Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Parametric spectral analysis: scale and shift   We introduce the paradigm of dilation and translation for use in the spectral
analysis of complex-valued univariate or multivariate data. The new procedure
stems from a search on how to solve ambiguity problems in this analysis, such
as aliasing because of too coarsely sampled data, or collisions in projected
data, which may be solved by a translation of the sampling locations.
  In Section 2 both dilation and translation are first presented for the
classical one-dimensional exponential analysis. In the subsequent Sections 3--7
the paradigm is extended to more functions, among which the trigonometric
functions cosine, sine, the hyperbolic cosine and sine functions, the Chebyshev
and spread polynomials, the sinc, gamma and Gaussian function, and several
multivariate versions of all of the above.
  Each of these function classes needs a tailored approach, making optimal use
of the properties of the base function used in the considered sparse
interpolation problem. With each of the extensions a structured linear matrix
pencil is associated, immediately leading to a computational scheme for the
spectral analysis, involving a generalized eigenvalue problem and several
structured linear systems.
  In Section 8 we illustrate the new methods in several examples: fixed width
Gaussian distribution fitting, sparse cardinal sine or sinc interpolation, and
lacunary or supersparse Chebyshev polynomial interpolation.

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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ex
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph