Classifying tight Weyl-Heisenberg frames

P. Cazsazza; A. J. E. M. Janssen; Ole Christensen

Classifying tight Weyl-Heisenberg frames

P. Cazsazza
, A. J. E. M. Janssen
, Ole Christensen

Research output: Contribution to journal › Journal article › Research

Abstract

A Weyl-Heisenberg frame for L^2(R) is a frame consisting of translates and modulates of a fixed function. In this paper we give necessary and sufficient conditions for this family to form a tight WH-frame. This allows us to write down explicitly all functions g for which all translates and modulates of g form an orthonormal basis for L^2(R). There are a number of consequences of this classification, including a simple direct classification of the alternate dual frames to a WH-frame (A result originally due to Janssen).

Original language	English
Journal	Unknown title
Pages (from-to)	1-22
Publication status	Published - 1999

OpenUrl availability

Check availability in DTU Findit

Cite this

@article{d057b10d5ba4400cb88c524e3bf6991f,

title = "Classifying tight Weyl-Heisenberg frames",

abstract = "A Weyl-Heisenberg frame for L\textasciicircum{}2(R) is a frame consisting of translates and modulates of a fixed function. In this paper we give necessary and sufficient conditions for this family to form a tight WH-frame. This allows us to write down explicitly all functions g for which all translates and modulates of g form an orthonormal basis for L\textasciicircum{}2(R). There are a number of consequences of this classification, including a simple direct classification of the alternate dual frames to a WH-frame (A result originally due to Janssen). ",

author = "P. Cazsazza and Janssen, \{A. J. E. M.\} and Ole Christensen",

year = "1999",

language = "English",

pages = "1--22",

journal = "Unknown title",

}

TY - JOUR

T1 - Classifying tight Weyl-Heisenberg frames

AU - Cazsazza, P.

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

AU - Christensen, Ole

PY - 1999

Y1 - 1999

N2 - A Weyl-Heisenberg frame for L^2(R) is a frame consisting of translates and modulates of a fixed function. In this paper we give necessary and sufficient conditions for this family to form a tight WH-frame. This allows us to write down explicitly all functions g for which all translates and modulates of g form an orthonormal basis for L^2(R). There are a number of consequences of this classification, including a simple direct classification of the alternate dual frames to a WH-frame (A result originally due to Janssen).

AB - A Weyl-Heisenberg frame for L^2(R) is a frame consisting of translates and modulates of a fixed function. In this paper we give necessary and sufficient conditions for this family to form a tight WH-frame. This allows us to write down explicitly all functions g for which all translates and modulates of g form an orthonormal basis for L^2(R). There are a number of consequences of this classification, including a simple direct classification of the alternate dual frames to a WH-frame (A result originally due to Janssen).

M3 - Journal article

SP - 1

EP - 22

JO - Unknown title

JF - Unknown title

ER -

Classifying tight Weyl-Heisenberg frames

Abstract

OpenUrl availability

Fingerprint

Cite this