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Analysis of problems of digital filtering and way of their solution
Authors
	Veligosha A.V.
Date of publication
	2016
Abstract
	One of varieties of devices of the digital signal processing (DSP) are devices, functioning on the basis of not radix notations allowing to process data on the principle of multisequencing of algorithms of execution of arithmetical operations. Application of not positional codes allows to provide high performance and reliability of TsOS devices. Functioning of the digital filters (DF) constructed on the modern element basis is connected to the following contradiction: increase of accuracy of computation reduces high-speed performance of computation of output counting or considerably increases the hardware expenses that is unacceptable. In article estimates for implementation of the modular TsF processing 16 bit input data from 16 in bit coefficients are carried out. Therefore, in case of execution of operation of multiplication in the computing channel of modular TsF the result shall be the 32nd bit since operation of rounding or truncation can't be applied for the reason that representation of the intermediate result in the system of residual classes (SRC) in each computing channel will change and the wrong resulting output counting of the filter will be received. The accounting of this circumstance demanded a choice of expanded system of the bases, Increase in quantity of the bases leads to increase in instrumental expenses. For the purpose of their reduction it is offered to carry out scaling of output counting of each computing channel of modular DSP. Scaling operation is performed by division, the received result in each computing channel on the scaling coefficient. Carrying out scaling leads to the considerable reduction of instrumental expenses in view of the fact that conversion of output counting, modular DSP will be carried out by smaller quantity of the bases. The offered method of reduction of the range of data representation in modular digital filters is effective and from the point of view of reduction of time expenditure for the reason that it isn't required to carry out computation of orthogonal bases and a rank of number in case of data transformation from SRC to radix notation by a traditional method. As in computation process of output counting in computing channels of modular DSP scaling operation was performed, after their conversion from SRC it is necessary to carry out multiplication to radix notation, the received result on a constant and for support of convergence of the scaled results with a response of the positional digital filter it is necessary to increase the received results by correction coefficient. Application of the offered scaling technique allowed to carry out procedure of inverse transformation from SRC in PSS, using 16-bit data. It allows to reduce circuit costs of operation of conversion to 1,78 times in comparison with use of the Chinese theorem of residuals (CRT). The basic principles of execution of not modular procedures in modular arithmetics which treat data transformation of radix notation to SRC and back and diagrams of devices them implementing are shown. The conclusion is drawn that application of modular codes provides high fail safety of DSP devices, at the expense of their unique adjusting opportunities.
Keywords
	digital filter, orthogonal bases, system of residual classes, modular codes, system of the bases, working bases, control bases, number rank, representation range, output counting, method, the adaptive digital filter.
Library reference
	Veligosha A.V. Analysis of problems of digital filtering and way of their solution // Problems of Perspective Micro- and Nanoelectronic Systems Development - 2016. Proceedings / edited by A. Stempkovsky, Moscow, IPPM RAS, 2016. Part 1. P. 195-201.
URL of paper
	http://www.mes-conference.ru/data/year2016/pdf/D190.pdf