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Basic relations valid for the Bernstein spaces B ² σ and their extensions to larger function spaces via a unified distance concept

P. L. Butzer, R. L. Stens, G. Schmeisser (2014)

Banach Center Publications

Some basic theorems and formulae (equations and inequalities) of several areas of mathematics that hold in Bernstein spaces B σ p are no longer valid in larger spaces. However, when a function f is in some sense close to a Bernstein space, then the corresponding relation holds with a remainder or error term. This paper presents a new, unified approach to these errors in terms of the distance of f from B σ p . The difficult situation of derivative-free error estimates is also covered.

Coarse quantization for random interleaved sampling of bandlimited signals

Alexander M. Powell, Jared Tanner, Yang Wang, Özgür Yılmaz (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The compatibility of unsynchronized interleaved uniform sampling with Sigma-Delta analog-to-digital conversion is investigated. Let f be a bandlimited signal that is sampled on a collection of N interleaved grids  {kT + Tn} k ∈ Zwith offsets { T n } n = 1 N [ 0 , T ] T n n = 1 N ⊂ [ 0 ,T ] . If the offsetsTn are chosen independently and uniformly at random from  [0,T]  and if the sample values of fare quantized with a first order Sigma-Delta algorithm, then with high probability the quantization error | f ( t ) - f ˜ ( t ) | | f ( t ) − x10ff65;...

Coarse quantization for random interleaved sampling of bandlimited signals∗∗∗

Alexander M. Powell, Jared Tanner, Yang Wang, Özgür Yılmaz (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

The compatibility of unsynchronized interleaved uniform sampling with Sigma-Delta analog-to-digital conversion is investigated. Let f be a bandlimited signal that is sampled on a collection of N interleaved grids  {kT + Tn} k ∈ Z with offsets { T n } n = 1 N [ 0 , T ] . If the offsets Tn are chosen independently and uniformly at random from  [0,T]  and if the sample values of f are quantized with a first order Sigma-Delta algorithm, then with high probability...

Construction of sampling and interpolating sequences for multi-band signals. the two-band case

Sergei Avdonin, Anna Bulanova, William Moran (2007)

International Journal of Applied Mathematics and Computer Science

Recently several papers have related the production of sampling and interpolating sequences for multi-band signals to the solution of certain kinds of Wiener-Hopf equations. Our approach is based on connections between exponential Riesz bases and the controllability of distributed parameter systems. For the case of two-band signals we derive an operator whose invertibility is equivalent to the existence of a sampling and interpolating sequence, and prove the invertibility of this operator.

Flow control in connection-oriented networks: a time-varying sampling period system case study

Przemysław Ignaciuk, Andrzej Bartoszewicz (2008)

Kybernetika

In this paper congestion control problem in connection-oriented communication network with multiple data sources is addressed. In the considered network the feedback necessary for the flow regulation is provided by means of management units, which are sent by each source once every M data packets. The management units, carrying the information about the current network state, return to their origin round trip time RTT after they were sent. Since the source rate is adjusted only at the instant of...

Information measures and uncertainty of particular symbols

Milan Mareš (2011)

Kybernetika

The measurement of information emitted by sources with uncertainty of random type is known and investigated in many works. This paper aims to contribute to analogous treatment of information connected with messages from other uncertain sources, influenced by not only random but also some other types of uncertainty, namely with imprecision and vagueness. The main sections are devoted to the characterization and quantitative representation of such uncertainties and measures of information produced...

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