Module Documentation¶
This page contains documentation to every Deconvoluted
tool.
deconvoluted.tranforms¶

deconvoluted.transforms.
determine_axes
(f, *vars)[source]¶ Determine the axes along which the FT should be performed.

deconvoluted.transforms.
determine_norm
(convention)[source]¶ Determine the normalization constant for this
convention
.Parameters: convention – tuple representing \((a, b)\). Returns: normalization constant.

deconvoluted.transforms.
fourier_transform
(f, *vars, convention=Convention(a=0, b=6.283185307179586))[source]¶ Performs the multidimensional Fourier transform of \(f(x_1, \ldots, x_n)\) with respect to any number of variables \(x_i\).
Examples:
# 1D transform F, k = fourier_transform(f, x) # 2D transform F_pq, p, q = fourier_transform(f_xy, x, y) # 2D function, transform only 1 axis F_py, p = fourier_transform(f_xy, x, None)
Parameters:  f – array representing a function \(f(x_1, \ldots, x_n)\)
 vars –
list of \(x_i\) w.r.t. which the Fourier transform has to be computed. In case of multidimensional functions \(f\) the number of
vars
has to match the dimension off
. Any axis that should be ignored should be provided asNone
:F_py, p = fourier_transform(f_xy, x, None)
 convention – The Fourier convention to be used. \(a=0\) and \(b= 2 \pi\) by default, which is the signal processing standard.
Returns: \(F(k_1, \ldots, k_n)\), the Fourier transform of \(f(x_1, \ldots, x_n)\).

deconvoluted.transforms.
inverse_fourier_transform
(F, *vars, convention=Convention(a=0, b=6.283185307179586))[source]¶ Perform an inverse Fourier transform. See
deconvoluted.transforms.fourier_transform()
for more info.Parameters:  F – Fourier transform \(F(k_1, \ldots, k_n)\) of \(f(x_1, \ldots, x_n)\).
 vars – Any number of \(k\) variables or
None
.  convention – The Fourier convention to be used. \(a=0\) and \(b= 2 \pi\) by default, which is the signal processing standard.
Returns: \(f(x_1, \ldots, x_n)\), the inverse fourier transform of \(F(k_1, \ldots, k_n)\)