Estimation of aliasing error in sampling theorem for signals not necessarily in wavelet subspaces

Some explicit error bounds are obtained in terms of a signal and a wavelet basis. An application of the error estimation in the computation of the wavelet transform coefficients by the Shensa algorithm is also discussed. From the error bounds, it is clear that a wavelet basis can be adjusted so that the aliasing error can be reduced for a fixed signal.<<ETX>>

[1]  Olivier Rioul,et al.  Fast algorithms for discrete and continuous wavelet transforms , 1992, IEEE Trans. Inf. Theory.

[2]  C.-C. Jay Kuo,et al.  On optimal prefiltering for wavelet coefficient computation , 1992, [1992] Conference Record of the Twenty-Sixth Asilomar Conference on Signals, Systems & Computers.

[3]  Mark J. Shensa,et al.  The discrete wavelet transform: wedding the a trous and Mallat algorithms , 1992, IEEE Trans. Signal Process..

[4]  A. Aldroubi,et al.  Families of wavelet transforms in connection with Shannon's sampling theory and the Gabor transform , 1993 .

[5]  Gilbert G. Walter,et al.  A sampling theorem for wavelet subspaces , 1992, IEEE Trans. Inf. Theory.

[6]  Xiang-Gen Xia,et al.  On sampling theorem, wavelets, and wavelet transforms , 1993, IEEE Trans. Signal Process..