pylops_distributed.signalprocessing.FFT

class pylops_distributed.signalprocessing.FFT(dims, dir=0, nfft=None, sampling=1.0, real=False, fftshift=False, compute=(False, False), chunks=(None, None), todask=(None, None), dtype='float64')

One dimensional Fast-Fourier Transform.

Apply Fast-Fourier Transform (FFT) along a specific direction dir of a multi-dimensional array of size dim.

Note that the FFT operator is an overload to the dask dask.array.fft.fft (or dask.array.fft.rfft for real models) in forward mode and to the dask dask.array.fft.ifft (or dask.array.fft.irfft for real models) in adjoint mode.

Scaling is properly taken into account to guarantee that the operator is passing the dot-test.

Note

For a real valued input signal, it is possible to store the values of the Fourier transform at positive frequencies only as values at negative frequencies are simply their complex conjugates. However as the operation of removing the negative part of the frequency axis in forward mode and adding the complex conjugates in adjoint mode is nonlinear, the Linear Operator FTT with real=True is not expected to pass the dot-test. It is thus only advised to use this flag when a forward and adjoint FFT is used in the same chained operator (e.g., FFT.H*Op*FFT) such as in pylops_distributed.waveeqprocessing.mdd.MDC.

Parameters:

dims : tuple

Number of samples for each dimension

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.

fftshift : bool, optional

Apply fftshift/ifftshift (True) or not (False)

compute : tuple, optional

Compute the outcome of forward and adjoint or simply define the graph and return a dask.array.array

chunks : tuple, optional

Chunk size for model and data. If provided it will rechunk the model before applying the forward pass and the data before applying the adjoint pass

todask : tuple, optional

Apply dask.array.from_array to model and data before applying forward and adjoint respectively

dtype : str, optional

Type of elements in input array.

Raises:

ValueError

If dims is not provided and if dir is bigger than len(dims)

Notes

Refer to pylops.signalprocessing.FFT for implementation details.

Attributes:

shape : tuple

Operator shape

explicit : bool

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

Methods

__init__(dims[, dir, nfft, sampling, real, …])	Initialize this LinearOperator.
adjoint()	Hermitian adjoint.
apply_columns(cols)	Apply subset of columns of operator
cond([uselobpcg])	Condition number of linear operator.
conj()	Complex conjugate operator
div(y[, niter])	Solve the linear problem \(\mathbf{y}=\mathbf{A}\mathbf{x}\).
dot(x)	Matrix-vector multiplication.
eigs([neigs, symmetric, niter, uselobpcg])	Most significant eigenvalues of linear operator.
matmat(X)	Matrix-matrix multiplication.
matvec(x)	Matrix-vector multiplication.
rmatmat(X)	Adjoint matrix-matrix multiplication.
rmatvec(x)	Adjoint Matrix-vector multiplication.
todense()	Return dense matrix.
tosparse()	Return sparse matrix.
transpose()	Transpose this linear operator.