This module implements the unitary fourier transform, also known as the ortho-normal transform. It is especially useful for convolution [1], as it respects the Parseval equality. The value of the null frequency is equal to
$$\frac{1}{\sqrt{n}} \sum_i x_i$$so the Fourier transform has the same energy as the original image (see image_quad_norm
function). The transform is applied from the last axis for performance (assuming a C-order array input).
Function of unitary fourier transform (uft) and utilities
Function of unitary fourier transform (uft) and utilities
This module implements the unitary fourier transform, also known as the ortho-normal transform. It is especially useful for convolution [1], as it respects the Parseval equality. The value of the null frequency is equal to
$$\frac{1}{\sqrt{n}} \sum_i x_i$$so the Fourier transform has the same energy as the original image (see image_quad_norm
function). The transform is applied from the last axis for performance (assuming a C-order array input).
<Unimplemented 'footnote' '.. [1] B. R. Hunt "A matrix theory proof of the discrete convolution\n theorem", IEEE Trans. on Audio and Electroacoustics,\n vol. au-19, no. 4, pp. 285-288, dec. 1971'>
Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.
Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)
SVG is more flexible but power hungry; and does not scale well to 50 + nodes.
All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them