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Maximum number of frequencies in oscillations generated by fractional order LTI systems

Tavazoei, M. S ; Sharif University of Technology | 2010

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  1. Type of Document: Article
  2. DOI: 10.1109/TSP.2010.2049568
  3. Publisher: 2010
  4. Abstract:
  5. In this paper, relation between the inner dimension of a fractional order LTI system and the maximum number of frequencies which exist in oscillations generated by the system is investigated. The considered system is defined in pseudo state space form and the orders of its involved fractional derivatives are rational numbers between zero and one. First, an upper bound is derived for the maximum number of frequencies. Then, using the restricted difference bases concept, a new method is introduced to design a multifrequency oscillatory fractional order system. Finally, based on the proposed method some lower bounds are derived for the maximum number of frequencies obtainable in solutions of a fractional order system having a fixed inner dimension
  6. Keywords:
  7. Fractional order system ; Frequency analysis ; Optimal ruler ; Restricted difference bases ; Fractional derivatives ; Fractional order ; Lower bounds ; LTI systems ; Multi frequency ; Oscillatory system ; Pseudo state ; Rational numbers ; Upper Bound ; Optimization ; Algebra
  8. Source: IEEE Transactions on Signal Processing ; Volume 58, Issue 8 , May , 2010 , Pages 4003-4012 ; 1053587X (ISSN)
  9. URL: http://ieeexplore.ieee.org/document/5458005/?reload=true