)
axes[1].plot(freqs, amplitude, 'r-', linewidth=0.8)
axes[1].set_xlabel('Frequency [Hz]')
axes[1].set_ylabel('Amplitude')
axes[1].set_title('FFT Amplitude Spectrum')
axes[1].set_xlim(0, 200)
axes[1].grid(True, alpha=0.3)
plt.tight_layout()
plt.savefig('fft_analysis.png', dpi=150, bbox_inches='tight')
2. Power Spectral Density (Welch Method)
from scipy.signal import welch, periodogram
# Welch PSD (better noise averaging than raw FFT)
freqs_w, psd_w = welch(signal, fs=fs, nperseg=256, noverlap=128)
# Periodogram (raw, no averaging)
freqs_p, psd_p = periodogram(signal, fs=fs)
fig, ax = plt.subplots(figsize=(10, 5))
ax.semilogy(freqs_p, psd_p, 'gray', alpha=0.3, label='Periodogram')
ax.semilogy(freqs_w, psd_w, 'r-', linewidth=2, label='Welch PSD')
ax.set_xlabel('Frequency [Hz]')
ax.set_ylabel('PSD [V²/Hz]')
ax.set_title('Power Spectral Density')
ax.legend()
ax.grid(True, alpha=0.3)
ax.set_xlim(0, 200)
plt.savefig('psd.png', dpi=150, bbox_inches='tight')
Welch parameters:
nperseg: Segment length (frequency resolution = fs/nperseg)noverlap: Overlap between segments (typically 50% = nperseg//2)window: Window function ('hann' default, 'blackman' for better sidelobe suppression)- Trade-off: longer segments → better frequency resolution, worse noise averaging
3. Spectrogram (Time-Frequency)
from scipy.signal import spectrogram
# Chirp signal (frequency sweeps from 10 to 200 Hz)
t_chirp = np.linspace(0, 2, 8000)
chirp = np.sin(2*np.pi * (10*t_chirp + 47.5*t_chirp**2))
f_spec, t_spec, Sxx = spectrogram(chirp, fs=4000, nperseg=256, noverlap=200)
fig, ax = plt.subplots(figsize=(10, 5))
pcm = ax.pcolormesh(t_spec, f_spec, 10*np.log10(Sxx + 1e-20),
shading='gouraud', cmap='inferno')
ax.set_ylabel('Frequency [Hz]')
ax.set_xlabel('Time [s]')
ax.set_title('Spectrogram')
plt.colorbar(pcm, ax=ax, label='PSD [dB/Hz]')
plt.savefig('spectrogram.png', dpi=150, bbox_inches='tight')
4. Wavelet Transform (Continuous)
from scipy.signal import cwt, morlet2
# Continuous wavelet transform with Morlet wavelet
widths = np.geomspace(1, 128, num=100) # scale parameters
cwtmatr = cwt(signal, morlet2, widths, w=6)
# Convert scales to frequencies: f = w * fs / (2*pi*scale)
frequencies = 6 * fs / (2 * np.pi * widths)
fig, ax = plt.subplots(figsize=(10, 5))
ax.pcolormesh(t, frequencies, np.abs(cwtmatr),
shading='gouraud', cmap='viridis')
ax.set_ylabel('Frequency [Hz]')
ax.set_xlabel('Time [s]')
ax.set_title('Continuous Wavelet Transform (Morlet)')
ax.set_ylim(0, 200)
plt.colorbar(ax.collections[0], ax=ax, label='|CWT|')
plt.savefig('cwt.png', dpi=150, bbox_inches='tight')
5. Cross-Spectral Analysis and Coherence
from scipy.signal import coherence, csd
# Two related signals
signal2 = 1.2 * np.sin(2*np.pi*50*t + 0.3) + 0.6 * np.random.randn(len(t))
# Coherence (how correlated are the two signals at each frequency)
f_coh, Cxy = coherence(signal, signal2, fs=fs, nperseg=256)
# Cross-spectral density
f_csd, Pxy = csd(signal, signal2, fs=fs, nperseg=256)
fig, axes = plt.subplots(2, 1, figsize=(10, 7))
axes[0].plot(f_coh, Cxy, 'b-', linewidth=1.5)
axes[0].set_ylabel('Coherence')
axes[0].set_title('Coherence between signals')
axes[0].set_xlim(0, 200)
axes[0].grid(True, alpha=0.3)
axes[1].semilogy(f_csd, np.abs(Pxy), 'r-', linewidth=1.5)
axes[1].set_xlabel('Frequency [Hz]')
axes[1].set_ylabel('|CSD| [V²/Hz]')
axes[1].set_title('Cross-Spectral Density')
axes[1].set_xlim(0, 200)
axes[1].grid(True, alpha=0.3)
plt.tight_layout()
plt.savefig('coherence.png', dpi=150, bbox_inches='tight')
6. Filtering
from scipy.signal import butter, sosfilt, sosfiltfilt
def bandpass_filter(data, lowcut, highcut, fs, order=4):
"""Apply zero-phase Butterworth bandpass filter."""
nyq = 0.5 * fs
sos = butter(order, [lowcut/nyq, highcut/nyq], btype='band', output='sos')
return sosfiltfilt(sos, data)
# Example: extract 45-55 Hz component
filtered = bandpass_filter(signal, 45, 55, fs, order=4)
Frequency Resolution vs Averaging Trade-off
| Parameter | Effect on Resolution | Effect on Noise |
|---|---|---|
Longer nperseg |
Better frequency resolution | More noise (fewer averages) |
Shorter nperseg |
Worse frequency resolution | Less noise (more averages) |
More noverlap |
Same resolution | Slightly less noise |
| Windowing (Hann) | Wider main lobe | Better sidelobe suppression |
Rule of thumb: Frequency resolution Δf = fs / nperseg
Common Pitfalls
| Pitfall | Fix |
|---|---|
| Aliasing (fs too low) | Nyquist: fs ≥ 2 × f_max |
| Spectral leakage | Apply window function (Hann, Blackman) |
| Zero-padding confusion | Zero-padding interpolates FFT, doesn't improve resolution |
| Wrong units on PSD | Check: V²/Hz for continuous, V² for discrete |
| DC component dominates | Subtract mean before FFT |
| Non-uniform sampling | Use Lomb-Scargle periodogram (scipy.signal.lombscargle) |
Version History
- e9844a4 Current 2026-07-11 17:32
Dependencies
-
required
scipy>=1.11.0 -
required
numpy>=1.24.0 -
required
matplotlib>=3.7.0
