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José M.N. Vieira, University of Aveiro (Portugal)
Paulo J.S.G. Ferreira, University of Aveiro (Portugal)
This paper uncovers relations between the topics mentioned in the title, relations that we believe to have gone nearly unnoticed so far. More precisely, we show that four often studied problems in signal processing, spectrum analysis, information theory, and computing are closely related or even equivalent in a certain sense (if one of them can be solved, so can any of the others, and using essentially the same algorithms). The problems are (i) a nonlinear band-limited finite-dimensional interpolation problem (ii) the problem of estimating a signal that is the superposition of a finite number of harmonics (iii) an error-control coding problem in the real field, and (iv) certain techniques that occur in algorithm-based fault tolerant computing. The advantages of recognizing these problems as equivalent are obvious: the techniques commonly used in one field can be imported to the others, the duplication of research efforts is prevented, and the overall degree of understanding of the four problems increases. New algorithms are suggested as a result of these investigations.
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Yannick Deville, LEP (France)
Nabil Charkani, LTIRF/INPG (France)
In this paper, we investigate the self-adaptive source separation problem for convolutively mixed signals. The proposed approach uses a recurrent structure adapted by a generic rule involving arbitrary separating functions. We first analyze the stability of this class of algorithms. We then apply these results to some classical rules for instantaneous and convolutive mixtures that were proposed in the literature but only partly analyzed. This provides a better understanding of the conditions of operation of these rules. Eventually, we define and analyze a normalized version of the proposed type of algorithms, which yields several attractive features.
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Alban Duverdier, ENSEEIHT (France)
Bernard Lacaze, ENSEEIHT (France)
In modern telecommunications, it is often desirable to scramble the contents of the information. This paper presents a particularly efficient method of analogue signal scrambling. A stationary process is subjected to scrambling by means of a linear periodic time-varying filter. We observe then a cyclostationary process. We demonstrate that perfect reconstruction is possible. In presence of overlapping spectra, unscrambling requires a time-varying filter. We apply this method to scramble stationary binary signals. Simulations show that the system is additive noise resistant.
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M. Pawlak, University of Manitoba (Canada)
U. Stadtmüller, University of Ulm (Germany)
The problem of recovering a signal in the class of band-limited functions is studied. We consider asituation when discrete data points are first grouped to the points of an uniform grid and then thereconstruction is carried out from such a reduced data set. The data grouping is common for computerrounding errors and may also be viewed as a data compression process. The accuracy of the proposedgrouping techniques is examined. These results are used to provide an understanding of the number of grid points required to achieve a given level of accuracy.
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Peter Hoeher, DLR (Germany)
Stefan Kaiser, DLR (Germany)
Patrick Robertson, DLR (Germany)
The potentials of pilot-symbol-aided channel estimation in two dimensions are explored. In order to procure this goal, the discrete shift-variant 2-D Wiener filter is derived and analyzed given an arbitrary sampling grid, an arbitrary (but possibly optimized) selection of observations, and the possibility of model mismatch. Filtering in two dimensions is revealed to outperform filtering in just one dimension with respect to overhead and mean-square error performance. However, two cascaded orthogonal 1-D filters are simpler to implement and shown to be virtually as good as true 2-D filters.
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Howard Hua Yang, RIKEN (Japan)
Shun-ichi Amari, RIKEN (Japan)
In the literature of blind equalization, algorithms developed for equalizing an SISO or SIMO channel fail sometimes when the channel condition is poor. We derive blind equalization algorithms from blind separation algorithms to equalize the SISO channel with fractionally sampling. The approach is also applied to equalize SIMO or MIMO channels. For switching channels, we use an updating rule to tune the learning rate of on-line algorithms automatically to follow the channel change. The idea is applicable to improve all blind equalization algorithms to equalize switching channels.
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Buyurman Baykal, Imperial College (U.K.)
Oguz Tanrkulu, Imperial College (U.K.)
Jonathon A. Chambers, Imperial College (U.K.)
Constant Modulus algorithms based on a deterministic error criterion are presented. Soft constraint satisfaction methods yield a general family of blind equalization algorithms employing nonlinear functions of the equalizer output which must satisfy certain conditions. The algorithms are also extended to cover fractionally-spaced blind equalization. A normalization factor which appears as a result of the deterministic formulation of the problem helps the blind equalizer improve its performance. Also, the family supports a wide range of nonlinear functions. Extensive simulations are presented to reveal convergence characteristics which also include signals from the Signal Processing Information Base (SPIB).
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Akram Aldroubi, NIH, Bethesda (U.S.A.)
Hans Georg Feichtinger, University of Vienna (Austria)
We prove that the exact reconstruction of a function f from its samples $f(x_i)$ on any "sufficiently dense" sampling set ${x_i}$ in $R^n$, where the index set is countable , can be obtained for a large class of spline-like spaces that belong to $L^p(R^n)$. Moreover, the reconstruction can be implemented using fast iterative algorithms. Since, a special case is the space of bandlimited functions, our result generalizes the classical Shannon-Whittacker sampling theorem on regular sampling and the Paley-Wiener theorem on nonuniform sampling.
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Sony John, Caltech (U.S.A.)
Uday Desai, IIT-Bombay (India)
This paper presents a new signal de-noising algorithm using wavelets. We have developed a filtering scheme in the wavelet domain, that involves selective smoothing at each scale of the time-frequency plot. The amount of smoothing is controlled by regularizing factors, and gradient-based switches are used to avoid distortion of signal features. The algorithm is seen to compare favorably to that of Mallat et al, as it is able to recover both the smooth portions as well as Brownian texture in the input, from the noisy signal.
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Stephen D. Casey, American University (U.S.A.)
Carlos A. Berenstein, American University (U.S.A.)
David F. Walnut, American University (U.S.A.)
A novel multisensor approach to deconvolution is developed. This theory circumvents the ill-posedness inherent in convolution equations by overdetermining the input signal by a multichannel system of convolvers ((mu)_i), chosen so that any information lost by one channel is retained by another. The deconvolution problem is then solved by constructing ``deconvolvers'' that allow us to construct the Dirac (delta) by filtering each (mu)_i by its deconvolver, and then adding the filtered channels together. This in turn allows us to reconstruct the original signal f. The process is linear and stable with respect to noise. The general multichannel theory is discussed. The deconvolution theory in radially symmetric domains is then developed in greater detail.
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Haralambos Pozidis, Drexel University (U.S.A.)
Athina P. Petropulu, Drexel University (U.S.A.)
We propose a method for the reconstruction of a complex signal from its Fourier phase only, where the phase is known within a linear phase term, and the sequence's length is unknown. The case of the phase known exactly has received a lot of attention in the past, however, in most cases the phase can be estimated up to a linear phase term whose slope is unknown. Moreover, in most cases of interest, the exact length of the sequence which is to be recovered is unknown. As an application of the reconstruction from phase technique, we propose a method for blind channel identification.
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