B &]\)@sddlmZmZmZddlZddlmZddlm Z ddl m Z m Z m Z ddlmZddd d d d gZd dZddZddd Zddd Zdd Zdd ZdS))divisionprint_functionabsolute_importN)eig)comb)linspacepiexp)convolvedaubqmfcascademorletrickercwtc stj}dkrtddkr8d|d}t||gSdkrz|dd}|d}|td|d|d|d|gSdkrNd|d}d|d |d d |d ||d d }t|}|dd}td|d|}t||}dt|} ||t|d|| d|d| d|d| dd| dgSd krzd krfd dtDddd} t| } n.fddtDddd} t| d} tddg}tdg} xjtdD]Z} | | }d|||d}dd|}||}t |dkr2||}| d| g} qW|t| } | t | |d} | j dddStddS)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?#cs"g|]}td||ddqS)r)exact)r).0k)p4lib/python3.7/site-packages/scipy/signal/wavelets.py 5szdaub..Ncs*g|]"}td||ddd|qS)r)rg@)r)rr)rrrr 8sz.Nr!)lenr(r#r&)hkNZasgnrrrr Qs csFt|d}|dt|dkr*td|dkr:tdtjd|d|f\}}td}tj|df}t|}tj|df}td||d|d} td||dd|d} t dd||fd } t || d| d <t || d| d <t || d| d <t || d| d <| |9} tj d|d|>t dd|>} d| } d| }t | d \}}tt|d}t|dd|f}t|}|dkr| }| }d||i}t| d |d|d<d|>}|d| dd|<|d| d|d>d|<t| d |d|dd|<t| d |d|d|d>d|<dgxtd|dD]}fddd D}d||>}x|D]}d}x4t|D](}||dkr|d|d|>7}qW||dd}t|d}t| d|f|}|||<|| ||d|<t| d|f||||d|<qW|qZW| | |fS)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. rzToo many levels.zToo few levels.Nrrr!d)rr)rr)rr)rr)Zdtype01cs"g|]}D]}d||fq qS)z%d%sr)rZxxZyy)prevkeysrrr szcascade..)r1r#Zlog2r%Zogridr$Zr_r ZclipzerosZtakearangefloatrZargminZabsoluter'r+dotr(int)r2Jr3ZnnZkks2ZthkZgkZtgkZindx1Zindx2mxZphiZpsiZlamvindZsmZbitdicsteplevelZnewkeysZfackeyZnumposZpastphiZiiZtempr)r9rr `sh      &   ( @?TcCsft| dt|dt|}td||}|rF|td|d8}|td|dtd9}|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. ry?ggп)rrr )MwsZcompleterBoutputrrrrs 3c Cstdtd|tjd}|d}td||dd}|d}d||}t| 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() rrg?rg?r)r#r$rr;r ) ZpointsaAZwsqZvecZxsqmodZgaussZtotalrrrrs%  cCsbtt|t|g}xFt|D]:\}}|td|t||}t||dd||ddf<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() rZsame)modeN)r#r:r1 enumerateminr )dataZwaveletZwidthsrNrDwidthZ wavelet_datarrrr7s 1)r4)rIrJT)Z __future__rrrZnumpyr#Z numpy.dualrZ scipy.specialrZscipyrrr Z scipy.signalr __all__r r r rrrrrrrs   E j >/