Measuring smoothness of trigonometric interpolation through incomplete sample points

Stephan Weiss; Jesus Selva; Malcolm D. Macleod

doi:10.23919/Eusipco47968.2020.9287694

Measuring smoothness of trigonometric interpolation through incomplete sample points

Stephan Weiss, Jesus Selva, Malcolm D. Macleod

Electronic And Electrical Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

2 Citations (Scopus)

2 Downloads (Pure)

Abstract

In this paper we present a metric to assess the smoothness of a trigonometric interpolation through an incomplete set of sample points. We measure smoothness as the power of a particular derivative of a 2π-periodic Dirichlet interpolant through some sample points. We show that we do not need to explicitly complete the sample set or perform the interpolation, but can simply work with the available sample points, under the assumption that any missing points are chosen to minimise the metric, and present a simple and robust approach to the computation of this metric. We assess the accuracy and computational complexity of this approach, and compare it to benchmarks.

Original language	English
Title of host publication	2020 28th European Signal Processing Conference (EUSIPCO)
Place of Publication	Piscataway, NJ
Publisher	IEEE
Number of pages	5
ISBN (Print)	9789082797053
DOIs	https://doi.org/10.23919/Eusipco47968.2020.9287694
Publication status	Published - 18 Dec 2020
Event	28th European Signal Processing Conference - Amsterdam, Netherlands Duration: 18 Jan 2021 → 22 Jan 2021

Conference

Conference	28th European Signal Processing Conference
Abbreviated title	EUSIPCO2020
Country/Territory	Netherlands
City	Amsterdam
Period	18/01/21 → 22/01/21

Keywords

broadband array processing
smoothness metric
broadband beamforming

Access to Document

10.23919/Eusipco47968.2020.9287694

Weiss-etal-EUSIPCO-2020-Measuring-smoothness-of-trigonometric-interpolation-throughAccepted author manuscript, 188 KB

Cite this

@inproceedings{009849a33c7c43f2b10bb429d1aefe5c,

title = "Measuring smoothness of trigonometric interpolation through incomplete sample points",

abstract = "In this paper we present a metric to assess the smoothness of a trigonometric interpolation through an incomplete set of sample points. We measure smoothness as the power of a particular derivative of a 2π-periodic Dirichlet interpolant through some sample points. We show that we do not need to explicitly complete the sample set or perform the interpolation, but can simply work with the available sample points, under the assumption that any missing points are chosen to minimise the metric, and present a simple and robust approach to the computation of this metric. We assess the accuracy and computational complexity of this approach, and compare it to benchmarks.",

keywords = "broadband array processing, smoothness metric, broadband beamforming",

author = "Stephan Weiss and Jesus Selva and Macleod, {Malcolm D.}",

note = "{\textcopyright} 2020 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. ; 28th European Signal Processing Conference, EUSIPCO2020 ; Conference date: 18-01-2021 Through 22-01-2021",

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day = "18",

doi = "10.23919/Eusipco47968.2020.9287694",

language = "English",

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booktitle = "2020 28th European Signal Processing Conference (EUSIPCO)",

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T1 - Measuring smoothness of trigonometric interpolation through incomplete sample points

AU - Weiss, Stephan

AU - Selva, Jesus

AU - Macleod, Malcolm D.

N1 - © 2020 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

PY - 2020/12/18

Y1 - 2020/12/18

N2 - In this paper we present a metric to assess the smoothness of a trigonometric interpolation through an incomplete set of sample points. We measure smoothness as the power of a particular derivative of a 2π-periodic Dirichlet interpolant through some sample points. We show that we do not need to explicitly complete the sample set or perform the interpolation, but can simply work with the available sample points, under the assumption that any missing points are chosen to minimise the metric, and present a simple and robust approach to the computation of this metric. We assess the accuracy and computational complexity of this approach, and compare it to benchmarks.

AB - In this paper we present a metric to assess the smoothness of a trigonometric interpolation through an incomplete set of sample points. We measure smoothness as the power of a particular derivative of a 2π-periodic Dirichlet interpolant through some sample points. We show that we do not need to explicitly complete the sample set or perform the interpolation, but can simply work with the available sample points, under the assumption that any missing points are chosen to minimise the metric, and present a simple and robust approach to the computation of this metric. We assess the accuracy and computational complexity of this approach, and compare it to benchmarks.

KW - broadband array processing

KW - smoothness metric

KW - broadband beamforming

UR - https://eusipco2020.org/

U2 - 10.23919/Eusipco47968.2020.9287694

DO - 10.23919/Eusipco47968.2020.9287694

M3 - Conference contribution book

SN - 9789082797053

BT - 2020 28th European Signal Processing Conference (EUSIPCO)

PB - IEEE

CY - Piscataway, NJ

T2 - 28th European Signal Processing Conference

Y2 - 18 January 2021 through 22 January 2021

ER -

Measuring smoothness of trigonometric interpolation through incomplete sample points

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Signal Processing in the Information Age (UDRC III)

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Measuring smoothness of trigonometric interpolation through incomplete sample points

Abstract

Conference

Keywords

Access to Document

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Signal Processing in the Information Age (UDRC III)

Cite this