pylops.signalprocessing.Shift

pylops.signalprocessing.Shift(dims, shift, dir=0, nfft=None, sampling=1.0, real=False, engine='numpy', dtype='complex128', **kwargs_fftw)[source]

Shift operator

Apply fractional shift in the frequency domain along a specific direction ] dir of a multi-dimensional array of size dim.

Parameters:
dims : tuple

Number of samples for each dimension

shift : float

Fractional shift to apply

dir : int, optional

Direction along which FFT is applied.

nfft : int, optional

Number of samples in Fourier Transform (same as input if nfft=None)

sampling : float, optional

Sampling step dt.

real : 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 : str, optional

Engine used for fft computation (numpy or fftw). Choose numpy when working with cupy arrays.

dtype : str, optional

Type of elements in input array.

**kwargs_fftw

Arbitrary keyword arguments for pyfftw.FTTW
Raises:
ValueError

If dims is provided and dir is bigger than len(dims)

NotImplementedError

If engine is neither numpy nor fftw

Notes

The Shift operator applies the forward Fourier transform, an element-wise scaling, and inverse fourier transform

\[\mathbf{y}= \mathbf{F}^{-1} \mathbf{S} \mathbf{F} \mathbf{x}\]

Here \(\mathbf{S}\) is a diagonal operator that scales the Fourier transformed input by \(e^{-j2\pi f t_S}\), whee \(t_S\) is the chosen shift.

Attributes:
shape : tuple

Operator shape

explicit : bool

Operator contains a matrix that can be solved explicitly (True) or not (False)

Examples using pylops.signalprocessing.Shift