scholarly journals On approximately dual frames for Hilbert C*-modules

Filomat ◽  
2019 ◽  
Vol 33 (12) ◽  
pp. 3869-3875
Author(s):  
Ljiljana Arambasic
Keyword(s):  
Dual Frame ◽  
Dual Frames ◽  
Outer Frame ◽  
Scalar Multiple

In this paper we discuss approximately dual frames for a frame or an outer frame of a Hilbert C*-module. We show that every frame or an outer frame, up to a scalar multiple, is approximately dual to itself. This enables us to get a canonical dual frame of a given frame (xn)n as a limit of approximately dual frames defined by (xn)n.

Partial Gabor frames and dual frames

2021 ◽  
pp. 2150035
Author(s):  
Yu Tian ◽  
Hui-Fang Jia ◽  
Guo-Liang He
Keyword(s):  
Density Theorem ◽  
Gabor Frame ◽  
Gabor Frames ◽  
Dual Frame ◽  
Gabor System ◽  
Dual Frames ◽  
Gabor Systems

The theory of Gabor frames has been extensively investigated. This paper addresses partial Gabor systems. We introduce the concepts of partial Gabor system, frame and dual frame. We present some conditions for a partial Gabor system to be a partial Gabor frame, and using these conditions, we characterize partial dual frames. We also give some examples. It is noteworthy that the density theorem does not hold for general partial Gabor systems.

OBLIQUE DUAL FRAMES IN FINITE-DIMENSIONAL HILBERT SPACES

2013 ◽  
Vol 11 (02) ◽  
pp. 1350011 ◽  
Author(s):  
XIANG-CHUN XIAO ◽  
YU-CAN ZHU ◽  
XIAO-MING ZENG
Keyword(s):  
Hilbert Spaces ◽  
Computational Efficiency ◽  
Tight Frame ◽  
Constructive Method ◽  
Dual Frame ◽  
Dual Frames ◽  
Finite Dimensional ◽  
Oblique Dual

A frame can be completed to a tight frame by adding some additional vectors. However, for the purpose of computational efficiency, we need to put restrictions to the number of added vectors. In this paper we propose a constructive method that allows to extend a given frame to an oblique dual frame pair such that the number of added vectors is in general much smaller than the number of added vectors used to extend it to a tight frame. We also present a uniqueness characterization and several equivalent characterizations for an oblique dual frame pair, it turns out that oblique dual frame pair provides more flexibilities than alternate dual frame pair.

DISCRETE-TIME WILSON FRAMES WITH GENERAL LATTICES

2012 ◽  
Vol 10 (05) ◽  
pp. 1250044 ◽  
Author(s):  
QIAOFANG LIAN ◽  
YUNFANG LIAN ◽  
MINGHOU YOU
Keyword(s):  
Discrete Time ◽  
Tight Frame ◽  
Gabor Frame ◽  
Dual Frame ◽  
Necessary And Sufficient Condition ◽  
Dual Frames ◽  
Gabor Dual ◽  
Bessel Sequences ◽  
Necessary And Sufficient

In this paper, we focus on the construction of Wilson frames and their dual frames for general lattices of volume [Formula: see text] (K even) in the discrete-time setting. We obtain a necessary and sufficient condition for two Bessel sequences having Wilson structure to be dual frames for l2(ℤ). When the window function satisfies some symmetry property, we obtain a characterization of a Wilson system to be a tight frame for l2(ℤ), show that a Wilson frame for l2(ℤ) can be derived from the underlying Gabor frame, and that the dual frame having Wilson structure can also be derived from the canonical Gabor dual of the underlying Gabor frame.

Wilson frames for ℂL with general lattices

2016 ◽  
Vol 14 (06) ◽  
pp. 1650055
Author(s):  
Minghou You ◽  
Junqiao Yang ◽  
Qiaofang Lian
Keyword(s):  
Digital Signal ◽  
Tight Frame ◽  
Gabor Frame ◽  
Dual Frame ◽  
Dual Frames ◽  
Volume Formula ◽  
Discrete Signals ◽  
Gabor Dual ◽  
Necessary And Sufficient

In digital signal and image processing one can only process discrete signals of finite length, and the space [Formula: see text] is the preferred setting. Recently, Kutyniok and Strohmer constructed orthonormal Wilson bases for [Formula: see text] with general lattices of volume [Formula: see text] ([Formula: see text] even). In this paper, we extend this construction to Wilson frames for [Formula: see text] with general lattices of volume [Formula: see text], where [Formula: see text] and [Formula: see text]. We obtain a necessary and sufficient condition for two sequences having Wilson structure to be dual frames for [Formula: see text]. When the window function satisfies some symmetry property, we obtain a characterization of a Wilson system to be a tight frame for [Formula: see text], show that a Wilson frame for [Formula: see text] can be derived from the underlying Gabor frame, and that the dual frame having Wilson structure can also be derived from the canonical Gabor dual of the underlying Gabor frame.

scholarly journals Dual-frame lek surveys for estimating greater sage-grouse populations

2018 ◽  
Vol 82 (8) ◽  
pp. 1689-1700 ◽  
Author(s):  
Jessica E. Shyvers ◽  
Brett L. Walker ◽  
Barry R. Noon
Keyword(s):  
Dual Frame ◽  
Sage Grouse
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