Aliasing Error of Sampling Series in Wavelet Subspaces

REFERENCES

• J.L. Brown , Jr. ( 1967 ). On the error in reconstructing non-bandlimited function by means of the bandpass sampling theorem . J. Math. Anal. Appl. 18 : 75 – 84 .
   Web of Science ®Google Scholar
• W. Chen and S. Itoh . ( 1998 ). A sampling theorem for shift invariant subspaces . IEEE Trans. Signal Processing 46 : 2822 – 2824 .
   Google Scholar
• C.K. Chui ( 1992 ). An Introduction to Wavelets . Academic Press , New York .
   Google Scholar
• O. Christensen ( 2003 ). An Introduction to Frames and Riesz Bases . Birkhäuser , Boston .
   Google Scholar
• A.G. García and G. Pérez-Villalón ( 2005 ). On the aliasing error in wavelet subspaces . J. Comput. Appl. Math. 183 : 153 – 167 .
   Google Scholar
• A.G. García and G. Pérez-Villalón ( 2006 ). Dual frames in L 2(0, 1) connected with generalized sampling in shift-invariant spaces . Appl. Comput. Harmon. Anal. 20 ( 3 ): 422 – 433 .
   Web of Science ®Google Scholar
• J.R. Higgins ( 1996 ). Sampling Theory in Fourier and Signal Analysis: Foundations . Oxford University Press , Oxford .
   Google Scholar
• J.M. Kim and K.H. Kwon . Sampling expansion in shift invariant spaces . Intern. J. Wavelets, Multiresolution and Inform. Processing ( To appear ).
   Google Scholar
• A.J.E.M. Janssen ( 1993 ). The Zak transform and sampling theorems for wavelet subspaces . IEEE Trans. Signal Process. 41 : 3360 – 3364 .
   Google Scholar
• M. Unser and A. Aldroubi ( 1994 ). A general sampling theory for nonideal acquisition devices . IEEE Trans. on Signal Process. 42 ( 11 ): 2915 – 2925 .
   Web of Science ®Google Scholar
• M. Unser ( 1999 ). Splines: A perfect fit for signal and image processing . IEEE Signal Processing Magazine 16 ( 6 ): 22 – 38 .
   Web of Science ®Google Scholar
• G.G. Walter ( 1992 ). A sampling theorem for wavelet subspaces . IEEE Trans. Inform. Theory 38 : 881 – 884 .
   Web of Science ®Google Scholar
• X.G. Xia and Z. Zhang ( 1993 ). Estimation of aliasing error in sampling theorem for signals not necessarily in wavelet subspaces . Proc. of ICASSP-93 Vol. 3 , Minneapolis , Minnesota , pp. 300 – 303 .
   Google Scholar
• X. Zhou and W. Sun ( 1999 ). On the sampling theorem for wavelet subspaces . J. Fourier Anal. Appl. 5 : 347 – 354 .
   Web of Science ®Google Scholar