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        "author": "Tiarles Guterres",
        "author_email": "tiarlesmoralles@hotmail.com",
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            "Programming Language :: Python :: 3"
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        "description": "# Statistical Processing: A Python Statistical Signal Processing Package\n\nA package that construct an interface for filtering wavelet coefficients (using PyWavelets) with statistical methods\n## Getting started\n\nFirst you can import some modules like:\n``` python\n    import pywt\n    import numpy as np\n\n    import statsWaveletFilt.filtration as fil\n    import statsWaveletFilt.signals as sig\n    import statsWaveletFilt.miscellaneous as misc\n```\nAnd follow some steps to make your filtrations:\n\n### First step: Signal modelling\n\nIn many test for filtration and/or estimation of error, showed in articles, are supose an known ideal signal, how show the code above:\n``` python\n    import matplotlib.pyplot as plt\n\n    dimension = 1024\n\n    t, idealSignal = sig.dopplerFunction(dimension)\n    plt.plot(t, idealSignal, 'k-')\n    plt.show()\n```\n\nThis package also gives a support for anothers three ideal signal: the **heavsine** (``sig.heavsineFunction()``), **bump** (``sig.bumpFunction()``) and **block** (``sig.blockFunction()``).\n\nAnd add to this a kind of noise, generally *gaussian* or, also called, *normal*.\n``` python\n    noise = np.random.normal(0, .02, size=dimension)\n    noisySignal = idealSignal + noise\n\n    plt.plot(t, noisySignal, 'k-')\n    plt.show()\n```\n\n### Second step: Wavelet transformation\n\nLet's do this using the ``pywt.wavedec`` function. With this you can 1) make a wavelet transform of your noisy signal, 2) choice wich wavelet function is used (``'haar', 'db', 'gaus', 'mexh'`` among others) and 3) choice any levels you want to evaluate the transform.\n``` python\n    noisyCoeff = pywt.wavedec(noisySignal, 'db8', level=5)\n```\nThe first position ``= noiseCoeff[0]`` has the scale coefficents of the last n\u00edvel. The consecutive elements `` = noiseCoeff[1:]`` has the wavelet coefficients of the last to the first level of transform.\n\nUsing ``misc.showWaveletCoeff`` function you can show all coefficients returned of the transform.\n\n``` python\n    misc.showWaveletCoeff(noisyCoeff, title='Noisy Coefficients')\n```\n\n### Thirth step: Filtration\n\nWith the ``fil.filtration`` function you can put yours 1) coefficients for filtration, 2) choice the method (``'visu', 'sure', 'bayes', 'spc'``) and, if necessary, 3) set method own parameters (more details in documentation).\n``` python\n    filtrateCoeff, limiars = fil.filtration(noisyCoeff, method='visu')\n```\nAnd, again, you can show the wavelet coefficients before and after the filtration, with the limiar used using the ``misc.showWaveletCoeff`` function.\n\n``` python\n    misc.showWaveletCoeff(noisyCoeff, threshold_value=limiars, title='Noisy Coefficients')\n    print('==============================================================')\n    misc.showWaveletCoeff(filtrateCoeff, threshold_value=limiars, title='Filtered Coefficients')\n```\n\n### Fourth step: Recovery wavelet transformation\n\nUsing the ``pywt.waverec`` function we can revovery the signal.\n\n``` python\n    filtrateSignal = pywt.waverec(filtrateCoeff, 'db8')\n\n    plt.plot(t, filtrateSignal, 'k-')\n    plt.show()\n```\n\n### Fifth step: Figures of merith\nUsing ``sig.differential_snr_dB`` we can avaliate the filtration using some figures of merith of different forms of evaluate the snr or cnr (see more in Documentation) of the signal.\n``` python\n    sig.differential_snr_dB(noisySignal, filtratedSignal, method='variances', idealSignal=idealSignal)\n```\n### Appendix: Miscelaneous\n\n* The ``misc.generateData`` function generate data using the signals showed here with different variances of noise and save in format ``.npy``.\n* The ``misc.normalizeData`` function normalize a data between a min and max value, this function is used in all signals modeled in sig module.\n\n### References\n\n* [DONOHO, JOHNSTONE (1992), Ideal Spatial Adaptation by Wavelet Shrinkage](http://statweb.stanford.edu/~imj/WEBLIST/1994/isaws.pdf)\n* [DONOHO, JOHNSTONE (1994), Adapting to Unknown Smoothness via Wavelet Shrinkage](http://statweb.stanford.edu/~imj/WEBLIST/1995/ausws.pdf)\n* [CHANG, YU, VETTERLI (2000),Adaptive Wavelet Thresholding for Image Denoisingand Compression](https://core.ac.uk/download/pdf/147900624.pdf)\n* [BAYER, KOZAKEVICIUS (2010), SPC-Threshold: Uma Proposta de Limiariza\u00e7\u00e3o para Filtragem Adaptativa de Sinais](https://tema.sbmac.org.br/tema/article/download/96/43)\n* [KOZAKEVICIUS, BAYER (2014), Filtragem de sinais via limiariza\u00e7\u00e3o de coeficientes wavelet](http://oaji.net/articles/2017/1602-1487163088.pdf)\n\n",
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