I.I. Levin – Dr.Sc.(Eng.), Professor, Head of Department of Intelligent and Multiprocessor Systems Supercomputers and Neurocomputers Research Center (Taganrog)

E-mail: levin@mvs.tsure.ru

D.V. Mikhailov – Post-graduate Student, 

Supercomputers and Neurocomputers Research Center (Taganrog) E-mail: mixailow.den@gmail.com

The article considers the problem of stability loss by recursive adaptive pipelined filters. Pipelining is considered not only as a way to implement parallel computing, but also as a factor that affects the stability of recursive filters. Adaptive filters are considered as a special case of recursive filters, since a change in their coefficients during the adaptation process is an additional factor that can lead to a loss of stability of the filter. It is concluded that the degree of pipelining can be used in order to adjust the stability of filters, in particular adaptive ones. An algorithm for predicting the stability of recursive adaptive pipelined filters is formulated, taking into account the degree of filter pipelining and its adaptation algorithm.

At present, adaptive filters are widely used in various fields of technology: mobile communications, radar, image filtering, etc. The main property of an adaptive system is time-varying functioning with self-regulation. The advantage of such functioning in communication systems and radar stations is the possibility of timely adjustment of the system for changes in both incoming signals and transmission medium conditions during the operation of the device.

If recursive filters are used in the implementation of adaptive systems, these systems get additional advantages: they require less equipment, allow you to achieve performance gains relatively non-recursive, achieve filter characteristics with fairly sharp transitions, etc. However, the use of recursive adaptive filters is associated with difficulties associated with the loss of stability filters when changing their characteristics as a result of adaptation.

Today, real-time digital signal processing requires a constant increase in computation speed, which necessitates the use of parallel computing. The most efficient parallelization method is pipelining computing. The introduction of pipeline registers in recursive filters can lead to a violation of the algorithm of the filter. This problem can be solved with the help of auto-substitution and resynchronization.

A recursive filter of an random order can be represented as a cascading inclusion of filters of the first and second order. The loss of stability of even one of the filters leads to the inoperability of the entire cascade circuit. Thus, the problem of determining the stability of an N-order filter can be reduced to the problem of constructing a cascade of second-order filters and determining the stability of each element of such a chain. In previous works, it was found that after the auto-substitution procedure, the filter may lose stability, but with an increase in the pipelining order it can again become stable.

Based on this, a method for determining the stability of a recursive adaptive pipelined filter is proposed. It consists in the fact that we take an initially stable recursive filter and present it as a cascade connection of second-order filters. Then we consider each cascade separately: we determine the range in which the adaptive filter parameters change, and for each value in this range we find the degree of conveyorization at which all the poles of the transfer function of this filter lie inside the unit circle. Next, we determine the necessary degree of pipelining of the next link, etc.

Thus, pipelining serves not only to achieve high computational performance of the filter, but also to adjust its stability. This is especially true for adaptive filters, which can lose stability as a result of changes in their parameters during adaptation.

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