Exact Relation Between Continuous and Discrete Linear Canonical Transforms

Creative Commons License

Öktem S. F., Özaktaş M. H.

IEEE SIGNAL PROCESSING LETTERS, cilt.16, sa.8, ss.727-730, 2009 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 16 Sayı: 8
  • Basım Tarihi: 2009
  • Doi Numarası: 10.1109/lsp.2009.2023940
  • Dergi Adı: IEEE SIGNAL PROCESSING LETTERS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.727-730
  • Anahtar Kelimeler: Bicanonical width product, fractional Fourier transform, linear canonical series, linear canonical transform, FRACTIONAL FOURIER-TRANSFORM, DIGITAL COMPUTATION, SERIES EXPANSION, SIGNALS, CONVOLUTION, THEOREMS
  • Orta Doğu Teknik Üniversitesi Adresli: Hayır

Özet

Linear canonical transforms (LCTs) are a family of integral transforms with wide application in optical, acoustical, electromagnetic, and other wave propagation problems. The Fourier and fractional Fourier transforms are special cases of LCTs. We present the exact relation between continuous and discrete LCTs (which generalizes the corresponding relation for Fourier transforms), and also express it in terms of a new definition of the discrete LCT (DLCT), which is independent of the sampling interval. This provides the foundation for approximately computing the samples of the LCT of a continuous signal with the DLCT. The DLCT in this letter is analogous to the DFT and approximates the continuous LCT in the same sense that the DFT approximates the continuous Fourier transform. We also define the bicanonical width product which is a generalization of the time-bandwidth product.