SVIBOR - Project code: 1-01-298

MINISTRY OF SCIENCE AND TECHNOLOGY

Strossmayerov trg 4, HR - 10000 ZAGREB
tel.: +385 1 459 44 44, fax: +385 1 459 44 69
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Project code: 1-01-298

THE SAMPLING THEORY OF STOCHASTIC SIGNALS

Main researcher: POGANJ, TIBOR (159666)

Assistants

Type of research: basic
Duration from: 09/01/91. to 12/31/93.

Papers on project (total): 19
Papers on project quoted in Current Contents: 5

Institution name: Pomorski fakultet, Rijeka (112)
Department/Institute: Department of Sciences
Address: Studentska 2
City: 51000 - Rijeka, Croatia

Communication: Phone: 385 (0)51 38411; Fax: 385 (0)51 36755

Summary: Mean - square and almost sure reconstruction is considered for spectrally band - limited and non - band - limited stochastic signals (weakly stationary stochastic processes, homogeneous random fields, random distributions). The reconstruction error upper bounds are derived in both of, above mentioned, approaches for stochastic signals. Necessary and sufficient conditions are derived for the existence of the Fourier - integral form spectral representation of the sampling cardinal series expansion of non -band - limited stochastic signals. In the case of multidimensional signals with correlated coordinates, the mean square (and the almost sure as well) sampling approximation error upper bounds are generalized to the so - called truncation cross - error upper bounds for the sampling cardinal series.

Keywords: Sampling theorems, Band - limited signals, Non - band - limited signals, Weakly stationary stochastic processes, Homogeneous random fields, Random distributions, Sampling cardinal series expansion, Truncation error, Mean square convergence, Almost sure convergence, Fourier - integral representation, Spectral representation, Multidimensional stochastic signals, Correlated signals, Chebyshev inequality, Borel - Cantelli lemma.

Research goals: In the whole investigations just non - band - limited stochastic signals will be considered, but the principal results involve many times certain before derived results for band - limited signals. MAIN GOALS: 1. Mean - square and almost sure sampling reconstruction of: 1.1. weakly stationary stochastic processes, 1.2. homogeneous random fields, 1.3. random distributions. 1.4. Approximation error upper bound evaluations for 1.1.-1.3.. 2. Fourier - integral form represenation for the sampling cardinal series expansion of non - band - limited stochastic signals: 2.1.scalar and vectorial processes, 2.2. homogeneous random fields, 2.3. random distributions. 3. Multidimensional analogons truncation error upper bound evaluations if the initial signal possesses correlated coordinates. EXPECTED RESULTS: The realization of above exposed research program contains these expaected results. Namely, some recent best results due to the researcher (see e.g. 1.3. and the pharagraph 2.). Certain improvements of these evaluations and obtaining the exact connections between the existence of the integral representations 2. and the continuity of the spectral distribution function of the considered signals leads us to expected results.

Other information about the project.


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