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PRINCIPLES OF DIGITAL WIENER FILTERING *
Author(s) -
ROBINSON ENDERS A.,
TREITEL SVEN
Publication year - 1967
Publication title -
geophysical prospecting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.735
H-Index - 79
eISSN - 1365-2478
pISSN - 0016-8025
DOI - 10.1111/j.1365-2478.1967.tb01793.x
Subject(s) - wiener filter , filter (signal processing) , noise (video) , computer science , autocorrelation , signal (programming language) , range (aeronautics) , trace (psycholinguistics) , process (computing) , algorithm , digital filter , signal processing , mathematics , digital signal processing , engineering , statistics , artificial intelligence , linguistics , philosophy , computer hardware , image (mathematics) , computer vision , programming language , aerospace engineering , operating system
The theory of statistical communication provides an invaluable framework within which it is possible to formulate design criteria and actually obtain solutions for digital filters. These are then applicable in a wide range of geophysical problems. The basic model for the filtering process considered here consists of an input signal, a desired output signal, and an actual output signal. If one minimizes the energy or power existing in the difference between desired and actual filter outputs, it becomes possible to solve for the so‐called optimum, or least squares filter, commonly known as the “Wiener” filter. In this paper we derive from basic principles the theory leading to such filters. The analysis is carried out in the time domain in discrete form. We propose a model of a seismic trace in terms of a statistical communication system. This model trace is the sum of a signal time series plus a noise time series. If we assume that estimates of the signal shape and of the noise autocorrelation are available, we may calculate Wiener filters which will attenuate the noise and sharpen the signal. The net result of these operations can then in general be expected to increase seismic resolution. We show a few numerical examples to illustrate the model's applicability to situations one might find in practice.