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Reconstruction of non-uniform sampled discrete-time signals with unknown sampling locations

Keywords:

S.V. Porshnev – Dr.Sc. (Eng.), Professor, Head of Department «Electronics Information Systems», Ural Federal University named after the first President of Russia B.N.Yeltsin, Ekaterinburg. E-mail: sergey_porshnev@mail.ru D.V. Kusaykin – Post-graduate Student, Ural Technical Institute of Communication and Computer Science, Ekaterinburg. E-mail: kusaykin@mail.ru


Irregularly sampled signals are employed in various areas of radio engineering and telecommunications, e.g. in stochastic and quasistochastic coding; in synchronous time division multiplexing; asynchronous transfer mode, in data transmission multiple access; in mobile telecommunication system by the consecutive, regular cell site’s search of the called zones where the object happens to be randomly located resulting in discrete-time irregular sampling; in satellite communication systems (especially in communication with airplanes) being time-sensitive due to constant communication delay (caused by mutual movements of destination and retranslator) and jump ones (caused by retranslator settings), etc. The paper is concerned with analyzing the known irregular sampling models, the results enabled to find enlarged irregular sampling class methods and classify them. Basing on the proposed classification we have drawn a conclusion that the problem of reconstruction of discrete-time signals with non-uniform sampling and discrete-time signals with irregular sampling falls into two groups: 1) discrete-time signals with non-uniform sampling with known sampling locations of non-uniform sampling; 2) discrete-time signals of the set location with unknown sampling locations. The first problem is similar to a well-known table-set function interpolation problem, meanwhile the development of the second problem solution methods has only recently started, and that is why their consideration and classification is bearing a practical aspect. Having implemented the analysis of the known methods of the reconstruction of irregularly sampled discrete-time bandlimited signals with unknown sampling locations we draw a conclusion that most of their reconstruction algorithms are treated as a combinatorial optimization problem to find all unknown sampling signal locations. However, neither of the works studied proposes any recommendations to select initial approximation parameters search areas, meanwhile, to guarantee a finding of a global rather than a local optimized function maximum seems to be of a problem. In this respect the following statements are certain to present practical value: firstly, an application of the considered algorithms to reconstruct irregularly sampled discrete-time bandlimited signals with unknown sampling locations, secondly, a development of the simpler «quasioptimal» methods to approximate the signals considering their local features. The paper is organized as follows. In Section 1 discussed are examples of technical systems employing irregular sampling; in Section 2 kinds of irregular sampling and their features are described; in Section 3 we provide classification of the irregular sampling kinds; in Section 4 considered are algorithms to reconstruct irregularly sampled discrete-time bandlimited signals with unknown sampling locations.
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