Source code for pylops.signalprocessing.Shift

import numpy as np

from pylops.basicoperators import Diagonal
from pylops.signalprocessing import FFT

[docs]def Shift( dims, shift, dir=0, nfft=None, sampling=1.0, real=False, engine="numpy", dtype="complex128", **kwargs_fftw ): r"""Shift operator Apply fractional shift in the frequency domain along a specific direction ``dir`` of a multi-dimensional array of size ``dim``. Parameters ---------- dims : :obj:`tuple` Number of samples for each dimension shift : :obj:`float` Fractional shift to apply in the same unit as ``sampling``. dir : :obj:`int`, optional Direction along which FFT is applied. nfft : :obj:`int`, optional Number of samples in Fourier Transform (same as input if ``nfft=None``) sampling : :obj:`float`, optional Sampling step :math:`\Delta t`. real : :obj:`bool`, optional Model to which fft is applied has real numbers (``True``) or not (``False``). Used to enforce that the output of adjoint of a real model is real. engine : :obj:`str`, optional Engine used for fft computation (``numpy``, ``scipy``, or ``fftw``). Choose ``numpy`` when working with CuPy arrays. dtype : :obj:`str`, optional Type of elements in input array. **kwargs_fftw Arbitrary keyword arguments for :py:class:`pyfftw.FTTW` Attributes ---------- shape : :obj:`tuple` Operator shape explicit : :obj:`bool` Operator contains a matrix that can be solved explicitly (``True``) or not (``False``) Raises ------ ValueError If ``dims`` is provided and ``dir`` is bigger than ``len(dims)`` NotImplementedError If ``engine`` is neither ``numpy``, ``scipy``, nor ``fftw`` Notes ----- The Shift operator applies the forward Fourier transform, an element-wise complex scaling, and inverse fourier transform .. math:: \mathbf{y}= \mathbf{F}^{-1} \mathbf{S} \mathbf{F} \mathbf{x} Here :math:`\mathbf{S}` is a diagonal operator that scales the Fourier transformed input by :math:`e^{-j2\pi f t_S}`, where :math:`t_S` is the chosen ``shift``. """ # TODO: Use offer the same keywords as new FFT Fop = FFT( dims, dir, nfft, sampling, real=real, engine=engine, dtype=dtype, **kwargs_fftw ) if isinstance(dims, int): dimsdiag = None else: dimsdiag = list(dims) dimsdiag[dir] = len(Fop.f) shift = np.exp(-1j * 2 * np.pi * Fop.f * shift) Sop = Diagonal(shift, dims=dimsdiag, dir=dir, dtype=Fop.cdtype) Op = Fop.H * Sop * Fop # force dtype to that of input (FFT always upcasts it to complex) Op.dtype = dtype return Op