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Conjugate-order systems for signal processing: stability, causality, boundedness, compactness

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Abstract

The fundamental system theory is presented for a class of real systems whose derivative order is complex. It is demonstrated that these so-called conjugate-order systems have a scale-invariance property in both the time and frequency domains, which makes them useful for describing certain phenomena in continuous media. The conditions for which these systems are guaranteed to be causal and stable are reviewed. The compactness properties of their Hankel operators, which allow them to admit finite-order approximations, are also discussed. A procedure is developed for choosing appropriate transfer-function parameter values to design a stable conjugate-order system whose frequency response meets given bandwidth, resonance, and ripple specifications.

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Correspondence to Jay L. Adams.

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Adams, J.L., Veillette, R.J. & Hartley, T.T. Conjugate-order systems for signal processing: stability, causality, boundedness, compactness. SIViP 6, 373–380 (2012). https://doi.org/10.1007/s11760-012-0327-z

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  • DOI: https://doi.org/10.1007/s11760-012-0327-z

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