M.Sc Thesis

M.Sc StudentGrossmann Liron
SubjectAn L1-Framework for the Design of Linear-Phase FIR Digital
DepartmentDepartment of Electrical and Computer Engineering
Supervisor PROF. Yonina Eldar
Full Thesis textFull thesis text - English Version


Linear-phase finite impulse response (FIR) digital filters play an important role in many signal processing applications, for example, in multirate systems, image processing, and communication systems, to mention a few. Consequently, design methods for linear-phase filters have been intensively researched in the digital signal processing literature for over almost half a decade.

The filter design of FIR filters has long been recognized as an approximation problem, where an ideal frequency response, usually a discontinuous functions, is approximated by a finite number of smooth functions. Such an approximation problem usually consists of a trade-off. On the one hand the resulting filter should preserve the discontinuous behavior of the ideal response, i.e. sharp transitions. On the other hand, these filters are also required to be as flat as possible in the passbands and stopbands.

This thesis considers the design of linear-phase finite impulse response digital filters using an L1 optimality criterion. The motivation for using such filters as well as a mathematical framework for their design is introduced. It is shown that L1 filters possess flat passbands and stopbands while keeping their transition band comparable to that of the least-squares filters.

The uniqueness of  L1 based filters is explored, and an alternation type theorem for the unique frequency response is derived. An efficient algorithm for calculating the optimal coefficients is proposed, which may be viewed as the analogue of the celebrated Remez exchange method.

A comparison with other techniques is made, demonstrating that the L1 approach may be a good alternative in several applications.