SOME MODERN APPROACHES TO DIGITAL FILTER REALIZATION AND IMPLEMENTATION

Abstract

The increasing speed and decreasing cost of present day digital technology has aroused considerable interest in digital processing of 1-D and 2-D signals. Digital filter is an integral part of these signal processing systems* This thesis is primarily concerned with the problem of realization and implementation ofdigital filters using some of the modern approaches with a view to evolve new struct ures suitable for hardware and software implementation. An attempt has been made to evolve new 2-D digital filter realizations by extending the existing 1-D technique to 2-D cases. In particular, the multiplier/delay extraction approach.of 1-D filter has been extended for realizing 2-D first and second-order all-pass structures. In this technique the transfer matrix parameters of a digital multi-pair are calculated from which the realization can be easily obtained. The realization of recursive digital filter is achieved by designing an intermediate minimum multiplier first-order 2-D all-pass filter having same denominator as that of given transfer function and by applying suitably weighted input sig nals at appropriate selected internal nodes. In many applicat ions, a digital filter is prescribed by phase characteristics.A useful class of such filters is zero-phase filter.Due to one ii quadrant, response, the recursive filter cannot have zero-phase characteristic. However,by proper combination of two or more recursive filters, filtering operation with zero-phase is achieved. The technique for 2-D notch type filter is also proposed. An alternative method for realizing 2-D filter using Routh's array has also been presented. Little work is available in literature on the realiza tion of multi-input multi-output digital filters. A step has been taken in this direction to realize multi-input multioutput filter. In the proposed technique the matrix coeff icients of continued fraction expansion forms are evaluated by constructing a Routh's array and the realization is achieved in terms of adders, multipliers, shift registers and their interconnections. Efforts have been directed in extending the existing 1-D digital filter realization to 2-D cases. The 2-D digital filter transfer functions have been realized in the direct and continued fraction forms. The state models for these forms have been obtained with a view to achieve a variety of filter realizations. Digital filter can be implemented by converting the input-output relations to a computational algorithms. With the advancement of microprocessors, the implementation can be conveniently done by storing the various coefficients in ROM. A novel approach to the digital filter implementa tion using negabinary arithmetic is proposed. The basic strategy is to utilize negabinary base which possesses sign-independent number representability and offers certain advantages over binary system when multi-operand addition is to be performed. The design technique that allows adoption of off-the shelf binary arithmetic circuits to perform multioperand addition and multiplication of negabinary number is proposed first. The multiple operand could be easily added with augmented binary adders connected in the form of a tree. The same hardware could be used to perform multiplication. But from LSI implementation point of view, the use of cellular array structures are explored and necessary changes for designing a combined binary/negabinary multiplier unit are outlined. The use of negabinary system in implementing various forms of digital filters has also been discussed. In this approach ROM table look-up method is used to avoid the multi plication operation. Direct realization of the filter is shown to require a large memory space. Proper partitioning of this problem is done to achieve serial, parallel and pseudo-parallel forms of digital filters. The two pseudoparallel forms are seen to be best forms from the ROM size and the speed of computation point of view. Based on the present work, a number of problems have been suggested in the area of realization and implementation of digital filters.