An optimal design of differentiators by recursive narrowband filters

✍ Scribed by Yasuo Tachibana; Hisakazu Maniwa; Hiroshi Kameda; Michimasa Kondo

• Publisher: John Wiley and Sons
• Year: 1996
• Tongue: English
• Weight: 637 KB
• Volume: 79
• Category: Article
• ISSN: 1042-0967
• DOI: 10.1002/ecjc.4430790206

✦ Synopsis

This paper proposes a narrowband filter, which is a finite impulse response (FIR) filter where the phase response exhibits a constant phase-linear characteristic, independently of the center frequency, and the execution format is a sum of stable recursive filters. The optimal design of the differentiator (differentiation filter) using that narrowband filter is discussed.

To realize a sharp narrowband characteristic, higherarder FIR filters are needed. The narrowband filter proposed in this paper has the feature that it is the sum of the recursive filters, and the operation can be executed with the number of operations which is independent of the order. The filter considered is obtained as a linear combination of a number of narrowband filters with distributed center frequencies.

By connecting the first-order sum or difference filter in series to the above filter, a filter can be constructed which has an arbitrary amplitude response and approximately constant Iinear-phase response. Especially, the optimal design procedure is given for the set of bandpass differentiator filters and application examples are shown for the estimation of the transfer function of the linear system.