Multiband signal reconstruction from finite samples

Abstract The minimum mean-squared error (MMSE) estimator has been used to reconstruct a band-limited signal from its finite samples in a bounded interval and shown to have many nice properties. In this research, we consider a special class of band-limited 1-D and 2-D signals which have a multiband structure in the frequency domain, and propose a new reconstruction algorithm to exploit the multiband feature of the underlying signals. The concept of the critical value and region is introduced to measure the performance of a reconstruction algorithm. We show analytically that the new algorithm performs better than the MMSE estimator for band-limited/multiband signals in terms of the critical value and region measure. Finally, numerical examples of 1-D and 2-D signal reconstruction are given for performance comparison of various methods.

[1]  M C Jackson,et al.  DIGITAL PROCESSING OF BANDPASS SIGNALS , 1986 .

[2]  Heinz-Josef Schlebusch,et al.  On a conjecture of J. L. C. Sanz and T. S. Huang , 1985, IEEE Trans. Acoust. Speech Signal Process..

[3]  J. Cadzow,et al.  An extrapolation procedure for band-limited signals , 1979 .

[4]  T. Parks,et al.  Optimal estimation for band-limited signals including time domain considerations , 1983 .

[5]  Marek A. Kowalski,et al.  Optimal complexity recovery of band- and energy-limited signals II , 1989, J. Complex..

[6]  Norman E. Hurt,et al.  Phase Retrieval and Zero Crossings , 1989 .

[7]  A. Papoulis.  A new algorithm in spectral analysis and band-limited extrapolation. , 1975 .

[8]  Rodney G. Vaughan,et al.  The theory of bandpass sampling , 1991, IEEE Trans. Signal Process..

[9]  Henry J. Landau,et al.  Extrapolating a band-limited function from its samples taken in a finite interval , 1986, IEEE Trans. Inf. Theory.

[10]  Dante C. Youla,et al.  Generalized Image Restoration by the Method of Alternating Orthogonal Projections , 1978 .

[11]  Charles A. Micchelli,et al.  A Survey of Optimal Recovery , 1977 .

[12]  T. J. Rivlin,et al.  Optimal Estimation in Approximation Theory , 1977 .

[13]  R. Gerchberg.  Super-resolution through Error Energy Reduction , 1974 .

[14]  Giancarlo Calvagno,et al.  New results on Yen's approach to interpolation from nonuniformly spaced samples , 1990, International Conference on Acoustics, Speech, and Signal Processing.

[15]  A. N. Tikhonov,et al.  Solutions of ill-posed problems , 1977 .

[16]  M. M. Dodson,et al.  The Distribution of Sampling Rates for Signals with Equally Wide, Equally Spaced Spectral Bands , 1993, SIAM J. Appl. Math..

[17]  W.M. Waters,et al.  Bandpass Signal Sampling and Coherent Detection , 1982, IEEE Transactions on Aerospace and Electronic Systems.

[18]  M. Zuhair Nashed,et al.  General sampling theorems for functions in reproducing kernel Hilbert spaces , 1991, Math. Control. Signals Syst..

[19]  Dale H. Mugler.  Computationally efficient linear prediction from past samples of a band-limited signal and its derivative , 1990, IEEE Trans. Inf. Theory.

[20]  Jan P. Allebach,et al.  Analysis of error in reconstruction of two-dimensional signals from irregularly spaced samples , 1987, IEEE Trans. Acoust. Speech Signal Process..

[21]  Z. Zhang,et al.  Error analysis of the MMSE estimator for multidimensional band-limited extrapolations from finite samples , 1994, Signal Process..

[22]  S. Liberty,et al.  Linear Systems , 2010, Scientific Parallel Computing.

[23]  F. Beutler.  Error-Free Recovery of Signals from Irregularly Spaced Samples , 1966 .

[24]  O. Grace,et al.  Quadrature Sampling of High‐Frequency Waveforms , 1968 .

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

[26]  B. M. Fulk.  MATH , 1992 .

[27]  W. Splettstosser,et al.  Difference methods for the predictions of band-limited signals , 1986 .

[28]  Sigmar Ries,et al.  Reconstruction of real and analytic band-pass signals from a finite number of samples , 1993, Signal Process..

[29]  D. Slepian.  Prolate spheroidal wave functions, fourier analysis, and uncertainty — V: the discrete case , 1978, The Bell System Technical Journal.

[30]  Xu Wenyuan,et al.  On the Extrapolation of Band-Limited Functions with Energy Constraints , 1982 .

[31]  L. Levi,et al.  Fitting a bandlimited signal to given points , 1965, IEEE Trans. Inf. Theory.

[32]  Christodoulos Chamzas,et al.  On the extrapolation of band-limited functions with energy constraints , 1983 .

[33]  Jack D. Gaskill,et al.  Linear systems, fourier transforms, and optics , 1978, Wiley series in pure and applied optics.

[34]  Rudolph E. Langer,et al.  On Numerical Approximation , 1959 .

[35]  V. A. Morozov,et al.  The Error Principle in the Solution of Operational Equations by the Regularization Method , 1968 .

[36]  J. Sanz,et al.  Some aspects of band-limited signal extrapolation: Models, discrete approximations, and noise , 1983 .

[37]  Lee C. Potter,et al.  Energy concentration in band-limited extrapolation , 1989, IEEE Trans. Acoust. Speech Signal Process..