A note on Unser-Zerubia generalized sampling theory applied to the linear interpolator

A.J.E.M. Janssen; A.A.C.M. Kalker

doi:10.1109/78.774781

A note on Unser-Zerubia generalized sampling theory applied to the linear interpolator

A.J.E.M. Janssen, A.A.C.M. Kalker

Research output: Contribution to journal › Article › Academic › peer-review

4 Citations (Scopus)

66 Downloads (Pure)

Abstract

In this correspondence, we calculate the condition number of the linear operator that maps sequences of samples f(2k), f(2k+a), k¿Z of an unknown continuous f¿L2 (R) consistently (in the sense of the Unser-Zeruhia generalized sampling theory) onto the set of continuous, piecewise linear functions in L2(R) with nodes at the integers as a function of a¿(0,2). It turns out that the minimum condition numbers occur at a=v2/3 and a=2-v2/3 and not at a=1 as we might have expected. The theory is verified using the example of video deinterlacing

Original language	English
Pages (from-to)	2332-2335
Number of pages	4
Journal	IEEE Transactions on Signal Processing
Volume	47
Issue number	8
DOIs	https://doi.org/10.1109/78.774781
Publication status	Published - 1999

Access to Document

10.1109/78.774781

Metis235380Final published version, 147 KB

Fingerprint Dive into the research topics of 'A note on Unser-Zerubia generalized sampling theory applied to the linear interpolator'. Together they form a unique fingerprint.

Cite this

@article{1870c04b5f144266a19b71bdad317b34,

title = "A note on Unser-Zerubia generalized sampling theory applied to the linear interpolator",

abstract = "In this correspondence, we calculate the condition number of the linear operator that maps sequences of samples f(2k), f(2k+a), k¿Z of an unknown continuous f¿L2 (R) consistently (in the sense of the Unser-Zeruhia generalized sampling theory) onto the set of continuous, piecewise linear functions in L2(R) with nodes at the integers as a function of a¿(0,2). It turns out that the minimum condition numbers occur at a=v2/3 and a=2-v2/3 and not at a=1 as we might have expected. The theory is verified using the example of video deinterlacing",

author = "A.J.E.M. Janssen and A.A.C.M. Kalker",

year = "1999",

doi = "10.1109/78.774781",

language = "English",

volume = "47",

pages = "2332--2335",

journal = "IEEE Transactions on Signal Processing",

issn = "1053-587X",

publisher = "Institute of Electrical and Electronics Engineers",

number = "8",

}

TY - JOUR

T1 - A note on Unser-Zerubia generalized sampling theory applied to the linear interpolator

AU - Janssen, A.J.E.M.

AU - Kalker, A.A.C.M.

PY - 1999

Y1 - 1999

N2 - In this correspondence, we calculate the condition number of the linear operator that maps sequences of samples f(2k), f(2k+a), k¿Z of an unknown continuous f¿L2 (R) consistently (in the sense of the Unser-Zeruhia generalized sampling theory) onto the set of continuous, piecewise linear functions in L2(R) with nodes at the integers as a function of a¿(0,2). It turns out that the minimum condition numbers occur at a=v2/3 and a=2-v2/3 and not at a=1 as we might have expected. The theory is verified using the example of video deinterlacing

AB - In this correspondence, we calculate the condition number of the linear operator that maps sequences of samples f(2k), f(2k+a), k¿Z of an unknown continuous f¿L2 (R) consistently (in the sense of the Unser-Zeruhia generalized sampling theory) onto the set of continuous, piecewise linear functions in L2(R) with nodes at the integers as a function of a¿(0,2). It turns out that the minimum condition numbers occur at a=v2/3 and a=2-v2/3 and not at a=1 as we might have expected. The theory is verified using the example of video deinterlacing

U2 - 10.1109/78.774781

DO - 10.1109/78.774781

M3 - Article

VL - 47

SP - 2332

EP - 2335

JO - IEEE Transactions on Signal Processing

JF - IEEE Transactions on Signal Processing

SN - 1053-587X

IS - 8

ER -