M-ary wavelet transform and formulation for perfect reconstruction in M-band filter bank

Author

Yaou, Ming-Haw ; Chang, Wen-Thong

Author_Institution

Inst. of Commun. Eng., Nat. Chiao Tung Univ., Hsinchu, Taiwan

Volume

42

Issue

12

fYear

1994

fDate

12/1/1994 12:00:00 AM

Firstpage

3508

Lastpage

3512

Abstract

The binary wavelet transform is generalized and extended to the M-ary biorthonormal case. The computational equivalence between the discrete wavelet analysis and the M-band multirate signal filtering is indicated. The equivalence allows the perfect reconstruction requirement in a filter bank to be investigated from the vector space decomposition/reconstruction in wavelet analysis. From the construction of the biorthonormal wavelet bases, the necessary and sufficient condition for the filters in a perfect reconstruction filter bank is formulated. Under this formulation, an additional optimization procedure is then used to model the frequency domain requirement in filter bank design

Keywords

digital filters; filtering theory; frequency-domain synthesis; optimisation; signal reconstruction; wavelet transforms; M-ary wavelet transform; M-band filter bank; binary wavelet transform; biorthonormal case; computational equivalence; discrete wavelet analysis; filter bank; frequency domain requirement; multirate signal filtering; optimization procedure; perfect reconstruction; perfect reconstruction requirement; vector space decomposition; vector space reconstruction; wavelet base; Design optimization; Discrete wavelet transforms; Filter bank; Filtering; Frequency domain analysis; Functional analysis; Signal analysis; Sufficient conditions; Wavelet analysis; Wavelet transforms;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.340784

Filename

340784