61,667 research outputs found
Role of anticausal inverses in multirate filter-banks. I. System-theoretic fundamentals
In a maximally decimated filter bank with identical decimation ratios for all channels, the perfect reconstructibility property and the nature of reconstruction filters (causality, stability, FIR property, and so on) depend on the properties of the polyphase matrix. Various properties and capabilities of the filter bank depend on the properties of the polyphase matrix as well as the nature of its inverse. In this paper we undertake a study of the types of inverses and characterize them according to their system theoretic properties (i.e., properties of state-space descriptions, McMillan degree, degree of determinant, and so forth). We find in particular that causal polyphase matrices with anticausal inverses have an important role in filter bank theory. We study their properties both for the FIR and IIR cases. Techniques for implementing anticausal IIR inverses based on state space descriptions are outlined. It is found that causal FIR matrices with anticausal FIR inverses (cafacafi) have a key role in the characterization of FIR filter banks. In a companion paper, these results are applied for the factorization of biorthogonal FIR filter banks, and a generalization of the lapped orthogonal transform called the biorthogonal lapped transform (BOLT) developed
Cluster Dynamical Mean Field Theories
Cluster Dynamical Mean Field Theories are analyzed in terms of their
semiclassical limit and their causality properties, and a translation invariant
formulation of the cellular dynamical mean field theory, PCDMFT, is presented.
The semiclassical limit of the cluster methods is analyzed by applying them to
the Falikov-Kimball model in the limit of infinite Hubbard interaction U where
they map to different classical cluster schemes for the Ising model.
Furthermore the Cutkosky-t'Hooft-Veltman cutting equations are generalized and
derived for non translation invariant systems using the Schwinger-Keldysh
formalism. This provides a general setting to discuss causality properties of
cluster methods. To illustrate the method, we prove that PCDMFT is causal while
the nested cluster schemes (NCS) in general and the pair scheme in particular
are not. Constraints on further extension of these schemes are discussed.Comment: 26 page
Logical Criticism of Buddhist Doctrines
Logical Criticism of Buddhist Doctrines is a âthematic compilationâ by Avi Sion. It collects in one volume the essays that he has written on this subject over a period of some 15 years after the publication of his first book on Buddhism, Buddhist Illogic. It comprises expositions and empirical and logical critiques of many (though not all) Buddhist doctrines, such as impermanence, interdependence, emptiness, the denial of self or soul. It includes his most recent essay, regarding the five skandhas doctrine
Causal structures and causal boundaries
We give an up-to-date perspective with a general overview of the theory of
causal properties, the derived causal structures, their classification and
applications, and the definition and construction of causal boundaries and of
causal symmetries, mostly for Lorentzian manifolds but also in more abstract
settings.Comment: Final version. To appear in Classical and Quantum Gravit
Quantum geometry with intrinsic local causality
The space of states and operators for a large class of background independent
theories of quantum spacetime dynamics is defined. The SU(2) spin networks of
quantum general relativity are replaced by labelled compact two-dimensional
surfaces. The space of states of the theory is the direct sum of the spaces of
invariant tensors of a quantum group G_q over all compact (finite genus)
oriented 2-surfaces. The dynamics is background independent and locally causal.
The dynamics constructs histories with discrete features of spacetime geometry
such as causal structure and multifingered time. For SU(2) the theory satisfies
the Bekenstein bound and the holographic hypothesis is recast in this
formalism.Comment: Latex 33 pages, 7 Figure, epsfi
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