TY - JOUR
T1 - An open question on the existence of Gabor frames in general linear position
AU - Krahmer, Felix
AU - Pfander, Götz E.
AU - Rashkov, Peter
N1 - Publisher Copyright:
© 2009 Dagstuhl Seminar Proceedings. All Rights Reserved.
PY - 2009
Y1 - 2009
N2 - Uncertainty principles for functions defined on finite Abelian groups generally relate the cardinality of a function to the cardinality of its Fourier transform. We examine how the cardinality of a function is related to the cardinality of its short-time Fourier transform. We illustrate that for some cyclic groups of small order, both, the Fourier and the short-time Fourier case, show a remarkable resemblance. We pose the question whether this correspondence holds for all cyclic groups.
AB - Uncertainty principles for functions defined on finite Abelian groups generally relate the cardinality of a function to the cardinality of its Fourier transform. We examine how the cardinality of a function is related to the cardinality of its short-time Fourier transform. We illustrate that for some cyclic groups of small order, both, the Fourier and the short-time Fourier case, show a remarkable resemblance. We pose the question whether this correspondence holds for all cyclic groups.
KW - Gabor systems
KW - erasure channels
KW - short-time Fourier transform
KW - time-frequency dictionaries
KW - uncertainty principle
UR - http://www.scopus.com/inward/record.url?scp=85174529997&partnerID=8YFLogxK
M3 - Conference article
AN - SCOPUS:85174529997
SN - 1862-4405
VL - 8492
JO - Dagstuhl Seminar Proceedings
JF - Dagstuhl Seminar Proceedings
T2 - Structured Decompositions and Efficient Algorithms 2008
Y2 - 30 November 2008 through 5 December 2008
ER -