Abstract
This paper presents some novel approaches which are useful for identifying, filtering, and smoothing a finite number of graphs or signals which are simultaneously present, assuming that some or all of the a priori information about the function of the signals, such as form and parameters, is known. Under some circumstances, such as seismic wave detection in connection with oil exploration experiments, only the discrete data points are available. Traditionally, when these discrete data points are scattered over a two-dimensional space they are processed manually, using a family of templates. The algorithms developed in this work will enable us to process these data points with the use of digital computers. This paper tries to answer the questions such as: "What is the best algorithm to process data of this kind in order to achieve optimal usage of the available data and accuracy of identification?" "What is the required computer memory capacity and speed of convergence of the algorithms?" etc.
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