Topic
Filter (mathematics)
About: Filter (mathematics) is a research topic. Over the lifetime, 599 publications have been published within this topic receiving 7809 citations. The topic is also known as: Filter (mathematics).
Papers published on a yearly basis
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Papers
TL;DR: The well-known Whittaker-Kotel'nikov-Shannon sampling theorem for frequency-bandlimited functions of time is extended to functions of multidimensional arguments and it is shown that a function whose spectrum is restricted to a finite region of wave-number space may be reconstructed from its samples taken over a periodic lattice having suitably small repetition vectors.
Abstract: The well-known Whittaker-Kotel'nikov-Shannon sampling theorem for frequency-bandlimited functions of time is extended to functions of multidimensional arguments. It is shown that a function whose spectrum is restricted to a finite region of wave-number space may be reconstructed from its samples taken over a periodic lattice having suitably small repetition vectors. The most efficient lattice (i.e., requiring minimum sampling points per unit hypervolume) is not in general rectangular, nor is a unique reconstruction function associated with a given sampling lattice. The above results also apply to homogeneous wave-number-limited stochastic processes in the sense of a vanishing mean-square error. It is also found that, given a particular sampling lattice, the optimum (mean-square) presampling filter for nonwave-number-limited processes effects an ideal wave-number cutoff appropriate to the specified sampling lattice. Particular attention is paid to isotropic processes: minimum sampling lattices are specified up to eight-dimensional spaces, and a number of typical reconstruction functions are calculated.
697 citations
TL;DR: In this article, a characterization of minimal prime filters in the lattice IX containing a given filter in IX by means of ultra-filters on X is presented, which enables us to characterize fuzzy compactness and fuzzy continuity.
Abstract: In the first paragraph we study filters in the lattice IX, where I is the unitinterval and X an arbitrary set. The main result of this section is a characterization of minimal prime filters in IX containing a given filter in IX by means of ultrafilters on X. In the second paragraph we apply the results of the previous section to define convergence in a fuzzy topological space which enables us to characterize fuzzy compactness and fuzzy continuity.
216 citations
8 Jun 2003
TL;DR: In this article, a new topology of high-performance dual-band filters is reported, which allows the control of two bandpasses separated by a transmission zero to ensure a high rejection level between them.
Abstract: This paper reports on a new topology of high-performance dual-band filters. This topology is derived from the Dual Behavior Resonator (DBR) filter. The resulting resonator is directly dual-band. It allows the control of two bandpasses separated by a transmission zero to ensure a high rejection level between them. Moreover, two other transmission zeros are located on either side of the two bandpasses. The possibilities offered by this structure are discussed and measurements are presented to validate the method.
179 citations
TL;DR: A family of invertible discrete-time signal transforms, referred to assymmetric extension transforms(SET's), for finite-length signals, is described and classifies and is shown to be complete in the sense that it contains all possible nonexpansive SET's.
157 citations
1 Jan 1984
TL;DR: In this paper, the authors present the basic theory, examples, and techniques of countable compactness and sequential compactness, and define the properties of filter bases as follows: (1) they can be sequentially compact, wherein every countably filter base has a finer countable filter base that is convergent.
Abstract: Publisher Summary The chapter presents the basic theory, examples, and techniques of countable compactness and sequential compactness. A space X is called sequentially compact if every sequence in X has a convergent subsequence. A space X is called countably compact if sequence in X has a cluster point. A space X is called totally countably compact if every sequence f in X has a subsequence f | A whose range is contained in a compact subset of X. A space X is called ω-bounded if for every sequence f in X, the range of f is contained in a compact subset of X. The properties of filter bases can be defined as follows: (1) they can be sequentially compact, wherein every countably filter base has a finer countable filter base that is convergent; (2) they can be countably compact, wherein every countable filter base has an adherent point, (3) they can be ω-bounded, in which every filter base on a countable set has an adherent point, and (4) they can be totally countably compact, wherein every countable filter base has a finer countable filter base which is total.
140 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2022 | 1 |
| 2021 | 29 |
| 2020 | 27 |
| 2019 | 23 |
| 2018 | 24 |
| 2017 | 26 |