KhwSrSSKJrJrJrJrJr SSKJrJ r /SQr \ \4r S Sjr \"\ SS9S S j5r\"\ SS9S S j5r\ "S5SS j5r\ "S5SS j5rg)z+ Discrete Fourier Transforms - _helper.py )integeremptyarangeasarrayroll)array_function_dispatch set_module)fftshift ifftshiftfftfreqrfftfreqNcU4$N)xaxess C/var/www/html/env/lib/python3.13/site-packages/numpy/fft/_helper.py_fftshift_dispatcherrs 4Kz numpy.fft)modulecV[U5nUc=[[UR55nURVs/sHo"S-PM nnOI[ U[ 5(aURUS-nO!UVs/sHo@RUS-PM nn[XU5$s snfs snf)a Shift the zero-frequency component to the center of the spectrum. This function swaps half-spaces for all axes listed (defaults to all). Note that ``y[0]`` is the Nyquist component only if ``len(x)`` is even. Parameters ---------- x : array_like Input array. axes : int or shape tuple, optional Axes over which to shift. Default is None, which shifts all axes. Returns ------- y : ndarray The shifted array. See Also -------- ifftshift : The inverse of `fftshift`. Examples -------- >>> import numpy as np >>> freqs = np.fft.fftfreq(10, 0.1) >>> freqs array([ 0., 1., 2., ..., -3., -2., -1.]) >>> np.fft.fftshift(freqs) array([-5., -4., -3., -2., -1., 0., 1., 2., 3., 4.]) Shift the zero-frequency component only along the second axis: >>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3) >>> freqs array([[ 0., 1., 2.], [ 3., 4., -4.], [-3., -2., -1.]]) >>> np.fft.fftshift(freqs, axes=(1,)) array([[ 2., 0., 1.], [-4., 3., 4.], [-1., -3., -2.]]) rtuplerangendimshape isinstance integer_typesrrrdimshiftaxs rr r s\  A |U166]#%&WW-WcW- D- ( ( ",01Db!D1 $  .2s B!8B&c\[U5nUc>[[UR55nURVs/sHo"S-*PM nnOK[ U[ 5(aURUS-*nO"UVs/sHo@RUS-*PM nn[XU5$s snfs snf)a The inverse of `fftshift`. Although identical for even-length `x`, the functions differ by one sample for odd-length `x`. Parameters ---------- x : array_like Input array. axes : int or shape tuple, optional Axes over which to calculate. Defaults to None, which shifts all axes. Returns ------- y : ndarray The shifted array. See Also -------- fftshift : Shift zero-frequency component to the center of the spectrum. Examples -------- >>> import numpy as np >>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3) >>> freqs array([[ 0., 1., 2.], [ 3., 4., -4.], [-3., -2., -1.]]) >>> np.fft.ifftshift(np.fft.fftshift(freqs)) array([[ 0., 1., 2.], [ 3., 4., -4.], [-3., -2., -1.]]) rrr s rr r MsH  A |U166]#()0!80 D- ( (''$-1$%/34t772;!#$t4 $  15s B$:B)c[U[5(d [S5eSX-- n[U[US9nUS- S-S-n[ SU[US9nXdSU&[ US-*S[US9nXtUS&XC-$) a Return the Discrete Fourier Transform sample frequencies. The returned float array `f` contains the frequency bin centers in cycles per unit of the sample spacing (with zero at the start). For instance, if the sample spacing is in seconds, then the frequency unit is cycles/second. Given a window length `n` and a sample spacing `d`:: f = [0, 1, ..., n/2-1, -n/2, ..., -1] / (d*n) if n is even f = [0, 1, ..., (n-1)/2, -(n-1)/2, ..., -1] / (d*n) if n is odd Parameters ---------- n : int Window length. d : scalar, optional Sample spacing (inverse of the sampling rate). Defaults to 1. device : str, optional The device on which to place the created array. Default: ``None``. For Array-API interoperability only, so must be ``"cpu"`` if passed. .. versionadded:: 2.0.0 Returns ------- f : ndarray Array of length `n` containing the sample frequencies. Examples -------- >>> import numpy as np >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5], dtype=float) >>> fourier = np.fft.fft(signal) >>> n = signal.size >>> timestep = 0.1 >>> freq = np.fft.fftfreq(n, d=timestep) >>> freq array([ 0. , 1.25, 2.5 , ..., -3.75, -2.5 , -1.25]) n should be an integer?)devicerrdtyper(N)rr ValueErrorrintr)ndr(valresultsNp1p2s rr r }sV a ' '122 -CAs6*G 1q1 A 1C /BBQK !Q$#f 5BABK =rc[U[5(d [S5eSX-- nUS-S-n[SU[US9nXS-$)a Return the Discrete Fourier Transform sample frequencies (for usage with rfft, irfft). The returned float array `f` contains the frequency bin centers in cycles per unit of the sample spacing (with zero at the start). For instance, if the sample spacing is in seconds, then the frequency unit is cycles/second. Given a window length `n` and a sample spacing `d`:: f = [0, 1, ..., n/2-1, n/2] / (d*n) if n is even f = [0, 1, ..., (n-1)/2-1, (n-1)/2] / (d*n) if n is odd Unlike `fftfreq` (but like `scipy.fftpack.rfftfreq`) the Nyquist frequency component is considered to be positive. Parameters ---------- n : int Window length. d : scalar, optional Sample spacing (inverse of the sampling rate). Defaults to 1. device : str, optional The device on which to place the created array. Default: ``None``. For Array-API interoperability only, so must be ``"cpu"`` if passed. .. versionadded:: 2.0.0 Returns ------- f : ndarray Array of length ``n//2 + 1`` containing the sample frequencies. Examples -------- >>> import numpy as np >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5, -3, 4], dtype=float) >>> fourier = np.fft.rfft(signal) >>> n = signal.size >>> sample_rate = 100 >>> freq = np.fft.fftfreq(n, d=1./sample_rate) >>> freq array([ 0., 10., 20., ..., -30., -20., -10.]) >>> freq = np.fft.rfftfreq(n, d=1./sample_rate) >>> freq array([ 0., 10., 20., 30., 40., 50.]) r&r'rr)rr*)rrr,rr-)r.r/r(r0r2r1s rr r sNd a ' '122 qs)C 1qAQV4G =rr)r'N)__doc__ numpy._corerrrrrnumpy._core.overridesrr __all__r-rrr r r r rrrr:s>=E ;g -kB6 C6 r-kB, C, ^ K33l K66r