Design of fractional delay filter, differintegrator, fractional Hilbert transformer, and differentiator in time domain with Peano kernel

Authors:
Soo-Chang Pei;Peng-Hua Wang;Chia-Huei Lin
Affiliations:
Department of Electrical Engineering, College of Electrical Engineering and Computer Science, National Taiwan University, Taipei, Taiwan;Graduate Institute of Communication Engineering, National Taipei University, Taipei, Taiwan;MStar Semiconductor Inc., Hsinchu, Taiwan
Venue:
IEEE Transactions on Circuits and Systems Part I: Regular Papers
Year:
2010

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Abstract

In this paper, we propose a fractional delay filter, an integer-order differintegrator, a fractional Hilbert transformer, and a fractional differintegrator. Through the time-domain analysis on the desired input and output signals of a linear time-invariant system, we derive a set of linear equations, which can be solved to obtain the coefficients of the desired filter. We also show that the difference between the desired output signal and the actual output of the system can be represented as the convolution of the derivative of the input signal and the Peano kernel.