`i5&dZddlZddlZddlmZejddddd Zd Zejd d d dddZ d!dZ ejddddddZ dZ ejdd ddddZ d"dZd ZdS)#a Wavelet-generating functions. Some of the functions defined here were ported directly from CuSignal under terms of the MIT license, under the following notice: Copyright (c) 2019-2023 NVIDIA CORPORATION & AFFILIATES. All rights reserved. Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. N)convolvez raw T coefzT outputzg const int sign { ( i & 1 ) ? -1 : 1 }; output = ( coef[_ind.size() - ( i + 1 )] ) * sign; _qmf_kernel)z -std=c++11)optionscftj|}t|t|S)z Return high-pass qmf filter from low-pass Parameters ---------- hk : array_like Coefficients of high-pass filter. size)cupyasarrayrlen)hks p/home/jaya/work/projects/VOICE-AGENT/VIET/agent-env/lib/python3.11/site-packages/cupyx/scipy/signal/_wavelets.pyqmfr.s, b  B rB ( ( ((z#float64 w, float64 s, bool completezcomplex128 outputa const double x { start + delta * i }; thrust::complex temp { exp( thrust::complex( 0, w * x ) ) }; if ( complete ) { temp -= exp( -0.5 * ( w * w ) ); } output = temp * exp( -0.5 * ( x * x ) ) * pow( M_PI, -0.25 ) _morlet_kernelzconst double end { s * 2.0 * M_PI }; const double start { -s * 2.0 * M_PI }; const double delta { ( end - start ) / ( _ind.size() - 1 ) };)r loop_prep@?Tc(t||||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 -------- cupyx.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. r)r)Mwscompletes r morletrSsf !Qq 1 1 11rz float64 az float64 totalz const double vec { i - ( _ind.size() - 1.0 ) * 0.5 }; const double xsq { vec * vec }; const double mod { 1 - xsq / wsq }; const double gauss { exp( -xsq / ( 2.0 * wsq ) ) }; total = A * mod * gauss; _ricker_kernelz[const double A { 2.0 / ( sqrt( 3 * a ) * pow( M_PI, 0.25 ) ) }; const double wsq { a * a };c>t|t|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 -------- >>> import cupyx.scipy.signal >>> import cupy as cp >>> import matplotlib.pyplot as plt >>> points = 100 >>> a = 4.0 >>> vec2 = cupyx.scipy.signal.ricker(points, a) >>> print(len(vec2)) 100 >>> plt.plot(cupy.asnumpy(vec2)) >>> plt.show() r)rint)pointsas r rickerrsL !#f++ . . ..rzfloat64 w, float64 sz const double x { ( i - ( _ind.size() - 1.0 ) * 0.5 ) / s }; thrust::complex temp { exp( thrust::complex( 0, w * x ) ) }; output = sqrt( 1 / s ) * temp * exp( -0.5 * ( x * x ) ) * pow( M_PI, -0.25 ) c@t||t|S)as 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 ----- 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 -------- >>> from cupyx.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: >>> from cupyx.scipy import signal >>> import matplotlib.pyplot as plt >>> 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)_morlet2_kernelr)rrrs r morlet2r$s H 1ac!ff - - --rc tj|ddjjdvr tj}n tj}tjt|t|g|}t|D]\}}tj dt|zt|g}tj ||t|ddd}t||d||ddf<|S) a Continuous wavelet transform. Performs a continuous wavelet transform on `data`, using the `wavelet` function. A CWT performs a convolution with `data` using the `wavelet` function, which is characterized by a width parameter and length parameter. Parameters ---------- data : (N,) ndarray data on which to perform the transform. wavelet : function Wavelet function, which should take 2 arguments. The first argument is the number of points that the returned vector will have (len(wavelet(length,width)) == length). The second is a width parameter, defining the size of the wavelet (e.g. standard deviation of a gaussian). See `ricker`, which satisfies these requirements. widths : (M,) sequence Widths to use for transform. Returns ------- cwt: (M, N) ndarray Will have shape of (len(widths), len(data)). Notes ----- :: length = min(10 * width[ii], len(data)) cwt[ii,:] = cupyx.scipy.signal.convolve(data, wavelet(length, width[ii]), mode='same') Examples -------- >>> import cupyx.scipy.signal >>> import cupy as cp >>> import matplotlib.pyplot as plt >>> t = cupy.linspace(-1, 1, 200, endpoint=False) >>> sig = cupy.cos(2 * cupy.pi * 7 * t) + cupyx.scipy.signal.gausspulse(t - 0.4, fc=2) >>> widths = cupy.arange(1, 31) >>> cwtmatr = cupyx.scipy.signal.cwt(sig, cupyx.scipy.signal.ricker, widths) >>> plt.imshow(abs(cupy.asnumpy(cwtmatr)), extent=[-1, 1, 31, 1], cmap='PRGn', aspect='auto', vmax=abs(cwtmatr).max(), vmin=-abs(cwtmatr).max()) >>> plt.show() FDG)dtype Nsame)mode)r r r(char complex128float64emptyr enumeratenpminrconjr) datawaveletwidthsr(outputindwidthN wavelet_datas r cwtr=sf |GGAqMM""(-66  ZVc$ii0 > > >F''CC U FBUOSYY/ 0 0yCJJ!7!7882> !$ 6BBBsAAAv Mr)rrT)r!)__doc__r numpyr2cupyx.scipy.signal._signaltoolsrElementwiseKernelrrrrrrr#r$r=rr rCsd4 444444%d$      ) ) )(')  N#.32323232l(' #$&/&/&/R)$( $D.D.D.D.N>>>>>r