An approximation of Daubechies wavelet matrices by perfect reconstruction filter banks with rational coefficients
Tóm tắt
It is described how the coefficients of Daubechies wavelet matrices can be approximated by rational numbers in such a way that the perfect reconstruction property of the filter bank be preserved exactly.
Tài liệu tham khảo
Daubechies, I.: Orthonormal bases of compactly supported wavelets. Commun. Pure Appl. Math. 41, 909–996 (1988)
Daubechies, I.: Ten Lectures on Wavelets. SIAM, Philadelhia, PA (1992)
Delsarte, P., Gelin, Y., Kamp, Y.: A simple approach to spectral factorization. IEEE Trans. Circuits Syst. 25, 943–946 (1978)
Ephremidze, L., Janashia, G., Lagvilava, E.: On the factorization of unitary matrix-functions. Proc. A. Razmadze Math. Inst. 116, 101–106 (1998)
Ephremidze, L., Janashia, G., Lagvilava, E.: A simple proof of matrix-valued Fejér–Riesz theorem. J. Fourier Anal. Appl. 15, 124–127 (2009). doi:10.1007/s00041-008-9051-z
Ephremidze, L., Lagvilava, E.: On parameterization of compact wavelet matrices. Bull. Georgian Nat. Acad. Sci. 2(4), 23–27 (2008)
Janashia, G., Lagvilava, E.: A method of approximate factorization of positive definite matrix functions. Stud. Math. 137(1), 93–100 (1999)
Janashia, G., Lagvilava, E., Ephremidze, L.: A new method of matrix spectral factorization. IEEE Trans. Inf. Theory 57(4), 2318–2326 (2011). doi:10.1109/TIT.2011.2112233
Mallat, S.: A Wavelet Tour of Signal Processing. Academic, New York (1998)
Resnikoff, H.L., Wells, R.O.: Wavelet Analysis. Springer (1998)