Design of Digital Integer order Differintegrator, Fractional Hilbert Transformer and Differentiator in Time Domain with Peano Kernel
Date Issued
2008
Date
2008
Author(s)
Lin, Chia-Huei
Abstract
In this dissertation, we propose an integer order differentiator, an integer order integrator, a fractional order differentiator and a Hilbert transformer. Using a time domain analysis method which is originally used in the derivation of a fractional delay filter, we find the derivations of these proposed filters are quite straightforward. By expanding the predefined ideal input and output signals of the filter into their Taylor series, we can approximate the desired filter with these Taylor series as input and output signals of a LTI system. After some simplification, we derive a set of linear equations which can be solved numerically for the filter’s coefficients. Aside form the derivations of these filters, this time domain analysis allows us to derive a Peano kernel for each proposed filter. A Peano kernel can represents the approximation error of the filter. Some designing examples are also demonstrated in this dissertation.
Subjects
IIR filter
fractional differentiator
differentiator
integrator
Hilbert transformer
Taylor series
Peano kernel
Type
thesis
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