Linear fractional shift invariant (LFSI) systems

Akay O.

7th International Symposium on Signal Processing and Its Applications, Paris, Fransa, 1 - 04 Temmuz 2003, ss.585-588, (Tam Metin Bildiri)

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Cilt numarası:
  • Doi Numarası: 10.1109/isspa.2003.1224771
  • Basıldığı Şehir: Paris
  • Basıldığı Ülke: Fransa
  • Sayfa Sayıları: ss.585-588
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

In this paper, we formulate continuous time linear fractional shift invariant (LFSI) systems that generalize the well-known linear time invariant (LTI) systems by means of an angle parameter phi. LTI systems are obtained as a special case of LFSI systems for phi = 0. LFSI systems belong to the large class of time-varying systems. Whereas LTI systems commute with time shifts, LFSI systems commute with fractional shifts defined on the time-frequency plane. Just as the conventional Fourier transform (FT) diagonalizes LTI systems, an LFSI system associated with angle phi is diagonalized by the fractional Fourier transform (FrFT) defined at the perpendicular angle phi + (pi/2). We show that the eigenfunctions of an LFSI system at angle phi are linear FM (chirp) signals with a sweep rate of tan phi. Finally, we demonstrate via a simulation example that, in certain cases, LFSI systems can outperform LTI systems.