Metadata-Version: 2.1
Name: ssqueezepy
Version: 0.5.0
Summary: Synchrosqueezing, wavelet transforms, and time-frequency analysis in Python 
Home-page: https://github.com/OverLordGoldDragon/ssqueezepy
Author: OverLordGoldDragon
Author-email: 16495490+OverLordGoldDragon@users.noreply.github.com
License: MIT
Description: <p align="center"><img src="https://user-images.githubusercontent.com/16495490/99882586-faa86f80-2c3a-11eb-899c-b3984e98b1c7.png" width="300"></p>
        
        
        # Synchrosqueezing in Python
        
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        Synchrosqueezing is a powerful _reassignment method_ that focuses time-frequency representations, and allows extraction of instantaneous amplitudes and frequencies. [Friendly overview.](https://dsp.stackexchange.com/a/71399/50076)
        
        
        ## Features
          - Forward & inverse CWT-based Synchrosqueezing
          - Forward & inverse Continuous Wavelet Transform (CWT)
          - Clean code with explanations and learning references
          - Wavelet visualizations
        
        ### Coming soon
          - Forward & inverse Short-Time Fourier Transform (STFT)
          - STFT-based Synchrosqueezing
          - Generalized Morse Wavelets
          
        ## Installation
        `pip install ssqueezepy`. Or, for latest version (most likely stable): 
        
        `pip install git+https://github.com/OverLordGoldDragon/ssqueezepy`
        
        ## Examples
        
        ### 1. Signal recovery under severe noise
        
        ![image](https://user-images.githubusercontent.com/16495490/99879090-b9f12c00-2c23-11eb-8a40-2011ce84df61.png)
        
        ### 2. Medical: EEG
        
        <img src="https://user-images.githubusercontent.com/16495490/99880110-c88f1180-2c2a-11eb-8932-90bf3406a20d.png">
        
        <img src="https://user-images.githubusercontent.com/16495490/99880131-f1170b80-2c2a-11eb-9ace-807df257ad23.png">
        
        ## Introspection
        
        `ssqueezepy` is equipped with a visualization toolkit, useful for exploring wavelet behavior across scales and configurations. (Also see [explanations and code](https://dsp.stackexchange.com/a/72044/50076))
        
        <p align="center">
          <img src="https://raw.githubusercontent.com/OverLordGoldDragon/ssqueezepy/master/examples/imgs/anim_tf_morlet20.gif" width="500">
        </p>
        
        <img src="https://raw.githubusercontent.com/OverLordGoldDragon/ssqueezepy/master/examples/imgs/morlet_5vs20_tf.png">
        <img src="https://raw.githubusercontent.com/OverLordGoldDragon/ssqueezepy/master/examples/imgs/morlet_5vs20_hm.png">
        
        <br>
        <hr>
        
        ## Minimal example
        
        ```python
        import numpy as np
        import matplotlib.pyplot as plt
        from ssqueezepy import ssq_cwt
        
        def viz(x, Tx, Wx):
            plt.plot(x);  plt.show()    
            plt.imshow(np.abs(Wx), aspect='auto', cmap='jet')
            plt.show()
            plt.imshow(np.flipud(np.abs(Tx)), aspect='auto', vmin=0, vmax=.1, cmap='jet')
            plt.show()   
            
        #%%# Define signal ####################################    
        N = 2048
        t = np.linspace(0, 10, N, endpoint=False)
        xo = np.cos(2 * np.pi * np.exp(t / 3))
        x = xo + np.sqrt(4) * np.random.randn(N)
        
        #%%# SSQ CWT + CWT ####################################
        Txo, _, Wxo, scales_xo, _ = ssq_cwt(xo, 'morlet')
        Wxo /= np.sqrt(scales_xo)  # L1 norm
        viz(xo, Txo, Wxo)
        
        Tx, _, Wx, scales_x, _ = ssq_cwt(x, 'morlet')
        Wx /= np.sqrt(scales_x)  # L1 norm 
        viz(x, Tx, Wx)
        ```
        
        ## References
        
        `ssqueezepy` was originally ported from MATLAB's [Synchrosqueezing Toolbox](https://github.com/ebrevdo/synchrosqueezing), authored by E. Brevdo and G. Thakur [1]. Synchrosqueezed Wavelet Transform was introduced by I. Daubechies and S. Maes [2], which was followed-up in [3]. Many implementation details draw from [4].
        
          1. G. Thakur, E. Brevdo, N.-S. Fučkar, and H.-T. Wu. ["The Synchrosqueezing algorithm for time-varying spectral analysis: robustness properties and new paleoclimate applications"](https://arxiv.org/abs/1105.0010), Signal Processing 93:1079-1094, 2013. 
          2. I. Daubechies, S. Maes. ["A Nonlinear squeezing of the CWT Based on Auditory Nerve Models"](https://services.math.duke.edu/%7Eingrid/publications/DM96.pdf). 
          3. I. Daubechies, J. Lu, H.T. Wu. ["Synchrosqueezed Wavelet Transforms: a Tool for Empirical Mode Decomposition"](https://arxiv.org/pdf/0912.2437.pdf), Applied and Computational Harmonic Analysis 30(2):243-261, 2011.
          4. Mallat, S. ["Wavelet Tour of Signal Processing 3rd ed"](https://www.di.ens.fr/~mallat/papiers/WaveletTourChap1-2-3.pdf).
        
        ## License
        
        ssqueezepy is MIT licensed, as found in the [LICENSE](https://github.com/OverLordGoldDragon/ssqueezepy/blob/master/LICENSE) file. Some source functions may be under other authorship/licenses; see [NOTICE.txt](https://github.com/OverLordGoldDragon/ssqueezepy/blob/master/NOTICE.txt).
        
Keywords: signal-processing python synchrosqueezing wavelet-transform cwt time-frequency time-frequency-analysis
Platform: UNKNOWN
Classifier: Programming Language :: Python :: 3.6
Classifier: Programming Language :: Python :: 3.7
Classifier: Programming Language :: Python :: 3.8
Classifier: Programming Language :: Python :: 3.9
Classifier: Operating System :: OS Independent
Classifier: Intended Audience :: Developers
Classifier: Intended Audience :: Information Technology
Classifier: Intended Audience :: Science/Research
Classifier: Topic :: Utilities
Classifier: Topic :: Scientific/Engineering
Classifier: Topic :: Scientific/Engineering :: Information Analysis
Classifier: Topic :: Software Development
Classifier: Topic :: Software Development :: Libraries :: Python Modules
Description-Content-Type: text/markdown
