Ug>ddlZddlZddlmZddlmZddlmZgdZ dZ dZ dZ dd Z ddZdZdZddZddZddZdS)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 "tjtdztdtj}dkrt ddkr$d|dz }t j||gSdkr@|ddz }|d}|t jd|zd|zd|z d|z gzSdkrd|d z}d |d |zd z zd |d ||d z zzd z z }t j|}|ddz }t j d|z d|z z}t j ||z}dt j |z} ||z t j|d|z| z d|zd| zz dz|d| zz dzd| z dgzSdkrPdkr9fdtDddd} t j | } n;fdtDddd} t j | dz } t j ddgz}t j dg} tdz D]K} | | }d|||dz zz}dd|zz }||z}t|dkr||z }| d| gz} L|t j | z} | t j| z |dz} | jdddSt d)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??#c@g|]}tdz |z|dS)rexactr.0kps U/var/www/surfInsights/venv3-11/lib/python3.11/site-packages/scipy/signal/_wavelets.py zdaub..@s0???a!eai!,,,???NcLg|] }tdz |z|dd|zz !S)rrg@rrs r"r#zdaub..CsI$$$a!eai!,,,sAv5$$$r$z>A% %dd2hhcBh.G(H1(L Lgbkk DGGaK Wa"fS) * * WR#X   _2v"a"frk1r6AF?Q3F"$q2v+/1r61">??? ? R r66????eAhh???"EA!BB$$$$(($$$$(DbD*A!qB Iq!f  q  IqcNNq1u  Aa5DttDD1H-...DDLEBB1}}T\QH AA  N q MDDGG #s44R4y122 2r$ctjtdztdt |dz }dt |dzD}|dddt j|zS)a Return high-pass qmf filter from low-pass .. deprecated:: 1.12.0 scipy.signal.qmf is deprecated in SciPy 1.12 and will be removed in SciPy 1.15. We recommend using PyWavelets instead. Parameters ---------- hk : array_like Coefficients of high-pass filter. Returns ------- array_like High-pass filter coefficients. rrrrc*g|]}ddd|dzS)rr%rrr)rr s r"r#zqmf..ss' 7 7 7QbMM!a% 7 7 7r$Nr%)r(r)r*r+lenr2r,r/)hkNasgns r"rr\si( M$, 2qAAAA B! A 7 7%A,, 7 7 7D ddd8bhtnn $$r$ctjtdztdt |dz }|dt j|dzz krtd|dkrtdt jd|d|f\}}t j d}t j |d f}t|}t j |d f}t j d|z|z d |dz} t j d|z|z dzd |dz} t j dd||fd } t j|| d | d <t j|| d | d <t j|| d | d<t j|| d | d<| |z} t jd |d|zzt d|zz } d | z} d | z}t#| d \}}t jt j|dz }t j|dd|f}t j|}|d kr| }| }d||z i}t j| d |d|d<d|z}|d| dd|<|d| d|dz zd|<t j| d|d|dd|<t j| d|d|d|dz zd|<dgt/d|dzD]}fdd D}d||z z}|D]}d }t/|D]}||dkr|d|dz |z zz }||dd}t1|d }t j| d |f|}|||<|| ||zd|<t j| d|f||||zd|<|| | |fS)a Return (x, phi, psi) at dyadic points ``K/2**J`` from filter coefficients. .. deprecated:: 1.12.0 scipy.signal.cascade is deprecated in SciPy 1.12 and will be removed in SciPy 1.15. We recommend using PyWavelets instead. Parameters ---------- hk : array_like Coefficients of low-pass filter. J : int, optional Values will be computed at grid points ``K/2**J``. Default is 7. Returns ------- x : ndarray The dyadic points ``K/2**J`` for ``K=0...N * (2**J)-1`` where ``len(hk) = len(gk) = N+1``. phi : ndarray The scaling function ``phi(x)`` at `x`: ``phi(x) = sum(hk * phi(2x-k))``, where k is from 0 to N. psi : ndarray, optional The wavelet function ``psi(x)`` at `x`: ``phi(x) = sum(gk * phi(2x-k))``, where k is from 0 to N. `psi` is only returned if `gk` is not None. Notes ----- The algorithm uses the vector cascade algorithm described by Strang and Nguyen in "Wavelets and Filter Banks". It builds a dictionary of values and slices for quick reuse. Then inserts vectors into final vector at the end. r rrrzToo many levels.zToo few levels.Nrr%d)rrrG)rr)rrdtype01c(g|]}D] }d||fz S)z%d%srH)rxxyyprevkeyss r"r#zcascade..s/IIIII"6RH$IIIIr$)r(r)r*r+rIr,log2r.ogridr-r_rclipemptytakearangefloatrargminabsoluter1r6dotr2int)rJJrKnnkks2thkgktgkindx1indx2mxphipsilamvindsmbitdicsteplevelnewkeysfackeynumpospastphiiitemprXs @r"r r wsJ M$"$61EEEE B! A BQ +,,, A*+++Xbqb"1"f FB B %A,C RB %A,C GAFRKQU + +E GAFRK!ORQ / /E !Q1s##Agc5!$$AdGgc5!$$AdGgc5!$$AdGgc5!$$AdGGA !Q!q&\///16:A a%C a%C4\\FC )BKa(( ) )C !!!S& A B Avv 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)r(r)r*r+r,linspacepiexp)Mwscompleterooutputs r"r r sN M$/#5!DDDD QBFRUNAEBEM155A VBFQJ  F("&A''' bfTQT]##been44F Mr$cjtjtdztdt ||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)r(r)r*r+_ricker)pointsas r"r r <s1T M$/#5!DDDD 61  r$cdtjd|ztjdzzz }|dz}tjd||dz dz z }|dz}d||z z }tj| d|zz }||z|z}|S)Nrrg?rrr)r,r-rr_r) rrAwsqvecxsqmodgausstotals r"rrjs RWQU^^rud{ +,A Q$C )Av  &3,!!3 3C q&C sSy=C FC41s7# $ $E GeOE Lr$cRtjtdztdt jd||dz dz z }||z }t jd|z|zt jd|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 rrrrrrrr) r(r)r*r+r,r_rrr-)rrrrowaveletrs r"r r usZ M$"$61EEEE !Q1s7a-'A AAfR!VaZ  26$A+#6#66GG WQqS\\G #F Mr$c jtjtdztdt ||||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)r(r)r*r+_cwt)datarwidthsrRkwargss r"r r s=` M$, 2qAAAA gvu 7 7 7 77r$c |Gtj|d|dfi|jjdvr tj}n tj}tjt|t|f|}t|D]e\}}tj d|zt|g}tj |||fi|ddd} t|| d||<f|S) NrrFDGrQrr%same)mode) r,asarrayrRchar complex128float64r]rI enumerateminr0r) rrrrRrrrtwidthrK wavelet_datas r"rrs } :gga55f55 6 6 < AU J JMEEJE Xs6{{CII.e < < rs%!!!!!! J J J I2I2I2X%%%6nnnnbQQQQh+++\SSSSlQ8Q8Q8Q8h      r$