Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On harmonic analysis of vector-valued signals   A vector-valued signal in N dimensions is a signal whose value at any time
instant is an N-dimensional vector, that is, an element of $\mathbb{R}^N$. The
sum of an arbitrary number of such signals of the same frequency is shown to
trace an ellipse in N-dimensional space, that is, to be confined to a plane.
The parameters of the ellipse (major and minor axes, represented by
N-dimensional vectors; and phase) are obtained algebraically in terms of the
directions of oscillation of the constituent signals, and their phases. It is
shown that the major axis of the ellipse can always be determined
algebraically. That is, a vector, whose value can be computed algebraically
(without decisions or comparisons of magnitude) from parameters of the
constituent signals, always represents the major axis of the ellipse. The
ramifications of this result for the processing and Fourier analysis of signals
with vector values or samples are discussed, with reference to the definition
of Fourier transforms, particularly discrete Fourier transforms, such as have
been defined in several hypercomplex algebras, including Clifford algebras. The
treatment in the paper, however, is entirely based on signals with values in
$\mathbb{R}^N$. Although the paper is written in terms of vector signals (which
are taken to include images and volumetric images), the analysis clearly also
applies to a superposition of simple harmonic motions in N dimensions.

18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
16
The categories of this paper are: stat