tKg>ddlZddlZddlmZddlmZddlmZgdZ dZ dZ dZ dd Z dd Zd Zd Zdd ZddZddZy)N)eig)comb)convolve)daubqmfcascademorletrickermorlet2cwtzvscipy.signal.%s is deprecated in SciPy 1.12 and will be removed in SciPy 1.15. We recommend using PyWavelets instead. c ,tjtdztdtj }|dkr t d|dk(r"d|dz }t j||gS|dk(r;|ddz }|d}|t jd|zd|zd|z d|z gzS|dk(rd|d z}d |d |zd z zd |d ||d z zzd z z }t j|}|ddz }t jd|z d|z z}t j||z}dt j|z} ||z t j|d|z| z d|zd| zz dz|d| zz dzd| z dgzS|dkrg|dkrGt|D cgc]} t|dz | z| dc} ddd} t j| } nOt|D cgc]} t|dz | z| dd| zz c} ddd} t j| dz } t jddg|z}t jdg} t|dz D]@} | | }d|||dz zz}dd|zz }||z}t|dkr||z }| d| gz} B|t j| z} | t j| z |dz} | j dddSt dcc} wcc} w)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??#)exactNg@zA% %d2hcBh.G(H1(L Lggbk GaK WWa"fS) * WWR#X  _2v"a"frk1r6AF?Q3F"$q2v+/1r61">?? ? R r66;Ah?ha!eai!,h?"EA!B ($"Qa!eai!,sAv5"$$(bD*A!qB IIq!f q  IIqcNq1uAa5DtDD1H-..DDLEBB1}T\QH A  N q MDG #ss4R4y12 21@$s ,L 3!Lctjtdztdt |dz }t |dzDcgc] }ddd|dz}}|dddt j|zScc}w)a Return high-pass qmf filter from low-pass .. deprecated:: 1.12.0 scipy.signal.qmf is deprecated in SciPy 1.12 and will be removed in SciPy 1.15. We recommend using PyWavelets instead. Parameters ---------- hk : array_like Coefficients of high-pass filter. Returns ------- array_like High-pass filter coefficients. rrrrrrrN)rrrr lenr'r!r$)hkNr5asgns r<rr\so( MM$, 2qA B! A*/A, 7,QbM!a% ,D 7 dd8bhhtn $$ 8sA4c htjtdztdt |dz }|dt j |dzz kDr td|dkr tdt jd|d|f\}}t jd}t j|d f}t|}t j|d f}t jd|z|z d |dz} t jd|z|z dzd |dz} t jdd||fd } t j|| d | d <t j|| d | d <t j|| d | d<t j|| d | d<| |z} t jd |d|zzt d|zz } d | z} d | z}t#| d \}}t j$t j&|dz }t j(|dd|f}t j*|}|d kr| }| }d||z i}t j,| d |d|d<d|z}|d| dd|<|d| d|dz zd|<t j,| d|d|dd|<t j,| d|d|d|dz zd|<dg}t/d|dzD]}d Dcgc]}|D] }d||fz }}}d||z z}|D]}d }t/|D]}||dk(s |d|dz |z zz }||dd}t1|d }t j,| d |f|} | ||<| | ||zd|<t j,| d|f||||zd|<|}| | |fScc}}w)a Return (x, phi, psi) at dyadic points ``K/2**J`` from filter coefficients. .. deprecated:: 1.12.0 scipy.signal.cascade is deprecated in SciPy 1.12 and will be removed in SciPy 1.15. We recommend using PyWavelets instead. Parameters ---------- hk : array_like Coefficients of low-pass filter. J : int, optional Values will be computed at grid points ``K/2**J``. Default is 7. Returns ------- x : ndarray The dyadic points ``K/2**J`` for ``K=0...N * (2**J)-1`` where ``len(hk) = len(gk) = N+1``. phi : ndarray The scaling function ``phi(x)`` at `x`: ``phi(x) = sum(hk * phi(2x-k))``, where k is from 0 to N. psi : ndarray, optional The wavelet function ``psi(x)`` at `x`: ``phi(x) = sum(gk * phi(2x-k))``, where k is from 0 to N. `psi` is only returned if `gk` is not None. Notes ----- The algorithm uses the vector cascade algorithm described by Strang and Nguyen in "Wavelets and Filter Banks". It builds a dictionary of values and slices for quick reuse. Then inserts vectors into final vector at the end. rrrrzToo many levels.zToo few levels.Nrrd)rrr>)rr)rrdtype01z%d%s)rrrr r?r!log2r#ogridr"r_rclipemptytakearangefloatrargminabsoluter&r+dotr'int)!r@JrAnnkks2thkgktgkindx1indx2mxphipsilamvindsmbitdicstepprevkeyslevelxxyynewkeysfackeynumpospastphiiitemps! r<rrwsJ MM$"$61E B! A BQ +,, A*++XXbqb"1"f FB B %%A,C RB %%A,C GGAFRKQU +E GGAFRK!ORQ /E !Q1s#Aggc5!$AdGggc5!$AdGggc5!$AdGggc5!$AdGGA !Q!q&\/16:A a%C a%C4\FC ))BKKa( )C !S& A B Av BS1r6]F&&4&+.F3K 6D+C$K &s Cq1u&&4&+.C$K "qws >> from scipy import signal >>> import matplotlib.pyplot as plt >>> M = 100 >>> s = 4.0 >>> w = 2.0 >>> wavelet = signal.morlet(M, s, w) >>> plt.plot(wavelet.real, label="real") >>> plt.plot(wavelet.imag, label="imag") >>> plt.legend() >>> plt.show() r rrrп)rrrr r!linspacepiexp)Mwscompleter`outputs r<r r sN MM$/#5!D QBFRUUNAEBEEM15A VVBFQJ F"&&A'' bffTQT]#beeen44F Mc`tjtdztdt ||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 rr)rrrr _ricker)pointsas r<r r <s'T MM$/#5!D 61 rcdtjd|ztjdzzz }|dz}tjd||dz dz z }|dz}d||z z }tj| d|zz }||z|z}|S)Nrrg?r?r)r!r"ryrPrz) rrAwsqvecxsqmodgausstotals r<rrjs RWWQU^ruud{ +,A Q$C ))Av &3,!!3 3C q&C sSy=C FFC41s7# $E GeOE Lrc`tjtdztdt j d||dz dz z }||z }t j d|z|zt j d|dzzztjdzz}t jd |z |z}|S) a Complex Morlet wavelet, designed to work with `cwt`. .. deprecated:: 1.12.0 scipy.signal.morlet2 is deprecated in SciPy 1.12 and will be removed in SciPy 1.15. We recommend using PyWavelets instead. Returns the complete version of morlet wavelet, normalised according to `s`:: exp(1j*w*x/s) * exp(-0.5*(x/s)**2) * pi**(-0.25) * sqrt(1/s) Parameters ---------- M : int Length of the wavelet. s : float Width parameter of the wavelet. w : float, optional Omega0. Default is 5 Returns ------- morlet : (M,) ndarray See Also -------- morlet : Implementation of Morlet wavelet, incompatible with `cwt` Notes ----- .. versionadded:: 1.4.0 This function was designed to work with `cwt`. Because `morlet2` returns an array of complex numbers, the `dtype` argument of `cwt` should be set to `complex128` for best results. Note the difference in implementation with `morlet`. The fundamental frequency of this wavelet in Hz is given by:: f = w*fs / (2*s*np.pi) where ``fs`` is the sampling rate and `s` is the wavelet width parameter. Similarly we can get the wavelet width parameter at ``f``:: s = w*fs / (2*f*np.pi) Examples -------- >>> import numpy as np >>> from scipy import signal >>> import matplotlib.pyplot as plt >>> M = 100 >>> s = 4.0 >>> w = 2.0 >>> wavelet = signal.morlet2(M, s, w) >>> plt.plot(abs(wavelet)) >>> plt.show() This example shows basic use of `morlet2` with `cwt` in time-frequency analysis: >>> t, dt = np.linspace(0, 1, 200, retstep=True) >>> fs = 1/dt >>> w = 6. >>> sig = np.cos(2*np.pi*(50 + 10*t)*t) + np.sin(40*np.pi*t) >>> freq = np.linspace(1, fs/2, 100) >>> widths = w*fs / (2*freq*np.pi) >>> cwtm = signal.cwt(sig, signal.morlet2, widths, w=w) >>> plt.pcolormesh(t, freq, np.abs(cwtm), cmap='viridis', shading='gouraud') >>> plt.show() r rrrrrrvrwr) rrrr r!rPrzryr")r{r}r|r`waveletrs r<r r usZ MM$"$61E !Q1s7a-'A AAffR!VaZ 266$A+#66GG WWQqS\G #F Mrc ftjtdztdt ||||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 rr)rrrr _cwt)datarwidthsrGkwargss r<r r s0` MM$, 2qA gvu 7 77rc |Wtj|d|dfi|jjdvrtj}ntj }tj t|t|f|}t|D]\\}}tjd|zt|g}tj|||fi|ddd} t|| d||<^|S) NrrFDGrFrrsame)mode) r!asarrayrGchar complex128float64rNr? enumerateminr%r) rrrrGrrrewidthrA wavelet_datas r<rrs } ::ga5f5 6 < < A AU JMMEJJE XXs6{CI.e rsX! J I2X%6nbQh+\SlQ8h r