h6lddlZddlmZddlmZddlmZgdZdZ dZ dd Z dd Z dZ ddZddZdS)N)eigcomb)convolve)daubqmfcascademorletrickermorlet2cwtc tj}dkrtddkr$d|dz }tj||gSdkr@|ddz }|d}|tjd|zd|zd|z d|z gzSdkrd|dz}d|d |zd z zd |d ||d z zzd z z }tj|}|ddz }tjd|z d|z z}tj||z}dtj|z} ||z tj|d|z| z d|zd| zz dz|d| zz dzd| z dgzSd krPd kr9fd t Dddd} tj| } n;fdt Dddd} tj| dz } tjddgz}tjdg} t dz D]K} | | }d|||dz zz}dd|zz }||z}t|dkr||z }| d| gz} L|tj| z} | tj | z |dz} | j dddStd)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??#c@g|]}tdz |z|dS)rexactr.0kps R/var/www/html/Sam_Eipo/venv/lib/python3.11/site-packages/scipy/signal/_wavelets.py zdaub..2s0???a!eai!,,,???NcLg|] }tdz |z|dd|zz !S)rrg@rrs r r!zdaub..5sI$$$a!eai!,,,sAv5$$$r"z>A% %dd2hhcBh.G(H1(L Lgbkk DGGaK Wa"fS) * * WR#X   _2v"a"frk1r6AF?Q3F"$q2v+/1r61">??? ? R r66????eAhh???"EA!BB$$$$(($$$$(DbD*A!qB Iq!f  q  IqcNNq1u  Aa5DttDD1H-...DDLEBB1}}T\QH AA  N q MDDGG #s44R4y122 2r"ct|dz }dt|dzD}|dddtj|zS)z Return high-pass qmf filter from low-pass Parameters ---------- hk : array_like Coefficients of high-pass filter. Returns ------- array_like High-pass filter coefficients. rc*g|]}ddd|dzS)rr#rrr)rrs r r!zqmf..^s' 7 7 7QbMM!a% 7 7 7r"Nr#)lenr,r&r))hkNasgns r rrNsM B! A 7 7%A,, 7 7 7D ddd8bhtnn $$r"cnt|dz }|dtj|dzz krtd|dkrtdtjd|d|f\}}tjd}tj|df}t|}tj|df}tjd|z|z d|dz} tjd|z|z dzd|dz} tj dd||fd } tj || d| d <tj || d| d <tj || d| d <tj || d| d <| |z} tj d|d|zztd|zz } d| z} d| z}t| d \}}tjtj|dz }tj|dd|f}tj|}|dkr| }| }d||z i}tj| d |d|d<d|z}|d| dd|<|d| d|dz zd|<tj| d |d|dd|<tj| d |d|d|dz zd|<dgt'd|dzD]}fdd D}d||z z}|D]}d}t'|D]}||dkr|d|dz |z zz }||dd}t)|d}tj| d|f|}|||<|| ||zd|<tj| d|f||||zd|<|| | |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)rrrA)rr)rrdtype01c(g|]}D] }d||fz S)z%d%srB)rxxyyprevkeyss r r!zcascade..s/IIIII"6RH$IIIIr")rCr&log2r(ogridr'r_rclipemptytakearangefloatrargminabsoluter+r0dotr,int)rDJrEnnkks2thkgktgkindx1indx2mxphipsilamvindsmbitdicsteplevelnewkeysfackeynumpospastphiiitemprRs @r r r bs@ 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) >>> plt.show() rrп)r&linspacepiexp)Mwscompleterioutputs r r r s@ QBFRUNAEBEM155A VBFQJ  F("&A''' bfTQT]##been44F Mr"cdtjd|ztjdzzz }|dz}tjd||dz dz z }|dz}d||z z }tj| d|zz }||z|z}|S)a Return a Ricker wavelet, also known as the "Mexican hat wavelet". 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() rrg?rr|r)r&r'rrYr) pointsaAwsqvecxsqmodgausstotals r r r sJ RWQU^^rud{ +,A Q$C )Av  &3,!!3 3C q&C sSy=C FC41s7# $ $E GeOE Lr"c tjd||dz dz z }||z }tjd|z|ztjd|dzzztjdzz}tjd|z |z}|S)aR Complex Morlet wavelet, designed to work with `cwt`. Returns the complete version of morlet wavelet, normalised according to `s`:: exp(1j*w*x/s) * exp(-0.5*(x/s)**2) * pi**(-0.25) * sqrt(1/s) Parameters ---------- M : int Length of the wavelet. s : float Width parameter of the wavelet. w : float, optional Omega0. Default is 5 Returns ------- morlet : (M,) ndarray See Also -------- morlet : Implementation of Morlet wavelet, incompatible with `cwt` Notes ----- .. versionadded:: 1.4.0 This function was designed to work with `cwt`. Because `morlet2` returns an array of complex numbers, the `dtype` argument of `cwt` should be set to `complex128` for best results. Note the difference in implementation with `morlet`. The fundamental frequency of this wavelet in Hz is given by:: f = w*fs / (2*s*np.pi) where ``fs`` is the sampling rate and `s` is the wavelet width parameter. Similarly we can get the wavelet width parameter at ``f``:: s = w*fs / (2*f*np.pi) Examples -------- >>> import numpy as np >>> from scipy import signal >>> import matplotlib.pyplot as plt >>> M = 100 >>> s = 4.0 >>> w = 2.0 >>> wavelet = signal.morlet2(M, s, w) >>> plt.plot(abs(wavelet)) >>> plt.show() This example shows basic use of `morlet2` with `cwt` in time-frequency analysis: >>> t, dt = np.linspace(0, 1, 200, retstep=True) >>> fs = 1/dt >>> w = 6. >>> sig = np.cos(2*np.pi*(50 + 10*t)*t) + np.sin(40*np.pi*t) >>> freq = np.linspace(1, fs/2, 100) >>> widths = w*fs / (2*freq*np.pi) >>> cwtm = signal.cwt(sig, signal.morlet2, widths, w=w) >>> plt.pcolormesh(t, freq, np.abs(cwtm), cmap='viridis', shading='gouraud') >>> plt.show() rr|rrr~rr)r&rYrrr')rrrriwaveletrs r r r Fs~P !Q1s7a-'A AAfR!VaZ  26$A+#6#66GG WQqS\\G #F Mr"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) a 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. 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() NrrFDGrKrr#same)mode) r&asarrayrLchar complex128float64rWrC enumerateminr*r) datarwidthsrLkwargsrrnwidthrE wavelet_datas r r r sX } :gga55f55 6 6 < AU J JMEEJE Xs6{{CII.e < < rs!!!!!! J J JB2B2B2J%%%(ggggTHHHHV,,,^LLLL^WWWWWWr"