Theory of wavelet transform over finite fields
- 1 January 1999
- conference paper
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- Vol. 3 (15206149) , 1213-1216 vol.3
- https://doi.org/10.1109/icassp.1999.756196
Abstract
We develop the theory of the wavelet transform over Galois fields. To avoid the limitations inherent in the number theoretic Fourier transform over finite fields, our wavelet transform relies on a basis decomposition in the time domain rather than in the frequency domain. First, we characterize the infinite dimensional vector spaces for which an orthonormal basis expansion of any sequence in the space can be obtained using a symmetric bilinear form. Then, by employing a symmetric, non-degenerate, canonical bilinear form we derive the necessary and sufficient condition that basis functions over finite fields must satisfy in order to construct an orthogonal wavelet transform. Finally, we give a design methodology to generate the mother wavelet and scaling function over Galois fields by relating the wavelet transform to a two channel paraunitary filter bank.Keywords
This publication has 6 references indexed in Scilit:
- Theory of wavelet transform over finite fieldsPublished by Institute of Electrical and Electronics Engineers (IEEE) ,1999
- Paraunitary filter banks over finite fieldsIEEE Transactions on Signal Processing, 1997
- A binary wavelet decomposition of binary imagesIEEE Transactions on Image Processing, 1996
- Finite-field wavelet transformsPublished by Springer Nature ,1996
- Wavelet transforms associated with finite cyclic groupsIEEE Transactions on Information Theory, 1993
- A discrete-time multiresolution theoryIEEE Transactions on Signal Processing, 1993