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� Zdd� Zdd� Zd dd�Zd dd�Zd dd�Zd dd�Zdd � Zd d � ZdS ) z"5Other wavelet related functions.6� N)�fft� )�ContinuousWavelet�DiscreteContinuousWavelet�Wavelet)7�integrate_wavelet�central_frequency�scale2frequency�frequency2scale�qmf�orthogonal_filter_bank�intwave�centrfrq�scal2frq�orthfiltzT`{old}` has been renamed to `{new}` and will be removed in a future version of pywt.c C s t �| �}||9 }|S )N)�npZcumsum)Zarr�stepZintegral� r �yE:\DocsHouse\542 percep lab latest\PerceptionLab\PerceptionLab_Portable\python_embed\Lib\site-packages\pywt/_functions.py�8_integrate s 9r c O �( t jddd�}t�|t� t| i |��S )Nr
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|�}t|�dkr`|\}}|d |d }t ||�|fS t|�dkrz|\}}}|d |d }t ||�|fS |\}} }12} }|d |d }t | |�t | |�|fS )ac 13 Integrate `psi` wavelet function from -Inf to x using the rectangle14 integration method.15 16 Parameters17 ----------18 wavelet : Wavelet instance or str19 Wavelet to integrate. If a string, should be the name of a wavelet.20 precision : int, optional21 Precision that will be used for wavelet function22 approximation computed with the wavefun(level=precision)23 Wavelet's method (default: 8).24 25 Returns26 -------27 [int_psi, x] :28 for orthogonal wavelets29 [int_psi_d, int_psi_r, x] :30 for other wavelets31 32 33 Examples34 --------35 >>> from pywt import Wavelet, integrate_wavelet36 >>> wavelet1 = Wavelet('db2')37 >>> [int_psi, x] = integrate_wavelet(wavelet1, precision=5)38 >>> wavelet2 = Wavelet('bior1.3')39 >>> [int_psi_d, int_psi_r, x] = integrate_wavelet(wavelet2, precision=5)40 41 z^Integration of a general signal is deprecated and will be removed in a future version of pywt.r r � � )�type�tuple�listr r r �42isinstancer r r r �asarrayr �wavefun�len) �wavelet� precisionr" �psi�xr �functions_approximations�phiZphi_dZpsi_dZphi_rZpsi_rr r r r : s* ! 43 44r c C s� t | ttf�s t| �} | �|�}t|�dkr|\}}n |d |d }}t|d |d �}|dks4J �t�t t45|�dd� ��d }|t|�d krSt|�| d }d||d S )a� 46 Computes the central frequency of the `psi` wavelet function.47 48 Parameters49 ----------50 wavelet : Wavelet instance, str or tuple51 Wavelet to integrate. If a string, should be the name of a wavelet.52 precision : int, optional53 Precision that will be used for wavelet function54 approximation computed with the wavefun(level=precision)55 Wavelet's method (default: 8).56 57 Returns58 -------59 scalar60 61 r% r �����r Ng �?) r* r r r r, r- �floatr Zargmax�absr )r. r/ r2 r0 r1 �domain�indexr r r r y s 62 63 r c C � t | |d�| S )a� Convert from CWT "scale" to normalized frequency.64 65 Parameters66 ----------67 wavelet : Wavelet instance or str68 Wavelet to integrate. If a string, should be the name of a wavelet.69 scale : scalar70 The scale of the CWT.71 precision : int, optional72 Precision that will be used for wavelet function approximation computed73 with ``wavelet.wavefun(level=precision)``. Default is 8.74 75 Returns76 -------77 freq : scalar78 Frequency normalized to the sampling frequency. In other words, for a79 sampling interval of `dt` seconds, the normalized frequency of 1.080 corresponds to (`1/dt` Hz).81 82 �r/ �r )r. �scaler/ r r r r � s r c C r9 )a Convert from to normalized frequency to CWT "scale".83 84 Parameters85 ----------86 wavelet : Wavelet instance or str87 Wavelet to integrate. If a string, should be the name of a wavelet.88 freq : scalar89 Frequency, normalized so that the sampling frequency corresponds to a90 value of 1.0.91 precision : int, optional92 Precision that will be used for wavelet function approximation computed93 with ``wavelet.wavefun(level=precision)``. Default is 8.94 95 Returns96 -------97 scale : scalar98 99 r: r; )r. �freqr/ r r r r100 � s r101 c C s2 t �| �ddd� }|ddd� |ddd�< |S )ad 102 Returns the Quadrature Mirror Filter(QMF).103 104 The magnitude response of QMF is mirror image about `pi/2` of that of the105 input filter.106 107 Parameters108 ----------109 filt : array_like110 Input filter for which QMF needs to be computed.111 112 Returns113 -------114 qm_filter : ndarray115 Quadrature mirror of the input filter.116 117 Nr4 r r% )r �array)ZfiltZ qm_filterr r r r � s r c C st t | �d dks td��tj| tjd�} t�d�| t�| � }|ddd� }t|�}|ddd� }||||f}|S )a, 118 Returns the orthogonal filter bank.119 120 The orthogonal filter bank consists of the HPFs and LPFs at121 decomposition and reconstruction stage for the input scaling filter.122 123 Parameters124 ----------125 scaling_filter : array_like126 Input scaling filter (father wavelet).127 128 Returns129 -------130 orth_filt_bank : tuple of 4 ndarrays131 The orthogonal filter bank of the input scaling filter in the order :132 1] Decomposition LPF133 2] Decomposition HPF134 3] Reconstruction LPF135 4] Reconstruction HPF136 137 r% r z'`scaling_filter` length has to be even.)ZdtypeNr4 )r- �138ValueErrorr r+ Zfloat64�sqrt�sumr )Zscaling_filterZrec_loZdec_loZrec_hiZdec_hiZorth_filt_bankr r r r � s r )r$ )�__doc__r �numpyr Z numpy.fftr Z_extensions._pywtr r r �__all__r r r
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