Measuring smoothness of real-valued functions defined by sample points on the unit circle

Research output: Contribution to conferencePaper

Abstract

In the context of extracting analytic eigen- or singular values from a polynomial matrix, a suitable cost function is the smoothness of continuous, real, and potentially symmetric periodic functions. This smoothness can be measured as the power of the derivatives of that function, and can be tied to a set of sample points on the unit circle that may be incomplete. We have previously explored the utility of this cost function, and here provide refinements by (i) analysing properties of the cost function and (ii) imposing additional constraints on its evaluation.
LanguageEnglish
Number of pages5
Publication statusAccepted/In press - 1 Mar 2019
EventSensor Signal Processing for Defence 2019 - Brighton, United Kingdom
Duration: 9 May 201910 May 2019

Conference

ConferenceSensor Signal Processing for Defence 2019
Abbreviated titleSSPD'19
CountryUnited Kingdom
CityBrighton
Period9/05/1910/05/19

Fingerprint

Cost functions
Polynomials
Derivatives

Keywords

  • functions
  • sample points
  • values

Cite this

Weiss, S., Proudler, I. K., & MacLeod, M. D. (Accepted/In press). Measuring smoothness of real-valued functions defined by sample points on the unit circle. Paper presented at Sensor Signal Processing for Defence 2019, Brighton, United Kingdom.
Weiss, Stephan ; Proudler, Ian K. ; MacLeod, Malcolm D. / Measuring smoothness of real-valued functions defined by sample points on the unit circle. Paper presented at Sensor Signal Processing for Defence 2019, Brighton, United Kingdom.5 p.
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Weiss, S, Proudler, IK & MacLeod, MD 2019, 'Measuring smoothness of real-valued functions defined by sample points on the unit circle' Paper presented at Sensor Signal Processing for Defence 2019, Brighton, United Kingdom, 9/05/19 - 10/05/19, .

Measuring smoothness of real-valued functions defined by sample points on the unit circle. / Weiss, Stephan; Proudler, Ian K.; MacLeod, Malcolm D.

2019. Paper presented at Sensor Signal Processing for Defence 2019, Brighton, United Kingdom.

Research output: Contribution to conferencePaper

TY - CONF

T1 - Measuring smoothness of real-valued functions defined by sample points on the unit circle

AU - Weiss, Stephan

AU - Proudler, Ian K.

AU - MacLeod, Malcolm D.

N1 - © 2019 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 - 2019/3/1

Y1 - 2019/3/1

N2 - In the context of extracting analytic eigen- or singular values from a polynomial matrix, a suitable cost function is the smoothness of continuous, real, and potentially symmetric periodic functions. This smoothness can be measured as the power of the derivatives of that function, and can be tied to a set of sample points on the unit circle that may be incomplete. We have previously explored the utility of this cost function, and here provide refinements by (i) analysing properties of the cost function and (ii) imposing additional constraints on its evaluation.

AB - In the context of extracting analytic eigen- or singular values from a polynomial matrix, a suitable cost function is the smoothness of continuous, real, and potentially symmetric periodic functions. This smoothness can be measured as the power of the derivatives of that function, and can be tied to a set of sample points on the unit circle that may be incomplete. We have previously explored the utility of this cost function, and here provide refinements by (i) analysing properties of the cost function and (ii) imposing additional constraints on its evaluation.

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KW - sample points

KW - values

UR - https://sspd.eng.ed.ac.uk/

M3 - Paper

ER -

Weiss S, Proudler IK, MacLeod MD. Measuring smoothness of real-valued functions defined by sample points on the unit circle. 2019. Paper presented at Sensor Signal Processing for Defence 2019, Brighton, United Kingdom.