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

Stephan Weiss; Ian K. Proudler; Malcolm D. MacLeod

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

Stephan Weiss, Ian K. Proudler, Malcolm D. MacLeod

Electronic And Electrical Engineering

Research output: Contribution to conference › Paper › peer-review

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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.

Original language	English
Number of pages	5
Publication status	Accepted/In press - 1 Mar 2019
Event	Sensor Signal Processing for Defence 2019 - Brighton, United Kingdom Duration: 9 May 2019 → 10 May 2019

Conference

Conference	Sensor Signal Processing for Defence 2019
Abbreviated title	SSPD'19
Country/Territory	United Kingdom
City	Brighton
Period	9/05/19 → 10/05/19

Keywords

functions
sample points
values

Access to Document

Weiss-etal-SSPD2019-Measuring-smoothness-of-real-valued-functions-defined-by-sample-pointsAccepted author manuscript, 384 KB

Cite this

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title = "Measuring smoothness of real-valued functions defined by sample points on the unit circle",

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.",

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author = "Stephan Weiss and Proudler, {Ian K.} and MacLeod, {Malcolm D.}",

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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.

KW - functions

KW - sample points

KW - values

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

M3 - Paper

T2 - Sensor Signal Processing for Defence 2019

Y2 - 9 May 2019 through 10 May 2019

ER -

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

Abstract

Conference

Keywords

Access to Document

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Signal Processing in the Information Age (UDRC III)

Cite this

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

Abstract

Conference

Keywords

Access to Document

Other files and links

Fingerprint

Projects

Signal Processing in the Information Age (UDRC III)

Cite this