Sampling Theorems for Nonbandlimited Signals

In recent years many of the results for bandlimited sampling have been extended to the case of nonbandlimited signals. These recent extensions have been found to be useful in digital signal processing applications such as image interpolation, equalization of communication channels, and multiresolution computation. In this chapter we give a brief overview of some of these ideas.

[1]  P. P. Vaidyanathan,et al.  Oversampling PCM techniques and optimum noise shapers for quantizing a class of nonbandlimited signals , 1999, IEEE Trans. Signal Process..

[2]  Akram Aldroubi,et al.  B-SPLINE SIGNAL PROCESSING: PART II-EFFICIENT DESIGN AND APPLICATIONS , 1993 .

[3]  P. P. Vaidyanathan,et al.  Efficient implementation of all-digital interpolation , 2001, IEEE Trans. Image Process..

[4]  A. Aldroubi Oblique projections in atomic spaces , 1996 .

[5]  Ingrid Daubechies,et al.  Ten Lectures on Wavelets , 1992 .

[6]  P. P. Vaidyanathan,et al.  Results on vector biorthogonal partners , 2001, 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221).

[7]  P. P. Vaidyanathan,et al.  Reconstruction of sequences from nonuniform samples , 1995, Proceedings of ISCAS'95 - International Symposium on Circuits and Systems.

[8]  Harry Nyquist Certain Topics in Telegraph Transmission Theory , 1928 .

[9]  P. P. Vaidyanathan,et al.  MIMO biorthogonal partners and applications , 2002, IEEE Trans. Signal Process..

[10]  Michael Unser,et al.  Oblique projections in discrete signal subspaces of l2 and the wavelet transform , 1994, Optics & Photonics.

[11]  S. Mallat A wavelet tour of signal processing , 1998 .

[12]  Lang Tong,et al.  Blind identification and equalization based on second-order statistics: a time domain approach , 1994, IEEE Trans. Inf. Theory.

[13]  Richard H. Sherman,et al.  Chaotic communications in the presence of noise , 1993, Optics & Photonics.

[14]  Akram Aldroubi,et al.  B-spline signal processing. II. Efficiency design and applications , 1993, IEEE Trans. Signal Process..

[15]  Stéphane Mallat,et al.  A Theory for Multiresolution Signal Decomposition: The Wavelet Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[16]  Michael Unser,et al.  B-spline signal processing. I. Theory , 1993, IEEE Trans. Signal Process..

[17]  P. P. Vaidyanathan,et al.  On sampling theorems for non bandlimited signals , 2001, 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221).

[18]  Akram Aldroubi,et al.  B-SPLINE SIGNAL PROCESSING: PART I-THEORY , 1993 .

[19]  A. Papoulis,et al.  Generalized sampling expansion , 1977 .

[20]  Khaled A. S. Abdel-Ghaffar,et al.  Reduced GMD decoding , 2003, IEEE Trans. Inf. Theory.

[21]  P. P. Vaidyanathan,et al.  Generalized sampling theorems in multiresolution subspaces , 1997, IEEE Trans. Signal Process..

[22]  Xiang-Gen Xia,et al.  New precoding for intersymbol interference cancellation using nonmaximally decimated multirate filterbanks with ideal FIR equalizers , 1997, IEEE Trans. Signal Process..

[23]  Inbar Fijalkow,et al.  Fractionally spaced equalizers , 1996, IEEE Signal Process. Mag..

[24]  J. Zerubia,et al.  A Generalized Sampling Theory without bandlimiting constraints , 1998 .

[25]  I. J. Schoenberg Cardinal Spline Interpolation , 1987 .

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

[27]  P. Vaidyanathan Multirate Systems And Filter Banks , 1992 .

[28]  Akram Aldroubi,et al.  Nonuniform Sampling and Reconstruction in Shift-Invariant Spaces , 2001, SIAM Rev..

[29]  Michael Unser,et al.  Wavelet Applications in Signal and Image Processing III , 1994 .

[30]  M. Unser Sampling-50 years after Shannon , 2000, Proceedings of the IEEE.

[31]  P. Vaidyanathan Generalizations of the sampling theorem: Seven decades after Nyquist , 2001 .

[32]  Michael Unser,et al.  Fast B-spline Transforms for Continuous Image Representation and Interpolation , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[33]  A. J. Jerri The Shannon sampling theorem—Its various extensions and applications: A tutorial review , 1977, Proceedings of the IEEE.