stockwell:适用于Python的Stockwell转换

# Stockwell Python package for time-frequency analysis through Stockwell transform. Based on original code from [NIMH MEG Core Facility]. [NIMH MEG Core Facility]: https://kurage.nimh.nih.gov/meglab/Meg/Stockwell. ## Installation ### C compiler Part of this Python package is written in C, so you will need a C compiler. On Linux (Debian or Ubuntu), install the `build-essential` package: sudo apt install build-essential On macOS, install the XCode Command Line Tools: xcode-select --install On Windows, install the [Microsoft C++ Build Tools]. [Microsoft C++ Build Tools]: https://visualstudio.microsoft.com/visual-cpp-build-tools ### FFTW Make sure that you have [FFTW](http://www.fftw.org) installed. If you use Anaconda (Linux, macOS, Windows): conda install fftw If you use Homebrew (macOS) brew install fftw If you use `apt` (Debian or Ubuntu) sudo apt install libfftw3-dev ### Install the Python package Finally, install this Python package using pip: pip install . Or, alternatively, in "editable" mode: pip install -e . ## Usage Example usage: ```python import numpy as np from scipy.signal import chirp import matplotlib.pyplot as plt from stockwell import st t = np.linspace(0, 10, 5001) w = chirp(t, f0=12.5, f1=2.5, t1=10, method='linear') fmin = 0 # Hz fmax = 25 # Hz df = 1./(t[-1]-t[0]) # sampling step in frequency domain (Hz) fmin_samples = int(fmin/df) fmax_samples = int(fmax/df) stock = st.st(w, fmin_samples, fmax_samples) extent = (t[0], t[-1], fmin, fmax) fig, ax = plt.subplots(2, 1, sharex=True) ax[0].plot(t, w) ax[0].set(ylabel='amplitude') ax[1].imshow(np.abs(stock), origin='lower', extent=extent) ax[1].axis('tight') ax[1].set(xlabel='time (s)', ylabel='frequency (Hz)') plt.show() ``` You should get the following output:  You can also compute the inverse Stockwell transform, ex: ```python inv_stock = st.ist(stock, fmin_samples, fmax_samples) fig, ax = plt.subplots(2, 1, sharex=True) ax[0].plot(t, w, label='original signal') ax[0].plot(t, inv_stock, label='inverse Stockwell') ax[0].set(ylabel='amplitude') ax[0].legend(loc='upper right') ax[1].plot(t, w - inv_stock) ax[1].set_xlim(0, 10) ax[1].set(xlabel='time (s)', ylabel='amplitude difference') plt.show() ```  ## References Stockwell, R.G., Mansinha, L. & Lowe, R.P., 1996. Localization of the complex spectrum: the S transform, IEEE Trans. Signal Process., 44(4), 998–1001, doi:[10.1109/78.492555](https://doi.org/10.1109/78.492555) [S transform on Wikipedia](https://en.wikipedia.org/wiki/S_transform).