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# Analytical interpolation of distributions in the identification scales space

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Y.N. Klikushin, V.Y. Kobenko

A method of interpolation position distribution of the signal between the reference points of the scale identity is provided. The possibility of using this method to compare the signals was demonstrated. The method is based on the ideas and methods of the theory of identification measurements, according to which the selective implementation of the signal can be displayed in a certain, specific number. This number is called the ID and its main property is the property of scale invariance. Due to the property of scale invariance identification number is independent of linear transformations of the original set. The most sensitive is the identifying number to the input waveform. Therefore, when ordering identification numbers, is arranging the waveform (the forms of distribution of instantaneous values). Logical correspondence between the identification number (shape parameter) and the linguistic term denoting a kind of distribution is established with a tool called Identity scale. Identification scale similar to the scale usually shows the device, which is complemented by digitized mark names of their respective distributions. If the needle of this instrument under the influence of the input signal deviated by an angle, then there is a problem reading the (interpolated) results. To solve this problem, we propose the following technique. First, the identification of the scale of the table is translated into an analytic representation. It uses the characteristics of the rank - the dependence of the ID numbers of the serial number on the identification scale distribution. To rank features selected (using special software) analytical description. Second, if, when analyzing the input signal generates an ID number, using previously obtained analytical description, the number is converted to the corresponding value of the rank. In general, the rank of the signal being analyzed will be a rational number, the whole of which points to a number of the nearest reference point. Fractional part of the ranking points to the grade of membership of the input digitized identification mark of the scale. Thus, the proposed method allows us not only to identify the distribution, but also to \"measure\" it, pointing quantifies the degree of uncertainty in the form of accessories. Prospects of application of analytical interpolation distributions in the space of identification scales associated with the recognition and identification of complex signals, such as the design and development of information-measuring and control systems, in solving problems of medical and technical diagnostics.
References:
1. Klikushin JU.N.Fraktalnaja shkala dlja izmerenija formy raspredelenijj verojatnosti // Radioehlektronika. 2000. № 3. http://jre.cplire.ru.
2. Klikushin JU.N. Identifikacionnye instrumenty analiza i sinteza formy signalov: monografija. Omsk: Izd-vo  OmGTU. 2010. 216 s.
3. Klikushin JU.N., Koshekov K.T., Koshekova B.V. Transljator kak universalnyjj instrument identifikacionnykh izmerenijj // Informacionno-izmeritelnye i upravljajushhie sistemy. 2008. № 9. T. 6.S.24 – 30.
4. Gorshenkov A.A., Klikushin JU.N. Predstavlenie modelejj signalov v sisteme identifikacionnykh parametrov // Radioehlektronika. 2010. № 9. http://jre.cplire.ru.
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