Design of FIR Hilbert transformers and differentiators in the complex domain

Author

Komodromos, Michael Z. ; Russell, Steve F. ; Tang, Ping Tak Peter

Author_Institution

Dept. of Electr. & Comput. Eng., Iowa State Univ., Ames, IA, USA

Volume

45

Issue

1

fYear

1998

fDate

1/1/1998 12:00:00 AM

Firstpage

64

Lastpage

67

Abstract

This paper presents a method for the design of FIR Hilbert transformers and differentiators in the complex domain. The method can be used to obtain conjugate-symmetric designs with smaller group delay compared to linear-phase designs. Non-conjugate symmetric Hilbert transformers are also designed. This paper is an extension of our previous work, which presented the algorithm for the design of standard frequency selective filters. The minimax criterion is used and the Chebychev approximation is posed as a linear optimization problem. The primal problem is converted to its dual and is solved using an efficient quadratically convergent algorithm developed by Tang (1988). When a constant group delay is specified, the filter designs have almost linear phase in the passbands. When the specified group delay is half the filter length, the algorithm results in exactly linear-phase designs

Keywords

Chebyshev approximation; FIR filters; Hilbert transforms; convergence of numerical methods; delay circuits; delays; differentiating circuits; digital filters; filtering theory; minimax techniques; Chebychev approximation; FIR Hilbert differentiators; FIR Hilbert transformers; complex domain; conjugate-symmetric designs; constant group delay; linear optimization problem; linear-phase designs; minimax criterion; nonconjugate symmetric Hilbert transformers; quadratically convergent algorithm; Algorithm design and analysis; Approximation algorithms; Delay; Design methodology; Finite impulse response filter; Frequency; Least squares approximation; Minimax techniques; Passband; Transformers;

fLanguage

English

Journal_Title

Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.660756

Filename

660756