Tight Weyl-Heisenberg frames in l(2)

Z Cvetkovic; M Vetterli

Tight Weyl-Heisenberg frames in l(2)

Z Cvetkovic^*, M Vetterli

^*Corresponding author for this work

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

74 Citations (Scopus)

Abstract

Tight Weyl-Heisenberg frames in t(2)(Z) are the tool far short-time Fourier analysis in discrete lime. They are closely related to paraunitary modulated fill er banks and are studied here using techniques of the filter bank theory c. Good resolution of short-time Fourier analysis in the joint time-frequency plane is not attainable unless some redundancy is introduced. That is the reason for considering overcomplete Weyl-Heisenberg expansions. The main result of this correspondence is a complete parameterization of finite length tight Weyl- Heisenberg frames in t(2)(Z) with arbitrary rational oversampling ratios, This parameterization follows from a factorization of polyphase matrices of paraunitary modulated filter banks, which is introduced first.

Original language	English
Pages (from-to)	1256-1259
Number of pages	4
Journal	IEEE Transactions on Signal Processing
Volume	46
Issue number	5
Publication status	Published - May 1998

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Cvetkovic, Z., & Vetterli, M. (1998). Tight Weyl-Heisenberg frames in l(2). IEEE Transactions on Signal Processing, 46(5), 1256-1259. https://www.google.co.uk/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0ahUKEwj2nIeDpI_PAhWHA8AKHTReBL8QFggeMAA&url=https%3A%2F%2Finfoscience.epfl.ch%2Frecord%2F33869%2Ffiles%2FCvetkovicV98b.pdf&usg=AFQjCNGtOj8RcHLG3TvI0kRReeKFz5nYJg&cad=rja

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title = "Tight Weyl-Heisenberg frames in l(2)",

abstract = "Tight Weyl-Heisenberg frames in t(2)(Z) are the tool far short-time Fourier analysis in discrete lime. They are closely related to paraunitary modulated fill er banks and are studied here using techniques of the filter bank theory c. Good resolution of short-time Fourier analysis in the joint time-frequency plane is not attainable unless some redundancy is introduced. That is the reason for considering overcomplete Weyl-Heisenberg expansions. The main result of this correspondence is a complete parameterization of finite length tight Weyl- Heisenberg frames in t(2)(Z) with arbitrary rational oversampling ratios, This parameterization follows from a factorization of polyphase matrices of paraunitary modulated filter banks, which is introduced first.",

author = "Z Cvetkovic and M Vetterli",

year = "1998",

month = may,

language = "English",

volume = "46",

pages = "1256--1259",

journal = "IEEE Transactions on Signal Processing",

issn = "1053-587X",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

number = "5",

}

Cvetkovic, Z & Vetterli, M 1998, 'Tight Weyl-Heisenberg frames in l(2)', IEEE Transactions on Signal Processing, vol. 46, no. 5, pp. 1256-1259. <https://www.google.co.uk/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0ahUKEwj2nIeDpI_PAhWHA8AKHTReBL8QFggeMAA&url=https%3A%2F%2Finfoscience.epfl.ch%2Frecord%2F33869%2Ffiles%2FCvetkovicV98b.pdf&usg=AFQjCNGtOj8RcHLG3TvI0kRReeKFz5nYJg&cad=rja>

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T1 - Tight Weyl-Heisenberg frames in l(2)

AU - Cvetkovic, Z

AU - Vetterli, M

PY - 1998/5

Y1 - 1998/5

N2 - Tight Weyl-Heisenberg frames in t(2)(Z) are the tool far short-time Fourier analysis in discrete lime. They are closely related to paraunitary modulated fill er banks and are studied here using techniques of the filter bank theory c. Good resolution of short-time Fourier analysis in the joint time-frequency plane is not attainable unless some redundancy is introduced. That is the reason for considering overcomplete Weyl-Heisenberg expansions. The main result of this correspondence is a complete parameterization of finite length tight Weyl- Heisenberg frames in t(2)(Z) with arbitrary rational oversampling ratios, This parameterization follows from a factorization of polyphase matrices of paraunitary modulated filter banks, which is introduced first.

AB - Tight Weyl-Heisenberg frames in t(2)(Z) are the tool far short-time Fourier analysis in discrete lime. They are closely related to paraunitary modulated fill er banks and are studied here using techniques of the filter bank theory c. Good resolution of short-time Fourier analysis in the joint time-frequency plane is not attainable unless some redundancy is introduced. That is the reason for considering overcomplete Weyl-Heisenberg expansions. The main result of this correspondence is a complete parameterization of finite length tight Weyl- Heisenberg frames in t(2)(Z) with arbitrary rational oversampling ratios, This parameterization follows from a factorization of polyphase matrices of paraunitary modulated filter banks, which is introduced first.

M3 - Article

SN - 1053-587X

VL - 46

SP - 1256

EP - 1259

JO - IEEE Transactions on Signal Processing

JF - IEEE Transactions on Signal Processing

IS - 5

ER -

Tight Weyl-Heisenberg frames in l(2)

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