# 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 $$(a, b)$$. 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 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. $$F(k_1, \ldots, k_n)$$, 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. $$f(x_1, \ldots, x_n)$$, the inverse fourier transform of $$F(k_1, \ldots, k_n)$$