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논문 기본 정보
- 자료유형
- 학술대회자료
- 저자정보
- 발행연도
- 2009.5
- 수록면
- 235 - 238 (4page)
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초록· 키워드
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For positive integers N, M ∈ N, let g<SUB>n</SUB>, ∈ L²(R) with supp(D<SUB>b</SUB>g<SUB>n</SUB>) ∪ supp(D<SUB>b</SUB>g<SUB>n</SUB>) ⊂ [0, M], where D<SUB>b</SUB>g(t) := b<SUP>?1/2</SUP>g(t/b), b ＞ 0 and n = 1, 2, ...,N. We give another set of necessary and sufficient conditions for the multiwindow Gabor system (G<SUB>N</SUB>; a, b) := {g<SUB>n;k,l</SUB>(t) := g<SUB>n</SUB>(t ? ka)e<SUP>2πilbt</SUP>}<SUB>n=1,...,N; k,l∈Z</SUB> and the corresponding Gabor system (G<SUB>N</SUB>; a, b) to form a pair of dual frames for the rational sampling ab = P/Q with P,Q ∈ N, in addition to the Zibulski-Zeevi and Janssen conditions. The conditions come from the back transform of Zibulski-Zeevi condition to the primal domain but are more informative for the applications. As an applications, we show that the Gabor system (G<SUB>N</SUB>; 1, 1) forms an orthonormal basis for L²(R) if and only if N = 1 and |g₁(t)| = ∑<SUB>M?1</SUB><SUB>m=0</SUB> x<SUB>m+Em</SUB>(t) a.e. where {E<SUB>m</SUB> <SUB>m=0,...,M?1</SUB> forms Lebesgue measurable partition of the unit interval [0, 1). Our criterions provides a rich family of multiwindow dual Gabor frames and multiwindow tight Gabor frames for L²(R) for the particular choices of P, Q, N, M ∈ N.
목차
ABSTRACT
INTRODUCTION AND THE MAIN RESULT
ILLUSTRATION AND EXAMPLES
REFERENCES
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UCI(KEPA) : I410-ECN-0101-2012-410-003697435