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wavelets.cpython-35.pyc
DB�W) � @ s� d d l m Z m Z m Z d d l Z d d l m Z d d l m Z d d l m Z m Z m Z d d l m Z d d d d d d g Z d d � Z d d � Z d d d � Z d d d d d � Z d d � Z d d � Z d S)� )�division�print_function�absolute_importN)�eig)�comb)�linspace�pi�exp)�convolve�daub�qmf�cascade�morlet�ricker�cwtc s> t j } � d k r! t d � � � d k rP d | d � } t j | | g � S� d k r� | d � d } | d � } | t j d | d | d | d | g � S� d k r�d | d � } d | d | � d d | d � | | d � d } t j | � } | d � d } t j d | d | � } t j | | � } d t j | � } | | t j | d | | d | d | d | d | d d | d g � S� d k r.� d k r�� f d d � t � � D� d d d � } t j | � } n? � f d d � t � � D� d d d � } t j | � d } t j d d g � � } t j d g � } x t � d � D]m } | | } d | | | d � } d d | } | | } t | � d k r�| | } | d | g } qyW| t j | � } | t j | � | d � } | j d d d � St d � � d S)aT The coefficients for the FIR low-pass filter producing Daubechies wavelets. p>=1 gives the order of the zero at f=1/2. There are 2p filter coefficients. Parameters ---------- p : int Order of the zero at f=1/2, can have values from 1 to 34. Returns ------- daub : ndarray Return � zp must be at least 1.� � � � � g �?� � y �?�# c s- g | ]# } t � d | | d d �� q S)r �exact)r )�.0�k)�p� � /wavelets.py� <listcomp>5 s zdaub.<locals>.<listcomp>Nc s5 g | ]+ } t � d | | d d �d | � q S)r r g @)r )r r )r r r r 8 s � z<Polynomial factorization does not work well for p too large.���r" r" ) �np�sqrt� ValueError�arrayZconj�real�range�rootsZpoly1d�abs�sum�c)r r$ r, �f�tmpZz1Zz1cZd0Za0Za1�PZyj�qr Zyval�part�constr )r r r sR - 8.! , c C sK t | � d } d d � t | d � D� } | d d d � t j | � S)z� Return high-pass qmf filter from low-pass Parameters ---------- hk : array_like Coefficients of high-pass filter. r c S s* g | ] } d d d d i | d � q S)r r r r" r )r r r r r r \ s zqmf.<locals>.<listcomp>Nr" )�lenr( r# r& )�hk�NZasgnr r r r Q s � c sL t | � d } | d t j | d � k r9 t d � � | d k rQ t d � � t j d | � d | � f \ } } t j d � } t j | d f } t | � } t j | d f } t j d | | d | d � } t j d | | d d | d � } t j d d | | f d � } t j | | d � | d <t j | | d � | d <t j | | d � | d <t j | | d � | d <| | 9} t j d | d | >d t �d | >} d | } d | } t | d � \ } } t j t j | d � � } t j | d d � | f � } t j | � } | d k r?| } | } d | | i } t j | d | d � | d <d | >} | d | d d | � <| d | d | d >d | � <t j | d | d � | d d | � <t j | d | d � | d | d >d | � <d g � x0t d | d � D]} � f d d � d d g D� } d | | >} x� | D]� } d } x: t | � D], } | | d k rs| d | d | >7} qsW| | d d � } t | d � } t j | d | f | � } | | | <| | | | d | � <t j | d | f | � | | | d | � <qZW| � q W| | | f S)a� Return (x, phi, psi) at dyadic points ``K/2**J`` from filter coefficients. Parameters ---------- hk : array_like Coefficients of low-pass filter. J : int, optional Values will be computed at grid points ``K/2**J``. Default is 7. Returns ------- x : ndarray The dyadic points ``K/2**J`` for ``K=0...N * (2**J)-1`` where ``len(hk) = len(gk) = N+1``. phi : ndarray The scaling function ``phi(x)`` at `x`: ``phi(x) = sum(hk * phi(2x-k))``, where k is from 0 to N. psi : ndarray, optional The wavelet function ``psi(x)`` at `x`: ``phi(x) = sum(gk * phi(2x-k))``, where k is from 0 to N. `psi` is only returned if `gk` is not None. Notes ----- The algorithm uses the vector cascade algorithm described by Strang and Nguyen in "Wavelets and Filter Banks". It builds a dictionary of values and slices for quick reuse. Then inserts vectors into final vector at the end. r � zToo many levels.zToo few levels.Nr r �dZdtype�0�1c s- g | ]# } � D] } d | | f � q q S)z%d%sr )r ZxxZyy)�prevkeysr r r � s zcascade.<locals>.<listcomp>r" r" )r r )r r )r r )r r )r r )r r )r r )r r )r3 r# �log2r% Zogridr$ Zr_r Zclip�zerosZtake�arange�floatr ZargminZabsoluter' r+ �dotr( �int) r4 �Jr5 ZnnZkk�s2ZthkZgkZtgkZindx1Zindx2�m�xZphiZpsiZlam�v�indZsmZbitdic�step�levelZnewkeysZfac�key�num�posZpastphiZiiZtempr )r; r r ` sh % !% ( '/ 1 g @g �?Tc C sy t | d t | d t | � } t d | | � } | rU | t d | d � 8} | t d | d � t d 9} | S)a� Complex Morlet wavelet. Parameters ---------- M : int Length of the wavelet. w : float, optional Omega0. Default is 5 s : float, optional Scaling factor, windowed from ``-s*2*pi`` to ``+s*2*pi``. Default is 1. complete : bool, optional Whether to use the complete or the standard version. Returns ------- morlet : (M,) ndarray See Also -------- scipy.signal.gausspulse Notes ----- The standard version:: pi**-0.25 * exp(1j*w*x) * exp(-0.5*(x**2)) This commonly used wavelet is often referred to simply as the Morlet wavelet. Note that this simplified version can cause admissibility problems at low values of `w`. The complete version:: pi**-0.25 * (exp(1j*w*x) - exp(-0.5*(w**2))) * exp(-0.5*(x**2)) This version has a correction term to improve admissibility. For `w` greater than 5, the correction term is negligible. Note that the energy of the return wavelet is not normalised according to `s`. The fundamental frequency of this wavelet in Hz is given by ``f = 2*s*w*r / M`` where `r` is the sampling rate. Note: This function was created before `cwt` and is not compatible with it. r y �?g �?g �?g �g �g п)r r r )�M�w�sZcompleterE �outputr r r r � s 3# c C s� d t j d | � t j d } | d } t j d | � | d d } | d } d | | } t j | d | � } | | | } | S)a� Return a Ricker wavelet, also known as the "Mexican hat wavelet". It models the function: ``A (1 - x^2/a^2) exp(-x^2/2 a^2)``, where ``A = 2/sqrt(3a)pi^1/4``. Parameters ---------- points : int Number of points in `vector`. Will be centered around 0. a : scalar Width parameter of the wavelet. Returns ------- vector : (N,) ndarray Array of length `points` in shape of ricker curve. Examples -------- >>> from scipy import signal >>> import matplotlib.pyplot as plt >>> points = 100 >>> a = 4.0 >>> vec2 = signal.ricker(points, a) >>> print(len(vec2)) 100 >>> plt.plot(vec2) >>> plt.show() r r g �?r g �?r )r# r$ r r> r ) Zpoints�a�AZwsqZvecZxsq�mod�gauss�totalr r r r s %" c C s� t j t | � t | � g � } xa t | � D]S \ } } | t d | t | � � | � } t | | d d �| | d d � f <q. W| S)aV Continuous wavelet transform. Performs a continuous wavelet transform on `data`, using the `wavelet` function. A CWT performs a convolution with `data` using the `wavelet` function, which is characterized by a width parameter and length parameter. Parameters ---------- data : (N,) ndarray data on which to perform the transform. wavelet : function Wavelet function, which should take 2 arguments. The first argument is the number of points that the returned vector will have (len(wavelet(length,width)) == length). The second is a width parameter, defining the size of the wavelet (e.g. standard deviation of a gaussian). See `ricker`, which satisfies these requirements. widths : (M,) sequence Widths to use for transform. Returns ------- cwt: (M, N) ndarray Will have shape of (len(widths), len(data)). Notes ----- :: length = min(10 * width[ii], len(data)) cwt[ii,:] = signal.convolve(data, wavelet(length, width[ii]), mode='same') Examples -------- >>> from scipy import signal >>> import matplotlib.pyplot as plt >>> t = np.linspace(-1, 1, 200, endpoint=False) >>> sig = np.cos(2 * np.pi * 7 * t) + signal.gausspulse(t - 0.4, fc=2) >>> widths = np.arange(1, 31) >>> cwtmatr = signal.cwt(sig, signal.ricker, widths) >>> plt.imshow(cwtmatr, extent=[-1, 1, 31, 1], cmap='PRGn', aspect='auto', ... vmax=abs(cwtmatr).max(), vmin=-abs(cwtmatr).max()) >>> plt.show() r �modeZsameN)r# r= r3 � enumerate�minr )�dataZwaveletZwidthsrP rG �widthZ wavelet_datar r r r 7 s 1!" )Z __future__r r r Znumpyr# Z numpy.dualr Z scipy.specialr Zscipyr r r Z scipy.signalr �__all__r r r r r r r r r r �<module> s E j> /
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__init__.cpython-35.opt-1.pyc
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_arraytools.cpython-35.opt-1.pyc
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_max_len_seq.cpython-35.opt-1.pyc
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_peak_finding.cpython-35.opt-1.pyc
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bsplines.cpython-35.opt-1.pyc
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bsplines.cpython-35.pyc
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filter_design.cpython-35.opt-1.pyc
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filter_design.cpython-35.pyc
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fir_filter_design.cpython-35.opt-1.pyc
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fir_filter_design.cpython-35.pyc
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lti_conversion.cpython-35.opt-1.pyc
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lti_conversion.cpython-35.pyc
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ltisys.cpython-35.opt-1.pyc
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ltisys.cpython-35.pyc
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setup.cpython-35.opt-1.pyc
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setup.cpython-35.pyc
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signaltools.cpython-35.opt-1.pyc
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signaltools.cpython-35.pyc
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spectral.cpython-35.opt-1.pyc
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spectral.cpython-35.pyc
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waveforms.cpython-35.opt-1.pyc
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waveforms.cpython-35.pyc
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wavelets.cpython-35.opt-1.pyc
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wavelets.cpython-35.pyc
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windows.cpython-35.opt-1.pyc
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windows.cpython-35.pyc
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