a BCCf>@sddlZddlZddlmZddlmZddlmZgdZ dZ ddZ d d Z dd d Z dddZddZddZd ddZd!ddZd"ddZdS)#N)eigcomb)convolve)daubqmfcascademorletrickermorlet2cwtzvscipy.signal.%s is deprecated in SciPy 1.12 and will be removed in SciPy 1.15. We recommend using PyWavelets instead. c stjtdtddtj}dkr*tddkrLd|d}t||gSdkr|dd}|d}|td|d|d|d|gSdkrbd|d }d |d |d d |d ||d d }t|}|dd}t d|d|}t ||}dt |} ||t|d|| d|d| d|d| dd| dgSdkrdkrfddt Dddd} t | } n.fddt Dddd} t | d} t ddg}t dg} t dD]Z} | | }d|||d}dd|}||}t |dkrD||}| d| g} q|t | } | t| |d} | jdddStddS)a The coefficients for the FIR low-pass filter producing Daubechies wavelets. .. deprecated:: 1.12.0 scipy.signal.daub is deprecated in SciPy 1.12 and will be removed in SciPy 1.15. We recommend using PyWavelets instead. 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 r stacklevelzp must be at least 1. g??#cs"g|]}td||ddqS)rexactr.0kpR/var/www/html/django/DPS/env/lib/python3.9/site-packages/scipy/signal/_wavelets.py @zdaub..Ncs*g|]"}td||ddd|qS)rrg@rrrr r!r"Csz.Nr$)r&r'r(r)lenr0r*r-)hkNZasgnr r r!r\s rcsNtjtdtddt|d}|dt|dkr>td|dkrNtdtjd|d|f\}}t d}tj |d f}t |}tj |d f}t d||d |d} t d||dd |d} t dd||fd } t|| d | d <t|| d | d <t|| d | d<t|| d | d<| |9} tjd |d|>tdd|>} d | } d | }t| d \}}tt|d}t|dd|f}t|}|d kr| }| }d||i}t| d |d|d<d|>}|d| dd|<|d| d|d>d|<t| d|d|dd|<t| d|d|d|d>d|<dgtd|dD]}fddd D}d||>}|D]}d }t|D](}||dkr|d|d|>7}q||dd}t|d }t| d |f|}|||<|| ||d|<t| d|f||||d|<q|ql| | |fS)a Return (x, phi, psi) at dyadic points ``K/2**J`` from filter coefficients. .. deprecated:: 1.12.0 scipy.signal.cascade is deprecated in SciPy 1.12 and will be removed in SciPy 1.15. We recommend using PyWavelets instead. Parameters ---------- hk : array_like Coefficients of low-pass filter. J : int, optional Values will be computed at grid points ``K/2**J``. Default is 7. Returns ------- x : ndarray The dyadic points ``K/2**J`` for ``K=0...N * (2**J)-1`` where ``len(hk) = len(gk) = N+1``. phi : ndarray The scaling function ``phi(x)`` at `x`: ``phi(x) = sum(hk * phi(2x-k))``, where k is from 0 to N. psi : ndarray, optional The wavelet function ``psi(x)`` at `x`: ``phi(x) = sum(gk * phi(2x-k))``, where k is from 0 to N. `psi` is only returned if `gk` is not None. Notes ----- The algorithm uses the vector cascade algorithm described by Strang and Nguyen in "Wavelets and Filter Banks". It builds a dictionary of values and slices for quick reuse. Then inserts vectors into final vector at the end. rr rrzToo many levels.zToo few levels.Nrr$d)rrr;)rr)rrdtype01cs"g|]}D]}d||fq qS)z%d%sr )rxxyyZprevkeysr r!r"r#zcascade..)r&r'r(r)r<r*log2r,Zogridr+Zr_rZclipemptyZtakearangefloatrZargminabsoluter/r3dotr0int)r=Jr>nnkks2ZthkZgkZtgkZindx1Zindx2mxphipsiZlamvindsmZbitdicsteplevelZnewkeysZfackeynumposZpastphiiitempr rHr!rwsj%      &   &r@?TcCstjtdtddt| dtj|dtj|}td||}|rd|td|d8}|td|dtjd9}|S)a% Complex Morlet wavelet. .. deprecated:: 1.12.0 scipy.signal.morlet is deprecated in SciPy 1.12 and will be removed in SciPy 1.15. We recommend using PyWavelets instead. 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 -------- morlet2 : Implementation of Morlet wavelet, compatible with `cwt`. 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. Examples -------- >>> from scipy import signal >>> import matplotlib.pyplot as plt >>> M = 100 >>> s = 4.0 >>> w = 2.0 >>> wavelet = signal.morlet(M, s, w) >>> plt.plot(wavelet.real, label="real") >>> plt.plot(wavelet.imag, label="imag") >>> plt.legend() >>> plt.show() r r rrп)r&r'r(r)r*Zlinspacepiexp)MwsZcompleterUoutputr r r!r sG$ r cCstjtdtddt||S)a Return a Ricker wavelet, also known as the "Mexican hat wavelet". .. deprecated:: 1.12.0 scipy.signal.ricker is deprecated in SciPy 1.12 and will be removed in SciPy 1.15. We recommend using PyWavelets instead. It models the function: ``A * (1 - (x/a)**2) * exp(-0.5*(x/a)**2)``, where ``A = 2/(sqrt(3*a)*(pi**0.25))``. 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 r)r&r'r(r)_ricker)pointsar r r!r <s*r c Cstdtd|tjd}|d}td||dd}|d}d||}t| d|}|||}|S)Nr rg?rrcr)r*r+rfrKrg) rmrnAZwsqZvecZxsqmodgausstotalr r r!rljs  rlcCsxtjtdtddtd||dd}||}td||td|dtjd}td ||}|S) a Complex Morlet wavelet, designed to work with `cwt`. .. deprecated:: 1.12.0 scipy.signal.morlet2 is deprecated in SciPy 1.12 and will be removed in SciPy 1.15. We recommend using PyWavelets instead. Returns the complete version of morlet wavelet, normalised according to `s`:: exp(1j*w*x/s) * exp(-0.5*(x/s)**2) * pi**(-0.25) * sqrt(1/s) Parameters ---------- M : int Length of the wavelet. s : float Width parameter of the wavelet. w : float, optional Omega0. Default is 5 Returns ------- morlet : (M,) ndarray See Also -------- morlet : Implementation of Morlet wavelet, incompatible with `cwt` Notes ----- .. versionadded:: 1.4.0 This function was designed to work with `cwt`. Because `morlet2` returns an array of complex numbers, the `dtype` argument of `cwt` should be set to `complex128` for best results. Note the difference in implementation with `morlet`. The fundamental frequency of this wavelet in Hz is given by:: f = w*fs / (2*s*np.pi) where ``fs`` is the sampling rate and `s` is the wavelet width parameter. Similarly we can get the wavelet width parameter at ``f``:: s = w*fs / (2*f*np.pi) Examples -------- >>> import numpy as np >>> from scipy import signal >>> import matplotlib.pyplot as plt >>> M = 100 >>> s = 4.0 >>> w = 2.0 >>> wavelet = signal.morlet2(M, s, w) >>> plt.plot(abs(wavelet)) >>> plt.show() This example shows basic use of `morlet2` with `cwt` in time-frequency analysis: >>> t, dt = np.linspace(0, 1, 200, retstep=True) >>> fs = 1/dt >>> w = 6. >>> sig = np.cos(2*np.pi*(50 + 10*t)*t) + np.sin(40*np.pi*t) >>> freq = np.linspace(1, fs/2, 100) >>> widths = w*fs / (2*freq*np.pi) >>> cwtm = signal.cwt(sig, signal.morlet2, widths, w=w) >>> plt.pcolormesh(t, freq, np.abs(cwtm), cmap='viridis', shading='gouraud') >>> plt.show() r r rrrcrrdrer) r&r'r(r)r*rKrgrfr+)rhrjrirUwaveletrkr r r!r us M.r cKs*tjtdtddt||||fi|S)aR Continuous wavelet transform. .. deprecated:: 1.12.0 scipy.signal.cwt is deprecated in SciPy 1.12 and will be removed in SciPy 1.15. We recommend using PyWavelets instead. 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. The `wavelet` function is allowed to be complex. 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. dtype : data-type, optional The desired data type of output. Defaults to ``float64`` if the output of `wavelet` is real and ``complex128`` if it is complex. .. versionadded:: 1.4.0 kwargs Keyword arguments passed to wavelet function. .. versionadded:: 1.4.0 Returns ------- cwt: (M, N) ndarray Will have shape of (len(widths), len(data)). Notes ----- .. versionadded:: 1.4.0 For non-symmetric, complex-valued wavelets, the input signal is convolved with the time-reversed complex-conjugate of the wavelet data [1]. :: length = min(10 * width[ii], len(data)) cwt[ii,:] = signal.convolve(data, np.conj(wavelet(length, width[ii], **kwargs))[::-1], mode='same') References ---------- .. [1] S. Mallat, "A Wavelet Tour of Signal Processing (3rd Edition)", Academic Press, 2009. Examples -------- >>> import numpy as np >>> 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) .. note:: For cwt matrix plotting it is advisable to flip the y-axis >>> cwtmatr_yflip = np.flipud(cwtmatr) >>> plt.imshow(cwtmatr_yflip, extent=[-1, 1, 1, 31], cmap='PRGn', aspect='auto', ... vmax=abs(cwtmatr).max(), vmin=-abs(cwtmatr).max()) >>> plt.show() r r r)r&r'r(r)_cwt)datartwidthsrCkwargsr r r!r sPr c Ks|dur:t|d|dfi|jjdvr4tj}ntj}tjt|t|f|d}t|D]R\}}t d|t|g}t |||fi|ddd} t || dd||<q\|S) NrrZFDGrBrr$Zsame)mode) r*ZasarrayrCcharZ complex128Zfloat64rJr< enumerateminr.r) rvrtrwrCrxrkrYwidthr>Z wavelet_datar r r!rus$"ru)r?)rbrcT)rs)N)N)r&numpyr*Z scipy.linalgrZ scipy.specialrZ scipy.signalr__all__r(rrrr r rlr r rur r r r!s   L q T. V T