Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convolution products for hypercomplex Fourier transforms   Hypercomplex Fourier transforms are increasingly used in signal processing
for the analysis of higher-dimensional signals such as color images. A main
stumbling block for further applications, in particular concerning filter
design in the Fourier domain, is the lack of a proper convolution theorem. The
present paper develops and studies two conceptually new ways to define
convolution products for such transforms. As a by-product, convolution theorems
are obtained that will enable the development and fast implementation of new
filters for quaternionic signals and systems, as well as for their higher
dimensional counterparts.

13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th