Saved in:
Bibliographic Details
Main Authors: Said, Karim A., Liu, Lingjia, A., A., Beex
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2401.09371
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866909076157366272
author Said, Karim A.
Liu, Lingjia
A., A.
Beex
author_facet Said, Karim A.
Liu, Lingjia
A., A.
Beex
contents It is well known that index (discrete-time)-limited sampled sequences leak outside the support set when a band-limiting operation is applied. Similarly, a fractional shift causes an index-limited sequence to be infinite in extent due to the inherent band-limiting. Index-limited versions of discrete prolate spheroidal sequences (DPSS) are known to experience minimum leakage after band-limiting. In this work, we consider the effect of a half-sample shift and provide upper bounds on the resulting leakage energy for arbitrary sequences. Furthermore, we find an orthonormal basis derived from DPSS with members ordered according to energy concentration after half sample shifts; the primary (first) member being the global optimum.
format Preprint
id arxiv_https___arxiv_org_abs_2401_09371
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Maximally Concentrated Sequences after Half-sample Shifts
Said, Karim A.
Liu, Lingjia
A., A.
Beex
Signal Processing
It is well known that index (discrete-time)-limited sampled sequences leak outside the support set when a band-limiting operation is applied. Similarly, a fractional shift causes an index-limited sequence to be infinite in extent due to the inherent band-limiting. Index-limited versions of discrete prolate spheroidal sequences (DPSS) are known to experience minimum leakage after band-limiting. In this work, we consider the effect of a half-sample shift and provide upper bounds on the resulting leakage energy for arbitrary sequences. Furthermore, we find an orthonormal basis derived from DPSS with members ordered according to energy concentration after half sample shifts; the primary (first) member being the global optimum.
title Maximally Concentrated Sequences after Half-sample Shifts
topic Signal Processing
url https://arxiv.org/abs/2401.09371