The problem of inaccurate two to four wire conversion is considered, and a conprehensive survey of the transhybrid responses of 1845 subscribers' lines is carried out.
Results on the optimum performance achieved by line matching techniques are presented, and a simulator which is capable of simulating actual transhybrid responses is described.
The theory of continuous analog recursive adaptive filters is developed, and use of a filtered error signal is shown to considerably simplify their implementation. A simple method of estimating the gradients of the error surface is proposed. A method of modelling the behaviour of the filters is described and used to investigate the effects of these simplifications.
Various filter structures are investigated in terms of suitability for use in an adaptive hybrid. The implementation of 3 types of analog adaptive filter is described, and the effects of circuit imperfections are investigated. Results are presented for the performance of the filters.
A 1st order filter, having a single pole and zero, is shown to provide adequate cancelled return loss against simulated lines. However, the dynamic performance of this filter is shown to be Inadequate unless it converges from a set of stored Initial conditions. It is concluded that implementation of an analog adaptive hybrid is impractical.
The effects of the process of A/D and D/A conversion on the complexity required of a digital adaptive filter are Investigated. It is shown that these effects can be simply compensated.
The implementation of an experimental digital recursive adaptive filter is described, and results are presented for the performance of filters of various orders against subscribers' lines. It 1s shown that a first order pole-zero filter gives adequate static and dynamic performance when using an adaptive step size algorithm. The implementation of the digital adaptive hybrid is discussed.