Overcomplete Discrete Wavelet Transforms With Rational Dilation Factors

Bayram I., SELESNICK I. W.

IEEE TRANSACTIONS ON SIGNAL PROCESSING, cilt.57, sa.1, ss.131-145, 2009 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 57 Sayı: 1
  • Basım Tarihi: 2009
  • Doi Numarası: 10.1109/tsp.2008.2007097
  • Dergi Adı: IEEE TRANSACTIONS ON SIGNAL PROCESSING
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.131-145
  • İstanbul Teknik Üniversitesi Adresli: Hayır

Özet

This paper develops an overcomplete discrete wavelet transform (DWT) based on rational dilation factors for discrete-time signals. The proposed overcomplete rational DWT is implemented using self-inverting FIR filter banks, is approximately shift-invariant, and can provide a dense sampling of the time-frequency plane. A straightforward algorithm is described for the construction of minimal-length perfect reconstruction filters with a specified number of vanishing moments; whereas, in the nonredundant rational case, no such algorithm is available. The algorithm is based on matrix spectral factorization. The analysis/synthesis functions (discrete-time wavelets) can be very smooth and can be designed to closely approximate the derivatives of the Gaussian function.