information:filtering, quality:correction, linguistic:paraphrasing
Convolution on matrices

If W {\displaystyle {\mathcal {W}}} is the Fourier transform matrix, then

where ∙ {\displaystyle \bullet } is face-splitting product, ⊗ {\displaystyle \otimes } denotes Kronecker product, ∘ {\displaystyle \circ } denotes Hadamard product (this result is an evolving of count sketch properties).

This can be generalized for appropriate matrices A, B {\displaystyle \mathbf {A},\mathbf {B} }:

from the properties of the face-splitting product.