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    "info": {
        "author": "Henrik Blidh",
        "author_email": "henrik.blidh@gmail.com",
        "bugtrack_url": null,
        "classifiers": [
            "Development Status :: 5 - Production/Stable",
            "Intended Audience :: Developers",
            "Intended Audience :: Science/Research",
            "License :: OSI Approved :: MIT License",
            "Operating System :: MacOS",
            "Operating System :: Microsoft :: Windows",
            "Operating System :: POSIX",
            "Operating System :: Unix",
            "Programming Language :: Python :: 2",
            "Programming Language :: Python :: 2.7",
            "Programming Language :: Python :: 3",
            "Programming Language :: Python :: 3.5",
            "Programming Language :: Python :: 3.6",
            "Programming Language :: Python :: 3.7",
            "Programming Language :: Python :: Implementation :: CPython",
            "Programming Language :: Python :: Implementation :: PyPy",
            "Topic :: Scientific/Engineering"
        ],
        "description": "\n# LSPOpt\n\n[![Build Status](https://dev.azure.com/hbldh/github/_apis/build/status/hbldh.lspopt?branchName=master)](https://dev.azure.com/hbldh/github/_build/latest?definitionId=7&branchName=master)\n[![Coverage Status](https://coveralls.io/repos/github/hbldh/lspopt/badge.svg?branch=master)](https://coveralls.io/github/hbldh/lspopt?branch=master)\n[![PyPI version](https://img.shields.io/pypi/v/lspopt.svg)](https://pypi.org/project/lspopt/)\n[![Code style: black](https://img.shields.io/badge/code%20style-black-000000.svg)](https://github.com/ambv/black)\n\nThis module is a Python implementation of the multitaper window method \ndescribed in [\\[1\\]](#references) for estimating Wigner spectra for certain locally\nstationary processes.\n\nAbstract from [\\[1\\]](#references):\n\n> This paper investigates the time-discrete multitapers that give a mean square error optimal Wigner spectrum estimate for a class\n> of locally stationary processes (LSPs). The accuracy in the estimation of the time-variable Wigner spectrum of the LSP is evaluated\n> and compared with other frequently used methods. The optimal multitapers are also approximated by Hermite functions, which is\n> computationally more efficient, and the errors introduced by this approximation are studied. Additionally, the number of windows\n> included in a multitaper spectrum estimate is often crucial and an investigation of the error caused by limiting this number is made.\n> Finally, the same optimal set of weights can be stored and utilized for different window lengths. As a result, the optimal multitapers\n> are shown to be well approximated by Hermite functions, and a limited number of windows can be used for a mean square error\n> optimal spectrogram estimate.\n\n## Installation\n\nInstall via pip:\n\n    pip install lspopt\n\n## Testing\n\nTest with `pytest`:\n\n    pytest tests/ \n\nTests are run at every commit to GitHub and the results of this, as well as test \ncoverage, can be studied at [Azure Pipelines](https://dev.azure.com/hbldh/github/_build/latest?definitionId=7&branchName=master).\n\n## Usage\n\nTo generate the taper windows only, use the `lspopt` method:\n\n```python\nfrom lspopt import lspopt\nH, w = lspopt(N=256, c_parameter=20.0)\n```\n\nThere 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)\nwith the `lspopt` multitaper windows:\n\n```python\nfrom lspopt import spectrogram_lspopt\nf, t, Sxx = spectrogram_lspopt(x, fs, c_parameter=20.0)\n```\n\nThis can then be plotted with e.g. [matplotlib](http://matplotlib.org/).\n\n### Example\n\nOne can generate a [chirp](https://docs.scipy.org/doc/scipy-0.16.0/reference/generated/scipy.signal.chirp.html)\nprocess realisation and run spectrogram methods on this. \n\n```python\nimport numpy as np\nfrom scipy.signal import chirp, spectrogram\nimport matplotlib.pyplot as plt\n\nfrom lspopt.lsp import spectrogram_lspopt\n\nfs = 10e3\nN = 1e5\namp = 2 * np.sqrt(2)\nnoise_power = 0.001 * fs / 2\ntime = np.arange(N) / fs\nfreq = np.linspace(1e3, 2e3, N)\nx = amp * chirp(time, 1e3, 2.0, 6e3, method='quadratic') + \\\n    np.random.normal(scale=np.sqrt(noise_power), size=time.shape)\n\nf, t, Sxx = spectrogram(x, fs)\n\nax = plt.subplot(211)\nax.pcolormesh(t, f, Sxx)\nax.set_ylabel('Frequency [Hz]')\nax.set_xlabel('Time [sec]')\n\nf, t, Sxx = spectrogram_lspopt(x, fs, c_parameter=20.0)\n\nax = plt.subplot(212)\nax.pcolormesh(t, f, Sxx)\nax.set_ylabel('Frequency [Hz]')\nax.set_xlabel('Time [sec]')\n\nplt.show()\n```\n\n![Spectrogram plot](https://hbldh.github.com/lspopt/images/plot.png)\n*Top: Using SciPy's spectrogram method. Bottom: Using LSPOpt's spectrogram solution.*\n\n## References\n\n\\[1\\] [Hansson-Sandsten, M. (2011). Optimal multitaper Wigner spectrum \nestimation of a class of locally stationary processes using Hermite functions. \nEURASIP Journal on Advances in Signal Processing, 2011, 10.](http://asp.eurasipjournals.com/content/pdf/1687-6180-2011-980805.pdf)\n\n\n",
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        "home_page": "https://github.com/hbldh/lspopt",
        "keywords": "Mathematical Statistics,Multitaper,Spectrogram",
        "license": "MIT",
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        "name": "lspopt",
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