Parametric spectral analysis: scale and shift

08/05/2020
by   Annie Cuyt, et al.
0

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.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

01/24/2020

Sparse Interpolation in Terms of Multivariate Chebyshev Polynomials

Sparse interpolation refers to the exact recovery of a function as a sho...
06/03/2017

Sparse Rational Function Interpolation with Finitely Many Values for the Coefficients

In this paper, we give new sparse interpolation algorithms for black box...
04/07/2021

Multivariate fractal interpolation functions: Some approximation aspects and an associated fractal interpolation operator

The natural kinship between classical theories of interpolation and appr...
07/29/2020

Asymptotically Equivalent Prediction in Multivariate Geostatistics

Cokriging is the common method of spatial interpolation (best linear unb...
12/15/2017

Revisit Randomized Kronecker Substitution based Sparse Polynomial Interpolation

In this paper, a new Monte Carlo interpolation algorithm for sparse mult...
10/21/2020

Multivariate Interpolation on Unisolvent Nodes – Lifting the Curse of Dimensionality

We present generalizations of the classic Newton and Lagrange interpolat...
03/30/2020

New exponential dispersion models for count data – properties and applications

In their fundamental paper on cubic variance functions (VFs), Letac and ...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.