Linear Phase IIR Hilbert Transformers Using Time Reversal Techniques

Atsushi HIROI  Hiroyuki KAMATA  Yoshihisa ISHIDA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E77-A   No.5   pp.864-867
Publication Date: 1994/05/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section LETTER (Special Section on Signal Processing and System Theory)
Hilbert transformer,  IIR digital filter,  

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This paper describes a new method of approximating ideal Hilbert transformers by using time reversal techniques. As is well known, an ideal Hilbert transformer is not physically realizable because it is not causal. Nevertheless, it is extremely imprortant conceptually in the area of digital signal processing. In this paper, we propose a method to approximately implement such a Hilbert transformer. The method divides the impulse response of the ideal Hilbert transformer into two parts, i.e., causal and noncausal parts. Although a causal filter is physically realizable, a noncausal filter is not realizable. A noncausal filter is realized using time reversal techniques for input signals to the filter, and then the Hilbert transformer can be approximately implemented by the parallel connection of causal and noncausal filters.