Source code for mars.tensor.fft.ifft

#!/usr/bin/env python
# -*- coding: utf-8 -*-
# Copyright 1999-2021 Alibaba Group Holding Ltd.
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
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# distributed under the License is distributed on an "AS IS" BASIS,
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import numpy as np

from ... import opcodes as OperandDef
from ..datasource import tensor as astensor
from .core import TensorComplexFFTMixin, validate_fft, TensorStandardFFT

class TensorIFFT(TensorStandardFFT, TensorComplexFFTMixin):
    _op_type_ = OperandDef.IFFT

    def __init__(self, n=None, axis=-1, norm=None, **kw):
        super().__init__(_n=n, _axis=axis, _norm=norm, **kw)

[docs]def ifft(a, n=None, axis=-1, norm=None): """ Compute the one-dimensional inverse discrete Fourier Transform. This function computes the inverse of the one-dimensional *n*-point discrete Fourier transform computed by `fft`. In other words, ``ifft(fft(a)) == a`` to within numerical accuracy. For a general description of the algorithm and definitions, see `mt.fft`. The input should be ordered in the same way as is returned by `fft`, i.e., * ``a[0]`` should contain the zero frequency term, * ``a[1:n//2]`` should contain the positive-frequency terms, * ``a[n//2 + 1:]`` should contain the negative-frequency terms, in increasing order starting from the most negative frequency. For an even number of input points, ``A[n//2]`` represents the sum of the values at the positive and negative Nyquist frequencies, as the two are aliased together. See `numpy.fft` for details. Parameters ---------- a : array_like Input tensor, can be complex. n : int, optional Length of the transformed axis of the output. If `n` is smaller than the length of the input, the input is cropped. If it is larger, the input is padded with zeros. If `n` is not given, the length of the input along the axis specified by `axis` is used. See notes about padding issues. axis : int, optional Axis over which to compute the inverse DFT. If not given, the last axis is used. norm : {None, "ortho"}, optional Normalization mode (see `numpy.fft`). Default is None. Returns ------- out : complex Tensor The truncated or zero-padded input, transformed along the axis indicated by `axis`, or the last one if `axis` is not specified. Raises ------ IndexError If `axes` is larger than the last axis of `a`. See Also -------- mt.fft : An introduction, with definitions and general explanations. fft : The one-dimensional (forward) FFT, of which `ifft` is the inverse ifft2 : The two-dimensional inverse FFT. ifftn : The n-dimensional inverse FFT. Notes ----- If the input parameter `n` is larger than the size of the input, the input is padded by appending zeros at the end. Even though this is the common approach, it might lead to surprising results. If a different padding is desired, it must be performed before calling `ifft`. Examples -------- >>> import mars.tensor as mt >>> mt.fft.ifft([0, 4, 0, 0]).execute() array([ 1.+0.j, 0.+1.j, -1.+0.j, 0.-1.j]) Create and plot a band-limited signal with random phases: >>> import matplotlib.pyplot as plt >>> t = mt.arange(400) >>> n = mt.zeros((400,), dtype=complex) >>> n[40:60] = mt.exp(1j*mt.random.uniform(0, 2*mt.pi, (20,))) >>> s = mt.fft.ifft(n) >>> plt.plot(t.execute(), s.real.execute(), 'b-', t.execute(), s.imag.execute(), 'r--') ... >>> plt.legend(('real', 'imaginary')) ... >>> """ a = astensor(a) validate_fft(a, axis, norm) op = TensorIFFT(n=n, axis=axis, norm=norm, dtype=np.dtype(np.complex_)) return op(a)