M.Sc Thesis | |

M.Sc Student | Grossmann Liron |
---|---|

Subject | An L1-Framework for the Design of Linear-Phase FIR Digital Filters |

Department | Department of Electrical and Computer Engineering |

Supervisor | PROF. Yonina Eldar |

Full Thesis text |

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 L_{1}
optimality criterion. The motivation for using such filters as well as a
mathematical framework for their design is introduced. It is shown that L_{1}
filters possess flat passbands and stopbands while keeping their transition
band comparable to that of the least-squares filters.

The uniqueness of L_{1}
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 L_{1} approach may be a good
alternative in several applications.