Inverse filters for decomposition of multi-exponential and related signals

Authors:
Vairis Shtrauss
Affiliations:
Institute of Polymer Mechanics, University of Latvia, Riga, Latvia
Venue:
ISTASC'07 Proceedings of the 7th Conference on 7th WSEAS International Conference on Systems Theory and Scientific Computation - Volume 7
Year:
2007

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Abstract

Decomposition of multi-exponential and related signals is generalized as a filtering problem on a logarithmic time or frequency scale and FIR filters operating with logarithmically sampled data are proposed to use for its implementation. The filter algorithms and types are found for various time-domain and frequency-domain mono-components. It is demonstrated that the ill-posedness in the multi-component decomposition manifests as high sampling-rate dependent noise amplification coefficients. The noise transformation control of a filter is provided by algorithm design, which integrates together the signal acquisition, the discrete-time filter design and the regularization based on choosing an optimum sampling rate. As an example, an algorithm is designed for the decomposition in the frequency-domain.