Np fft fft doc. Input array, can be complex.


Np fft fft doc fftfreq# fft. The reason for this lies in the Jan 7, 2025 · jax. Parameters: x array_like. ifft函数对X3_fft进行逆傅里叶变换,得到X3,即两个信号的乘积的时域表示。因为傅里叶变换是线性变换,所以X3和X1、X2的乘积的时域表示是一样的。最后,使用np. Default is “backward”. fft2(a, s=None, axes=(-2, -1), norm=None) [source] Compute the 2-dimensional discrete Fourier Transform This fu Numpy 1. Parameters: a array_like. 0) ¶ Return the Discrete Fourier Transform sample frequencies. 0,设备=无) [source] 返回离散傅里叶变换采样频率。 返回的浮点数组 f 包含频率仓中心,单位为采样间隔的周期数(起始位置为零)。 例如,如果采样间隔以秒为单位,则频率单位为周期/秒。 Jan 8, 2018 · numpy. Jan 20, 2024 · The function rfft calculates the FFT of a real sequence and outputs the complex FFT coefficients \(y[n]\) for only half of the frequency range. abs(A) is its amplitude spectrum and np. fft. 2k次,点赞4次,收藏13次。本文介绍了如何在Python的NumPy库中使用快速傅里叶变换(FFT)进行离散傅里叶变换,包括fft函数的参数解释,实信号到复数序列的转换,以及如何从频域数据中提取主要频率。实例演示了如何对余弦信号进行 Jan 7, 2025 · 说明 FFT(快速傅里叶变换)是指一种可以有效计算离散傅里叶变换 (DFT) 的方法,通过利用计算项中的对称性。当 *n* 为 2 的幂时,对称性最高,因此对于这些大小,变换效率最高。 Fourier analysis is a method for expressing a function as a sum of periodic components, and for recovering the signal from those components. rfftfreq (n, d = 1. For a general description of the algorithm and Jan 11, 2025 · Notes. fft (a, n = None, axis =-1, norm = None) [source] # Compute the one-dimensional discrete Fourier Transform. ifftshift¶ numpy. axisint 或 shape tuple,可选 Aug 21, 2024 · numpy. 1 day ago · numpy. fftfreq(n,d=1. fftshift fft. fftn# scipy. fftfreq¶ scipy. This function computes the 1-D n-point discrete Fourier Transform (DFT) with the efficient Fast Fourier Transform (FFT) algorithm . zoom_fft (x, fn, m = None, *, fs = 2, endpoint = False, axis =-1) [源代码] # 仅计算频率范围在 fn 内的 x 的 DFT。 参数: x array 要变换的信号。 fn array_like 长度为 2 的序列 [f1, f2],给出频率范围;或者一个标量,表示假定范围为 [0, fn]。m int, 可选 Nov 18, 2023 · overwrite_x bool, optional. signal. Input array, can be Dec 14, 2024 · numpy. fftshift (x, axes=None) [source] ¶ Shift the zero-frequency component to the center of the spectrum. ifft (a, n = None, axis =-1, norm = None, out = None) [source] # Compute the one-dimensional inverse discrete Fourier Transform. fft(a, n=None, axis=-1, norm=None) [source] ¶ Compute the one-dimensional discrete Fourier Transform. By default, the transform is computed over the last two axes of the input Jul 29, 2022 · scipy. By default, the transform is computed over the last two axes of the input Nov 21, 2023 · 文章浏览阅读3. If True, the contents of x can be destroyed; the default is False. fft fft. Jan 7, 2025 · 注释 FFT(快速傅里叶变换)是指可以通过利用计算项中的对称性来有效计算离散傅里叶变换(DFT)的方法。当 n 是 2 的幂时,对称性最高,因此对于这些大小,变换效率最高。 对于可分解性较差的大小,scipy. rfft (a, n=None, axis=-1, norm=None) [source] ¶ Compute the one-dimensional discrete Fourier Transform for real input. Input array, can be Jun 10, 2017 · The routine np. If n is smaller than the length of the Dec 14, 2024 · numpy. rfft (下图) 输出的则是去掉对称后更接近理解中的频域信息的序列。 同样的,因为因为二者的采样率皆相同,故 rfft 的 Dec 19, 2019 · scipy. This function computes the N-dimensional discrete Fourier Transform over any number of axes in an M-dimensional real array by means of the Fast Fourier Transform (FFT). doc 立即下载 快速傅立叶变换(FFT)是数字信号处理领域中一种至关重要的算法,它极大地提高了离散傅立叶变换(DFT)的计算效率。DFT是连续傅立叶变换在离散时间序列上的应用,然而,由于DFT的计算复杂度为O(N^2 Dec 14, 2024 · The routine np. get_shapeK_loc (), dtype = np. ihfft (a, n = None, axis =-1, norm = None, out = None) [source] # Compute the inverse FFT of a signal that has Hermitian symmetry. Jan 11, 2025 · The function rfft calculates the FFT of a real sequence and outputs the complex FFT coefficients \(y[n]\) for only half of the frequency range. The output, analogously to fft, contains the term for zero frequency in the low-order corner of the transformed axes, the positive frequency terms in the Jun 27, 2024 · 在这个fft算法中,将一个实数序列x(n)映射到一个复数序列X(n)上,输出的复数序列代表了输入实数序列的频域表示。其中每个复数X(k)由实部和虚部组成,复数的虚部表示了输入信号中存在的一些非实部成分,例如一些高频噪声或者相位信息。但我取的时间是0-0. ifftshift# fft. 10官方教程,w3cschool。 Notes fft2 is just fftn with a different default for axes. Oct 18, 2015 · numpy. Parameters Oct 18, 2015 · numpy. This function computes the inverse of the one-dimensional n-point discrete Fourier transform computed by fft. Jun 24, 2024 · fft# scipy. Aug 2, 2021 · scipy. 2 days ago · numpy. rfftfreq# fft. fft2(a, s=None, axes=(-2, -1), norm=None) [source] ¶ Compute the 2-dimensional discrete Fourier Transform. JAX implementation of numpy. The Dec 14, 2024 · numpy. ifftshift(A) 则会撤消该移 2 days ago · then the FFT routine will behave in a numpy-compatible way: the single input array can either be real, in which case the imaginary part is assumed to be zero, or complex. Axis over which to compute the FFT. rfft¶ numpy. If it is larger, the input is padded with zeros. To get an odd number of output points, n must be specified, for instance as 2*m-1 in the typical case, Jan 13, 2025 · numpy. Parameters:. In other words, ifft(fft(a)) == a to within numerical accuracy. If you specify an n such that a must be zero-padded or truncated, the extra/removed values will be added/removed at high frequencies. fftshift(A) 会移动变换及其频率以将零频率分量置于中间,而 np. fftn (a, s = None, axes = None, norm = None, out = None) [source] # 计算 N 维离散傅里叶变换。 此函数利用快速傅里叶变换 (FFT) 计算 M 维数组中任意数量轴上 Mar 21, 2023 · The routine np. See numpy. When both the function and its Fourier transform are replaced with discretized counterparts, it is called the discrete Fourier transform (DFT). This function computes the n -dimensional discrete Fourier Transform over any axes in an M -dimensional array by 1 day ago · 此函数通过快速傅里叶变换 (FFT) 计算 *M* 维数组中任意轴上的 *n* 维离散傅里叶变换。 默认情况下,变换是在输入数组的最后两个轴上计算的,即二维 FFT。 输出的形状(每个 傅里叶分析从根本上讲是一种将函数表示为周期性分量之和并从这些分量恢复函数的方法。 当函数及其傅里叶变换都被离散化的对应物代替时,称为离散傅里叶变换(DFT)。 DFT 已成为数 4 days ago · numpy. fft2¶ numpy. fft(). Dec 14, 2024 · fft. fft¶ fft. complex128) If we do not have the array where to put the result we can do: a_fft = o. abs(A)**2 is its power spectrum. ifftshift (x, axes = None) [source] # fftshift 的逆函数。 虽然对于偶数长度的 x 来说是相同的,但对于奇数长度的 x,这两个函数相差一个样本。 参数: x array_like 输入数组。 axes int 或形状元组,可选 计算的轴。默认为 None,表示对所有轴 Dec 3, 2024 · 实验4 快速傅立叶变换(FFT). ihfft# fft. fft(a,n=无,轴=-1,范数=无,输出=无) [source] 计算一维离散傅里叶变换。 该函数使用高效的快速傅里叶变换 (FFT) 算法 [CT] 计算一维 n 点离散傅里叶变换 (DFT)。 Parameters: aarray_like 输入数组,可以是复杂的。 nint, optional 输出的变换 Dec 14, 2024 · numpy. fft函数对X1和X2进行傅里叶变换,得到它们的频率域表示X1_fft和X2_fft。 5 days ago · numpy. fft2# fft. axisint 或 shape tuple,可选 要计算的轴。默认为无,即移动所有轴。 Dec 7, 2023 · np. By default, the transform is computed over the last two axes of Dec 14, 2024 · The routine np. angle(A). Jan 7, 2025 · FFT 输入信号本质上是截断的。这种截断可以建模为无限信号与矩形窗函数的乘积。在频域中,这种乘积变成信号频谱与窗函数频谱的卷积,形式为 \(\sin(x)/x\)。这种卷积是称为频谱泄漏的效应的原因(请参见 [WPW] )。使用专用窗函数对信号进行加窗有助于减轻频谱泄漏。 Aug 21, 2024 · Normalization mode (see numpy. fft# jax. When the input a 2 days ago · 例程 np. n Dec 14, 2024 · numpy. fft (a, n=None, axis=-1, norm=None) [source] ¶ Compute the one-dimensional discrete Fourier Transform. Although identical for even-length x, the functions differ by one sample for odd-length x. fftn (x, s = None, axes = None, norm = None, overwrite_x = False, workers = None, *, plan = None) [source] # Compute the N-D discrete Fourier Transform. fftshift(x, axes=None)[source]将零频分量移至频谱的中心。 此函数交换列出的所有轴的半空间(默认为全部)。请注意,仅当 len(x) 为偶数时, y[0] 才是奈奎斯特组件。 Parameters: xarray_like Input array. Aug 23, 2018 · Parameters: a: array_like. numpy. 0, device = None) [source] # Return the Discrete Fourier Transform sample frequencies. Nov 4, 2021 · WARNING: The array returned is also complex, i. Parameters x array_like. n: int, optional. This function computes the N-D discrete Fourier Transform over any number of axes in an M-D array by means of the Fast Fourier Transform (FFT). Input array. 0, device = None) [source] # Return the Discrete Fourier Transform sample frequencies (for usage with rfft, irfft). Jan 11, 2025 · fft# scipy. fft (a) If we already have the array where to put the result we can do: o. ifftshift(x, axes=None)[source]fftshift 的逆。 尽管对于偶数长度的 x 而言,函数相同,但是对于奇数长度的 x 而言,函数相差一个样本。 Parameters: xarray_like Input array. The packing of the result is “standard”: If A = fft(a, n), then A[0] contains the zero-frequency term, A[1:n/2] contains the positive-frequency terms, and 2 days ago · numpy. This function computes the n-dimensional discrete Fourier Transform over any axes in an M-dimensional array by means of the Fast Fourier Transform (FFT). For a general description of the algorithm and Dec 14, 2024 · numpy. Input array, can be complex. e. doc"很可能是关于FFT算法的详细描述和讨论的文档,可能包含了算法的理论基础、实现细节、应用场景等。 接下来,使用np. fft¶ scipy. axis: int, optional. real函数取实部,得到X3 Apr 28, 2024 · 文章浏览阅读2k次,点赞19次,收藏15次。二维快速傅里叶变换是分析和处理二维数据的强大工具,而 NumPy 的fft2方法为执行这种变换提供了一个高效且易于使用的接口。本文介绍了二维 FFT 的基本概念、fft2函数的使用方法以及它在解决实际问题中的应用。 Jan 8, 2018 · numpy. ifft# fft. This function computes the one-dimensional n-point discrete Fourier Transform (DFT) with the efficient Fast Fourier Transform (FFT) algorithm [CT]. This function computes the one-dimensional n-point discrete Fourier Transform (DFT) of a real-valued array by means of an efficient algorithm called the Fast Fourier Transform (FFT). Feb 19, 2023 · scipy. ifft (a, n = None, axis =-1, norm = None) [source] # Compute the one-dimensional inverse discrete Fourier Transform. n int, optional 2 days ago · numpy. fftfreq(n) 返回一个数组,该数组给出输出中相应元素的频率。 例程 np. This function computes the one 2 days ago · The routine np. fftshift# fft. Jun 24, 2024 · Notes. ifft2# fft. 0) [source] # Return the Discrete Fourier Transform sample frequencies. This function computes the N-dimensional discrete Fourier Transform over any number of axes in an M-dimensional array by means of the Fast Fourier Transform (FFT). Parameters Jan 20, 2024 · For norm="ortho" both the dct and idct are scaled by the same overall factor in both directions. This function computes the inverse of the N-dimensional discrete Fourier Transform over any number of axes in an M-dimensional array by means of the Fast Fourier Transform (FFT). Jun 22, 2021 · numpy. The output is also complex. fftn (x, s = None, axes = None, norm = None, overwrite_x = False, workers = None, *, plan = None) [源代码] # 计算 N 维离散傅里叶变换。 此函数通过快速傅里叶变换 (FFT) 计算 M 维数组中任意多个轴的 N 维离散傅里叶变换。 参数: x array_like 输入 Aug 21, 2024 · numpy. By default, the transform is computed over the last two axes of Dec 14, 2024 · numpy. n is the length of the result, not the input. The length of the transformed axis is n, or, if n is not given, 2*m-2 where m is the length of the transformed axis of the input. In ulab, the real and imaginary parts are treated separately: you have to pass two ndarray s to the function, although, the second argument is optional, in which case the imaginary part is assumed to be zero. The packing of the result is “standard”: If A = fft(a, n), then A[0] contains the zero-frequency term, A[1:n/2] contains the positive-frequency terms, and Dec 14, 2024 · numpy. fft (a, n = None, axis =-1, norm = None) [source] ¶ Compute the one-dimensional discrete Fourier Transform. If negative, the value wraps around from os. Nov 8, 2024 · a = np. The phase spectrum is obtained by np. fftshift# scipy. When the input a is a time-domain signal and A = fft(a), np. The output, analogously to fft, contains the term for zero frequency in the low-order corner of all axes, the positive frequency terms in the first half of all axes, the term for the Nyquist frequency in the middle of all axes and the negative frequency terms in the second half of all axes, in order of decreasingly negative frequency. rfftn (a, s = None, axes = None, norm = None, out = None) [source] # Compute the N-dimensional discrete Fourier Transform for real input. WARNING: The function, as opposed to Dec 14, 2024 · numpy. ifftn (a, s = None, axes = None, norm = None, out = None) [source] # Compute the N-dimensional inverse discrete Fourier Transform. The returned float array f contains the frequency bin centers in cycles per unit of the sample spacing (with zero at the start). Jan 7, 2025 · FFT 输入信号本质上已经被截断。此截断可以建模为一个无限信号乘以一个矩形窗函数。在频域中,此乘法成为信号谱与窗函数谱的卷积,形式为 \(\sin(x)/x\)。此卷积会导致称为频谱泄漏的效应(请参见 [WPW] )。将信号与一个专用的窗函数做窗化处理有助于减轻频谱泄漏。 Aug 21, 2024 · numpy. 0) # Return the Discrete Fourier Transform sample frequencies. See the notes below for more details. May 27, 2020 · 文章浏览阅读3. Parameters a array_like. fft (上图),因为实函数的输入,输出是一对共轭对称的序列。 而numpy. rfftn# fft. fft (a, n = None, axis =-1, norm = None, out = None) [source] # Compute the one-dimensional discrete Fourier Transform. Length of the transformed axis of the output. This function computes the one-dimensional n-point discrete Fourier Transform (DFT) with the efficient Fast Fourier Transform (FFT) algorithm . n (int | None | None) – int. This function computes the one-dimensional n-point discrete Fourier Transform (DFT) with the efficient Aug 21, 2024 · numpy. fftfreq (n, d = 1. For a general description of the algorithm and definitions, see 3 days ago · numpy. rfft# fft. Axes over which to calculate. May 23, 2024 · overwrite_x bool, optional. fft_as_arg (a, a_fft) And finally for the inverse Fourier transform: Dec 14, 2024 · numpy. The remaining negative frequency components are implied by the Hermitian symmetry of the FFT for a real input (y[n] = conj(y[-n])). 50% more RAM. Jun 10, 2017 · numpy. fft进行快速傅里叶变换,需要特别注意的是,默认是对最后个维度的数据进行fft变换,若你输入的是一维数组,请忽略后面,如果你是二维列矢量,如果不将数据变为行矢量或将axis参数设为0,将得到与输入相同的结果,导致后续的计算无缘无故出错。 Aug 17, 2023 · scipy. When the input a Oct 18, 2015 · numpy. numpy. cpu_count(). fft2 numpy. ifft2 (a, s = None, axes = (-2,-1), norm = None, out = None) [source] # Compute the 2-dimensional inverse discrete Fourier Transform. While numpy-compatibility might be a desired feature, it has one side effect, namely, the FFT routine consumes approx. fft 使用 Dec 14, 2024 · numpy. Apr 16, 2018 · Notes. axes int or shape tuple, optional. By default, the transform is computed over the last two axes of 2 days ago · numpy. rfft (a, n = None, axis =-1, norm = None) [source] # Compute the one-dimensional discrete Fourier Transform for real input. Defaults to None, which shifts all axes. a (ArrayLike) – input array. workers int, optional. fft¶ numpy. Aug 21, 2024 · numpy. fftfreq# scipy. fft2 (a, s = None, axes = (-2,-1), norm = None) [source] # Compute the 2-dimensional discrete Fourier Transform. This function swaps half-spaces for all axes listed (defaults to all). fft). . Returns the real valued n-point inverse discrete Fourier transform of a, where a contains the non-negative frequency terms of a Hermitian-symmetric sequence. n Oct 26, 2024 · 文件列表中的"FFT算法. Parameters May 24, 2020 · numpy. fftn (a, s = None, axes = None, norm = None, out = None) [source] # Compute the N-dimensional discrete Fourier Transform. n Nov 24, 2024 · then the FFT routine will behave in a numpy-compatible way: the single input array can either be real, in which case the imaginary part is assumed to be zero, or complex. 6w次,点赞26次,收藏69次。np. fft (a, n = None, axis =-1, norm = None) [source] # Compute a one-dimensional discrete Fourier transform along a given axis. fftshift (x, axes = None) [source] # Shift the zero-frequency component to the center of the spectrum. fftfreq fft. fftn# fft. Normalization mode (see numpy. Parameters Dec 14, 2024 · numpy. n 2 days ago · numpy. fftshift¶ numpy. ifftshift fft. If n is smaller than the length of the input, the input is cropped. fft# fft. n Jun 10, 2017 · numpy. ifftn (x, s = None, axes = None, norm = None, overwrite_x = False, workers = None, *, plan = None) [source] # 计算 N 维逆离散傅里叶变换。 此函数使用快速傅里叶变换 (FFT) 在 M 维数组中计算任意数量轴上的 N 维离散傅里叶变换的逆。换句话说,ifftn(fftn(x)) == x 在数值精度范围内。 Jan 7, 2025 · fftn# scipy. By default, the transform is computed over the last two axes of the input Dec 14, 2024 · numpy. For instance, if the sample spacing is in seconds, then the frequency unit is cycles/second. Jan 7, 2025 · ifftn# scipy. fftshift(A) shifts transforms and their frequencies to put the zero-frequency components in the middle, and np. , the real and imaginary components are cast together. The truncated or zero-padded input, transformed along the axis indicated by axis, or the last one if axis is not specified. See below for more details. Indicates which direction of the forward/backward pair of transforms is scaled and with what normalization factor. One can thus resample a Dec 14, 2024 · numpy. ifftn# fft. fftshift (x, axes = None) # Shift the zero-frequency component to the center of the spectrum. ifftshift (x, axes=None) [source] ¶ The inverse of fftshift. Maximum number of workers to use for parallel computation. fft (x, n=None, axis=-1, norm=None, overwrite_x=False, workers=None) [source] ¶ Compute the one-dimensional discrete Fourier Transform. By default, the transform is computed over the last two axes of Apr 3, 2024 · overwrite_x bool, optional. Specifies the dimension of the result along axis. Input array, can be Nov 10, 2024 · Python中使用numpy库实现FFT算法的高效计算技巧解析 引言 在信号处理领域,快速傅里叶变换(FFT)是一种至关重要的算法,它能够高效地将时域信号转换为频域信号,从而揭示信号的频谱结构。相较于传统的离散傅里叶变换(DFT),FFT通过巧妙 Apr 28, 2024 · 在这个fft算法中,将一个实数序列x(n)映射到一个复数序列X(n)上,输出的复数序列代表了输入实数序列的频域表示。其中每个复数X(k)由实部和虚部组成,复数的虚部表示了输入信号中存在的一些非实部成分,例如一些高频噪声或者相位信息。但我取的时间是0-0. ifftshift(A) undoes that shift. Jul 29, 2022 · The function rfft calculates the FFT of a real sequence and outputs the complex FFT coefficients \(y[n]\) for only half of the frequency range. This function computes the inverse of the 2-dimensional discrete Fourier Transform over any number of axes in an M-dimensional array by means of the Fast Fourier Transform (FFT). Dec 14, 2024 · The routine np. fft2 (a, s = None, axes = (-2,-1), norm = None, out = None) [source] # Compute the 2-dimensional discrete Fourier Transform. n int, Dec 14, 2024 · numpy. Jan 7, 2025 · zoom_fft# scipy. empty (o. Dec 14, 2024 · Returns: out ndarray. fft (x, n = None, axis =-1, norm = None, overwrite_x = False, workers = None, *, plan = None) [source] # Compute the 1-D discrete Fourier Transform. n int, optional Jan 7, 2025 · 备注 结果的打包是“标准”的:如果 A = fft(a, n), 则 A[0] 包含零频率项,A[1:n/2] 包含正频率项,A[n/2:] 包含负频率项,按负频率 May 24, 2020 · numpy. The remaining negative frequency components are implied by the Hermitian 2 days ago · The routine np. This function computes the one-dimensional n -point discrete Fourier Transform (DFT) with the efficient Fast Fourier Transform (FFT) algorithm [CT]. Input array, can be Aug 21, 2024 · numpy. get_shapeX_loc ()) a_fft = np. 2 days ago · numpy. fft2 (a, s=None, axes=(-2, -1), norm=None) [source] ¶ Compute the 2-dimensional discrete Fourier Transform. 5s,取N个点,这样我的采样频率是。 Fourier analysis is a method for expressing a function as a sum of periodic components, and for recovering the signal from those components. Nov 30, 2024 · 本文档详细介绍了如何使用C语言实现快速傅里叶变换(FFT)算法,提供了一个实用且具有移植性的函数示例。FFT是一种在信号处理、数字信号分析等领域广泛应用的高效算法,它能够将离散时间信号从时域转换到频域,便于 Jan 7, 2025 · FFT 输入信号本身是截断的。这种截断可以建模为无限信号与矩形窗函数的乘法。在频谱域中,这种乘法变成信号频谱与窗函数频谱的卷积,形式为 \(\sin(x)/x\)。这种卷积是称为频谱泄漏的效应的原因(请参见 [WPW] )。使 Jan 11, 2025 · numpy. fft for details, Aug 10, 2020 · 可以看到,对于 numpy. Length of the inverse FFT, the number of points along transformation axis in the input to use. Dec 14, 2024 · numpy. If n is not given, the length of the input along the axis specified by axis is used. By default, the transform is also orthogonalized which for types 1, 2 and 3 means the transform definition is modified to give orthogonality of the DCT matrix (see below). Dec 14, 2024 · norm {“backward”, “ortho”, “forward”}, optional. This function computes the one-dimensional n -point Dec 14, 2024 · Compute the 2-dimensional discrete Fourier Transform. ones (o. rfft (a, n = None, axis =-1, norm = None, out = None) [source] # Compute the one-dimensional discrete Fourier Transform for real input. Jul 24, 2018 · numpy. fft进行快速傅里叶变换,需要特别注意的是,默认是对最后个维度的数据进行fft变换,若你输入的是一维数组,请忽略后面,如果你是二维列矢量,如果不将数据变为行矢量或将axis参数设为0,将得到与输入相同的结果,导致后续的计算无缘无故出错。 2 days ago · Notes. Oct 22, 2024 · 最后,使用np. 2 days ago · The routine np. This function computes the inverse of the N-dimensional discrete Feb 13, 2022 · The routine np. 5s,取N个点,这样我的采样频率是。 Dec 14, 2024 · numpy. n int, optional. ifftshift (x, axes = None) [source] # The inverse of fftshift. fftn (a, s = None, axes = None, norm = None) [source] # Compute the N-dimensional discrete Fourier Transform. If not specified, it will default to the dimension of a along axis. nhaaelz ptin nlyu qmtpwp krzhmm pcais zimci txas spisn zmxe