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The Differentiation by a Wavelet and Its Application to the Estimation of a Transfer Function
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 1998/06/25
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Digital Signal Processing
wavelet, digital filter, differential filters, digital signal processing, identification, parameters estimation, step response,
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This paper deals with a set of differential operators for calculating the differentials of an observed signal by the Daubechies wavelet and its application for the estimation of the transfer function of a linear system by using non-stationary step-like signals. The differential operators are constructed by iterative projections of the differential of the scaling function for a multiresolution analysis into a dilation subspace. By the proposed differential operators we can extract the arbitrary order differentials of a signal. We propose a set of identifiable filters constructed by the sum of multiple filters with the first order lag characteristics. Using the above differentials and the identifiable filters we propose an identification method for the transfer function of a linear system. In order to ensure the appropriateness and effectiveness of the proposed method some numerical simulations are presented.