pylops.signalprocessing.Convolve1D¶
-
class
pylops.signalprocessing.
Convolve1D
(N, h, offset=0, dims=None, dir=0, dtype='float64')[source]¶ 1D convolution operator.
Apply one-dimensional convolution with a compact filter to model (and data) along a specific direction of a multi-dimensional array depending on the choice of
dir
.Parameters: - N :
int
Number of samples in model.
- h :
numpy.ndarray
1d compact filter to be convolved to input signal
- offset :
int
Index of the center of the compact filter
- dims :
tuple
Number of samples for each dimension (
None
if only one dimension is available)- dir :
int
, optional Direction along which convolution is applied
- dtype :
str
, optional Type of elements in input array.
Notes
The Convolve1D operator applies convolution between the input signal \(x(t)\) and a compact filter kernel \(h(t)\) in forward model:
\[y(t) = \int_{-\inf}^{\inf} h(t-\tau) x(\tau) d\tau\]This operation can be discretized as follows
\[y[n] = \sum_{m=-\inf}^{\inf} h[n-m] x[m]\]as well as performed in the frequency domain.
\[Y(f) = \mathscr{F} (h(t)) * \mathscr{F} (x(t))\]Convolve1D operator uses
scipy.signal.convolve
that automatically chooses the best domain for the operation to be carried out for one dimensional inputs. The fft implementationscipy.signal.fftconvolve
is however enforced for signals in 2 or more dimensions as this routine efficently operates on multi-dimensional arrays.As the adjoint of convolution is correlation, Convolve1D operator applies correlation in the adjoint mode.
In time domain:
\[x(t) = \int_{-\inf}^{\inf} h(t+\tau) x(\tau) d\tau\]or in frequency domain:
\[y(t) = \mathscr{F}^{-1} (H(f)^* * X(f))\]Attributes: Methods
__init__
(self, N, h[, offset, dims, dir, dtype])Initialize this LinearOperator. adjoint
(self)Hermitian adjoint. cond
(self, \*\*kwargs_eig)Condition number of linear operator. conj
(self)Complex conjugate operator div
(self, y[, niter])Solve the linear problem \(\mathbf{y}=\mathbf{A}\mathbf{x}\). dot
(self, x)Matrix-matrix or matrix-vector multiplication. eigs
(self[, neigs, symmetric, niter])Most significant eigenvalues of linear operator. matmat
(self, X)Matrix-matrix multiplication. matvec
(self, x)Matrix-vector multiplication. rmatvec
(self, x)Adjoint matrix-vector multiplication. transpose
(self)Transpose this linear operator. - N :