Markov random processes are neither bandlimited nor recoverable from samples or after quantization

This paper considers basic questions regarding Markov random processes. It shows that continuous-time, continuous-valued, wide-sense stationary, Markov processes that have absolutely continuous second-order distribution and finite second moment are not bandlimited. It also shows that continuous-time, stationary, Markov processes that are continuous-valued or discrete-valued and satisfy additional mild conditions cannot be recovered from uniform sampling. Further it shows that continuous-time, continuous-valued, stationary, Markov processes that have absolutely continuous second-order distributions and are continuous almost surely, cannot be recovered without error after quantization. Finally, it provides necessary and sufficient conditions for stationary, discrete-time, Markov processes to have zero entropy rate, and relates this to information singularity

Markov Random Processes are not Recoverable After Quantization and Mostly not Recoverable From Samples

Markov random processes and general random processes are considered. It is shown that continuous-time, continuous-valued, wide-sense stationary, Markov random processes that have absolutely continuous second order distributions are not bandlimited. It is also shown that when these processes are strictly stationary and continuous almost surely, they cannot be recovered without error from their quantized versions. Further, it is shown that continuous-time, discrete-valued Markov random processes, which are uniformly bounded and satisfy an additional condition, can be recovered with zero average distortion from an appropriate set of samples for a general distortion measure. A similar result is shown for general continuous-time random processes with rth power distortion measure. Additionally, it is shown that under a milder condition on the Markov processes and a different condition on the sampling times (e.g., uniform sampling), such processes cannot be recovered with zero average distortion. Finally, the notion of information-singularity is extended to continuous-time random processes, and it is shown that both continuous- and discrete-time Markov processes are not information-singular

Image reconstruction from incomplete information

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The Telecommunications and Data Acquisition Report

This quarterly publication provides archival reports on developments in programs managed by JPL's Office of Telecommunications and Data Acquisition (TDA). In space communications, radio navigation, radio science, and ground-based radio and radar astronomy, it reports on activities of the Deep Space Network (DSN) in planning, supporting research and technology, implementation, and operations. Also included are standards activity at JPL for space data and information systems and reimbursable DSN work performed for other space agencies through NASA

Mathematical linguistics

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Proceedings of the Fifth International Mobile Satellite Conference 1997

Satellite-based mobile communications systems provide voice and data communications to users over a vast geographic area. The users may communicate via mobile or hand-held terminals, which may also provide access to terrestrial communications services. While previous International Mobile Satellite Conferences have concentrated on technical advances and the increasing worldwide commercial activities, this conference focuses on the next generation of mobile satellite services. The approximately 80 papers included here cover sessions in the following areas: networking and protocols; code division multiple access technologies; demand, economics and technology issues; current and planned systems; propagation; terminal technology; modulation and coding advances; spacecraft technology; advanced systems; and applications and experiments

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described