Module Documentation

This page contains documentation to every Deconvoluted tool.

deconvoluted.tranforms

deconvoluted.transforms.determine_axes(f, *vars)

Determine the axes along which the FT should be performed.

deconvoluted.transforms.determine_norm(convention)

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))

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 multi-dimensional functions \(f\) the number of vars has to match the dimension of f. Any axis that should be ignored should be provided as None:

  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))

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 \(F(k_1, \ldots, k_n)\)