https://github.com/hbldh/lspopt
Python implementation of a multitaper window method for estimating Wigner spectra for certain locally stationary processes
https://github.com/hbldh/lspopt
estimation histogram multitaper-windows optimal-multitapers python spectrum stochastic-processes
Last synced: about 1 year ago
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Python implementation of a multitaper window method for estimating Wigner spectra for certain locally stationary processes
- Host: GitHub
- URL: https://github.com/hbldh/lspopt
- Owner: hbldh
- License: mit
- Created: 2015-12-02T17:52:39.000Z (over 10 years ago)
- Default Branch: master
- Last Pushed: 2025-01-07T16:23:29.000Z (over 1 year ago)
- Last Synced: 2025-03-24T09:03:53.547Z (about 1 year ago)
- Topics: estimation, histogram, multitaper-windows, optimal-multitapers, python, spectrum, stochastic-processes
- Language: Python
- Homepage:
- Size: 675 KB
- Stars: 22
- Watchers: 5
- Forks: 4
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- Changelog: CHANGELOG.md
- License: LICENSE
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README
# LSPOpt
[](https://pypi.org/project/lspopt/)
[](https://github.com/ambv/black)
This module is a Python implementation of the multitaper window method
described in [\[1\]](#references) for estimating Wigner spectra for certain locally
stationary processes.
Abstract from [\[1\]](#references):
> This paper investigates the time-discrete multitapers that give a mean square error optimal Wigner spectrum estimate for a class
> of locally stationary processes (LSPs). The accuracy in the estimation of the time-variable Wigner spectrum of the LSP is evaluated
> and compared with other frequently used methods. The optimal multitapers are also approximated by Hermite functions, which is
> computationally more efficient, and the errors introduced by this approximation are studied. Additionally, the number of windows
> included in a multitaper spectrum estimate is often crucial and an investigation of the error caused by limiting this number is made.
> Finally, the same optimal set of weights can be stored and utilized for different window lengths. As a result, the optimal multitapers
> are shown to be well approximated by Hermite functions, and a limited number of windows can be used for a mean square error
> optimal spectrogram estimate.
## Installation
Install via pip:
pip install lspopt
If you prefer to use `conda`, see [instructions in this repo](https://github.com/conda-forge/lspopt-feedstock).
## Testing
Test with `pytest`:
pytest tests/
See test badge at the top of this README for link to test coverage and reports.
## Usage
To generate the taper windows only, use the `lspopt` method:
```python
from lspopt import lspopt
H, w = lspopt(n=256, c_parameter=20.0)
```
There is also a convenience method for using the [SciPy spectrogram method](https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.spectrogram.html#scipy.signal.spectrogram)
with the `lspopt` multitaper windows:
```python
from lspopt import spectrogram_lspopt
f, t, Sxx = spectrogram_lspopt(x, fs, c_parameter=20.0)
```
This can then be plotted with e.g. [matplotlib](http://matplotlib.org/).
### Example
One can generate a [chirp](https://docs.scipy.org/doc/scipy-0.16.0/reference/generated/scipy.signal.chirp.html)
process realisation and run spectrogram methods on this.
```python
import numpy as np
from scipy.signal import chirp, spectrogram
import matplotlib.pyplot as plt
from lspopt.lsp import spectrogram_lspopt
fs = 10000
N = 100000
amp = 2 * np.sqrt(2)
noise_power = 0.001 * fs / 2
time = np.arange(N) / fs
freq = np.linspace(1000, 2000, N)
x = amp * chirp(time, 1000, 2.0, 6000, method='quadratic') + \
np.random.normal(scale=np.sqrt(noise_power), size=time.shape)
f, t, Sxx = spectrogram(x, fs)
ax = plt.subplot(211)
ax.pcolormesh(t, f, Sxx)
ax.set_ylabel('Frequency [Hz]')
ax.set_xlabel('Time [sec]')
f, t, Sxx = spectrogram_lspopt(x, fs, c_parameter=20.0)
ax = plt.subplot(212)
ax.pcolormesh(t, f, Sxx)
ax.set_ylabel('Frequency [Hz]')
ax.set_xlabel('Time [sec]')
plt.tight_layout()
plt.show()
```
*Top: Using SciPy's spectrogram method. Bottom: Using LSPOpt's spectrogram solution.*
## References
\[1\] [Hansson-Sandsten, M. (2011). Optimal multitaper Wigner spectrum
estimation of a class of locally stationary processes using Hermite functions.
EURASIP Journal on Advances in Signal Processing, 2011, 10.](https://dx.doi.org/10.1155/2011/980805)