The GDST Frame and Inverse Transforms

Yusong Yan; Hongmei Zhu

doi:10.1109/ICSIDP47821.2019.9173153

The GDST Frame and Inverse Transforms

Yusong Yan, Hongmei Zhu

School of Information and Electronics

York University Toronto

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Citation (Scopus)

Abstract

Generalization of the Discrete Stockwell Transform (GDST) provides a constructive framework to unify and expand various existing discrete Stockwell transforms. Under the developed framework, we are able to flexibly adjust the time/frequency sampling resolution, tailor the amount of information redundancy and computational complexity, reserve the absolutely reference phases as well. In this paper, we propose an admissible condition and prove that any GDST satisfy this condition will constitute a frame in the Hilbert Space, which guides us to derive the explicit formula for the inverse of GDST through finding its canonical dual frame.

Original language	English
Title of host publication	ICSIDP 2019 - IEEE International Conference on Signal, Information and Data Processing 2019
Publisher	Institute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)	9781728123455
DOIs	https://doi.org/10.1109/ICSIDP47821.2019.9173153
Publication status	Published - Dec 2019
Event	2019 IEEE International Conference on Signal, Information and Data Processing, ICSIDP 2019 - Chongqing, China Duration: 11 Dec 2019 → 13 Dec 2019

Publication series

Name	ICSIDP 2019 - IEEE International Conference on Signal, Information and Data Processing 2019

Conference

Conference	2019 IEEE International Conference on Signal, Information and Data Processing, ICSIDP 2019
Country/Territory	China
City	Chongqing
Period	11/12/19 → 13/12/19

Keywords

Discrete Stockwell Transform
GDST
frame
invert transform
time-frequency analysis

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10.1109/ICSIDP47821.2019.9173153

Cite this

Yan, Y., & Zhu, H. (2019). The GDST Frame and Inverse Transforms. In ICSIDP 2019 - IEEE International Conference on Signal, Information and Data Processing 2019 Article 9173153 (ICSIDP 2019 - IEEE International Conference on Signal, Information and Data Processing 2019). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICSIDP47821.2019.9173153

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title = "The GDST Frame and Inverse Transforms",

abstract = "Generalization of the Discrete Stockwell Transform (GDST) provides a constructive framework to unify and expand various existing discrete Stockwell transforms. Under the developed framework, we are able to flexibly adjust the time/frequency sampling resolution, tailor the amount of information redundancy and computational complexity, reserve the absolutely reference phases as well. In this paper, we propose an admissible condition and prove that any GDST satisfy this condition will constitute a frame in the Hilbert Space, which guides us to derive the explicit formula for the inverse of GDST through finding its canonical dual frame.",

keywords = "Discrete Stockwell Transform, GDST, frame, invert transform, time-frequency analysis",

author = "Yusong Yan and Hongmei Zhu",

note = "Publisher Copyright: {\textcopyright} 2019 IEEE.; 2019 IEEE International Conference on Signal, Information and Data Processing, ICSIDP 2019 ; Conference date: 11-12-2019 Through 13-12-2019",

year = "2019",

month = dec,

doi = "10.1109/ICSIDP47821.2019.9173153",

language = "English",

series = "ICSIDP 2019 - IEEE International Conference on Signal, Information and Data Processing 2019",

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

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Yan, Y & Zhu, H 2019, The GDST Frame and Inverse Transforms. in ICSIDP 2019 - IEEE International Conference on Signal, Information and Data Processing 2019., 9173153, ICSIDP 2019 - IEEE International Conference on Signal, Information and Data Processing 2019, Institute of Electrical and Electronics Engineers Inc., 2019 IEEE International Conference on Signal, Information and Data Processing, ICSIDP 2019, Chongqing, China, 11/12/19. https://doi.org/10.1109/ICSIDP47821.2019.9173153

The GDST Frame and Inverse Transforms. / Yan, Yusong; Zhu, Hongmei.
ICSIDP 2019 - IEEE International Conference on Signal, Information and Data Processing 2019. Institute of Electrical and Electronics Engineers Inc., 2019. 9173153 (ICSIDP 2019 - IEEE International Conference on Signal, Information and Data Processing 2019).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Zhu, Hongmei

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N2 - Generalization of the Discrete Stockwell Transform (GDST) provides a constructive framework to unify and expand various existing discrete Stockwell transforms. Under the developed framework, we are able to flexibly adjust the time/frequency sampling resolution, tailor the amount of information redundancy and computational complexity, reserve the absolutely reference phases as well. In this paper, we propose an admissible condition and prove that any GDST satisfy this condition will constitute a frame in the Hilbert Space, which guides us to derive the explicit formula for the inverse of GDST through finding its canonical dual frame.

AB - Generalization of the Discrete Stockwell Transform (GDST) provides a constructive framework to unify and expand various existing discrete Stockwell transforms. Under the developed framework, we are able to flexibly adjust the time/frequency sampling resolution, tailor the amount of information redundancy and computational complexity, reserve the absolutely reference phases as well. In this paper, we propose an admissible condition and prove that any GDST satisfy this condition will constitute a frame in the Hilbert Space, which guides us to derive the explicit formula for the inverse of GDST through finding its canonical dual frame.

KW - Discrete Stockwell Transform

KW - GDST

KW - frame

KW - invert transform

KW - time-frequency analysis

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DO - 10.1109/ICSIDP47821.2019.9173153

M3 - Conference contribution

AN - SCOPUS:85091921672

T3 - ICSIDP 2019 - IEEE International Conference on Signal, Information and Data Processing 2019

BT - ICSIDP 2019 - IEEE International Conference on Signal, Information and Data Processing 2019

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2019 IEEE International Conference on Signal, Information and Data Processing, ICSIDP 2019

Y2 - 11 December 2019 through 13 December 2019

ER -

The GDST Frame and Inverse Transforms

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