Multichannel FIR Systems Research Articles

Blind system identification using precise and quantized observations

This paper studies the blind identification of multi-channel FIR systems using precise and quantized observations. First, a new deterministic blind identification (DBI) algorithm is presented for multi-channel FIR systems using precise observations, in which the system parameters can be consistently estimated and the common source signal can be stably recovered. When the observed samples are quantized by a static finite-level quantizer, an iterative deterministic blind identification (IDBI) method is then provided. The asymptotic characters of the proposed IDBI method are discussed and the quantization effect on the identification performance is analyzed. Numerical simulations are given to support the developed DBI method and IDBI method.

Blind identification and equalization of multichannel FIR systems in unbalanced noise environments

This paper considers the problem of identifying and equalizing a set of FIR channels driven by the same input sequence and with outputs affected by unknown amounts of additive noise. The new procedure proposed here allows the estimation of the variances of the noises, of the order of the channels and of their parameters. This procedure leads to good results also when applied to short sequences of data as required in fast-varying environments like mobile communication ones.

A Technical Note on the Fitting of A Multichannel Subset FIR System Within a Potentially Nonstationary Environment, Using the Prewindowed Case - Financial and Economic Forecasting (chapter 9)

The development of a recursive forward and backward time-update algorithm, together with a recursive order-update algorithm, for fitting multichannel subset FIR systems within a potentially nonstationary environment, this method is shown to be efficient and provides linkages between subset AR models and subset FIR systems at consecutive time instants.

Blind identification of multichannel FIR systems based on linear prediction

A blind identification algorithm for multichannel FIR systems is proposed. In the approach, the identification of each channel is decoupled, and channel responses are estimated separately without having to solve for the augmented channel responses. The algorithm can be implemented using linear prediction techniques. It is computationally efficient and suitable for real-time applications. Computer simulations are used to demonstrate the effectiveness of the proposed algorithm.

A least-squares approach to blind channel identification

Conventional blind channel identification algorithms are based on channel outputs and knowledge of the probabilistic model of channel input. In some practical applications, however, the input statistical model may not be known, or there may not be sufficient data to obtain accurate enough estimates of certain statistics. In this paper, we consider the system input to be an unknown deterministic signal and study the problem of blind identification of multichannel FIR systems without requiring the knowledge of the input statistical model. A new blind identification algorithm based solely on the system outputs is proposed. Necessary and sufficient identifiability conditions in terms of the multichannel systems and the deterministic input signal are also presented.

On the Erdös Conjecture Concerning Minimal Norm Interpolation on the Unit Circle

Previous article Next article On the Erdös Conjecture Concerning Minimal Norm Interpolation on the Unit CircleL. Brutman and A. PinkusL. Brutman and A. Pinkushttps://doi.org/10.1137/0717031PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractThe purpose of this note is to complete the proof of the Erdös conjecture concerning optimal points of polynomial interpolation on the unit circle when the number of these points is even.[1] Carl de Boor and , Allan Pinkus, Proof of the conjectures of Bernstein and Erdo˝s concerning the optimal nodes for polynomial interpolation, J. Approx. Theory, 24 (1978), 289–303 10.1016/0021-9045(78)90014-X 80d:41003 0412.41002 CrossrefISIGoogle Scholar[2] L. Brutman, On the polynomial and rational projections in the complex plane, SIAM J. Numer. Anal., 17 (1980), 366–372 10.1137/0717030 82b:30043 0506.30025 LinkISIGoogle Scholar[3] P. Erdös, Problems and results on the convergence and divergence properties of the Lagrange interpolation polynomials and some extremal problems, Mathematica (Cluj), 10 (33) (1967), 65–73 38:1437 Google Scholar[4] Theodore A. Kilgore, A characterization of the Lagrange interpolating projection with minimal Tchebycheff norm, J. Approx. Theory, 24 (1978), 273–288 10.1016/0021-9045(78)90013-8 80d:41002 0428.41023 CrossrefISIGoogle Scholar[5] A. H. Tureckiinodoť, Theory of Interpolation in Problem Form, Izdat. Vyšeišaja Škola, Minsk, 1968, (In Russian.) Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Rootfinding and Function EvaluationA Graduate Introduction to Numerical Methods | 21 November 2013 Cross Ref Classical (Unweighted) and Weighted InterpolationA Panorama of Hungarian Mathematics in the Twentieth Century I | 1 Jan 2006 Cross Ref Computation of the Riesz-Herglotz transform and its application to quadrature formulas over the unit circleNumerische Mathematik, Vol. 93, No. 1 | 1 Nov 2002 Cross Ref Blind identification of multichannel FIR systems based on linear predictionIEEE Transactions on Signal Processing, Vol. 48, No. 9 | 1 Sep 2000 Cross Ref Paul Erdős (1913–1996)Journal of Approximation Theory, Vol. 94, No. 1 | 1 Jul 1998 Cross Ref A Minimax Problem Admitting the Equioscillation Characterization of Bernstein and ErdősJournal of Approximation Theory, Vol. 92, No. 3 | 1 Mar 1998 Cross Ref Estimation of model qualityAutomatica, Vol. 31, No. 12 | 1 Dec 1995 Cross Ref Polynomial Interpolation on Quasi-Equidistributed Nodes on the Unit DiskHiroshi Sugiura and Tatsuo ToriiSIAM Journal on Numerical Analysis, Vol. 29, No. 4 | 14 July 2006AbstractPDF (1151 KB)Polynomial Extrapolation from $[ - 1,1]$ to the Unit DiscL. BrutmanSIAM Journal on Numerical Analysis, Vol. 28, No. 2 | 14 July 2006AbstractPDF (549 KB)The Fourier operator of even order and its application to an extremum problem in interpolationAlgorithms for Approximation II | 1 Jan 1990 Cross Ref Optimal interpolation in a general setting—A beginningJournal of Approximation Theory, Vol. 55, No. 3 | 1 Dec 1988 Cross Ref Properties of projections obtained by averaging certain polynomial interpolantsApproximation Theory, Tampa | 19 September 2006 Cross Ref On the optimal Lebesgue constants for polynomial interpolationActa Mathematica Hungarica, Vol. 47, No. 1-2 | 1 Mar 1986 Cross Ref A Note on functions with interlacing rootsJournal of Approximation Theory, Vol. 43, No. 1 | 1 Jan 1985 Cross Ref Optimal interpolation with incomplete polynomialsJournal of Approximation Theory, Vol. 41, No. 3 | 1 Jul 1984 Cross Ref The signal subspace approach for multiple wide-band emitter locationIEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. 31, No. 6 | 1 Dec 1983 Cross Ref On the Polynomial and Rational Projections in the Complex PlaneL. BrutmanSIAM Journal on Numerical Analysis, Vol. 17, No. 3 | 17 July 2006AbstractPDF (712 KB)An efficient blind identification algorithm for multichannel FIR systems using linear predictionProceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181) Cross Ref Volume 17, Issue 3| 1980SIAM Journal on Numerical Analysis333-477 History Submitted:10 October 1979Published online:17 July 2006 InformationCopyright © 1980 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0717031Article page range:pp. 373-375ISSN (print):0036-1429ISSN (online):1095-7170Publisher:Society for Industrial and Applied Mathematics