Synthesis of complete orthonormal fractional basis functions with prescribed poles

Akcay H.

IEEE TRANSACTIONS ON SIGNAL PROCESSING, cilt.56, sa.10, ss.4716-4728, 2008 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 56 Sayı: 10
  • Basım Tarihi: 2008
  • Doi Numarası: 10.1109/tsp.2008.928163
  • Dergi Adı: IEEE TRANSACTIONS ON SIGNAL PROCESSING
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.4716-4728
  • Anahtar Kelimeler: completeness, fractional calculus, orthonormal basis, SYSTEMS, LAGUERRE
  • Anadolu Üniversitesi Adresli: Hayır

Özet

In this paper, fractional orthonormal basis functions that generalize the well-known fixed pole rational basis functions are synthesized. For a range of noninteger differentiation orders and under mild restrictions on the choice of the basis poles, the synthesized basis functions are shown to be complete in the space of functions which are analytic on the open right-half plane and square-integrable on the imaginary axis. This presents an extension of the completeness results for the fractional Laguerre and Kautz bases to fractional orthonormal bases with prescribed pole locations.