期刊
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
卷 61, 期 -, 页码 1-24出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.acha.2022.05.002
关键词
AP-frames; Stationary random fields and processes
资金
- University of Buenos Aires [20020170100266BA]
- CONICET, Buenos Aires, Argentina [112 201701 00608]
This paper establishes a necessary and sufficient condition for a Gabor system to be an L-2(R)-frame in terms of Gaussian stationary random processes, based on the Ergodic Theorem. Density conditions for associated stationary sequences in relation to a wide sense stationary random process are also investigated.
It is known that, in general, an AP-frame is an L-2(R)-frame and conversely. Here, in part as a consequence of the Ergodic Theorem, we prove a necessary and sufficient condition for a Gabor system {g(t-k)e(il(t-k)),l is an element of L=omega(0)Z,k is an element of K=t(0)Z} to be an L-2(R)-Frame in terms of Gaussian stationary random processes. In addition, if X=(X(t))(t is an element of R )is a wide sense stationary random process, we study density conditions for the associated stationary sequences {, l is an element of L,k is an element of K}. (C) 2022 Elsevier Inc. All rights reserved.
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