Introduction. 1. Two Dimensional Systems and Mathematical Preliminaries. 2. Image Perception. 3. Image Sampling and Quantization. 4. Image Transforms. 5. Image Representation by Stochastic Models. 6. Image Enhancement. 7. Image Filtering and Restoration. 8. Image Analysis and Computer Vision. 9. Image Reconstruction From Projections. 10. Image Data Compression.

Fundamentals of digital image processing

A summary of many of the new techniques developed in the last two decades for spectrum analysis of discrete time series is presented in this tutorial. An examination of the underlying time series model assumed by each technique serves as the common basis for understanding the differences among the various spectrum analysis approaches. Techniques discussed include the classical periodogram, classical Blackman-Tukey, autoregressive (maximum entropy), moving average, autotegressive-moving average, maximum likelihood, Prony, and Pisarenko methods. A summary table in the text provides a concise overview for all methods, including key references and appropriate equations for computation of each spectral estimate.

Spectrum analysis&#8212;A modern perspective

Adaptive Signal Processing

1. Basic Concepts. 2. Nonparametric Methods. 3. Parametric Methods for Rational Spectra. 4. Parametric Methods for Line Spectra. 5. Filter Bank Methods. 6. Spatial Methods. Appendix A: Linear Algebra and Matrix Analysis Tools. Appendix B: Cramer-Rao Bound Tools. Appendix C: Model Order Selection Tools. Appendix D: Answers to Selected Exercises. Bibliography. References Grouped by Subject. Subject Index.

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Spectral analysis of signals

Introduction to linear and nonlinear programming

In this paper, the Fast Cholesky algorithms, both by columns and by rows, are reviewed. It is shown that the algorithms lead naturally to a prediction error feedback filter. In addition, if this filter is used as the whitening filter for a moving average process, it is of fixed order but has time-varying coefficients. Simulation results for the case when the data came from the output of a moving average process driven by white Gaussian noise confirms theoretical results on convergence and stability of the triangular factors. In addition, the bandedness of the process being identified is revealed. Finally, from a VLSI implementation standpoint, it is shown that an array of CORDIC processors may be configured and controlled to factor a covariance matrix. In particular, there exists a method of factorization where the partial correlations associated with the given matrix are stored within the processors.

Fast Cholesky algorithms and adaptive feedback filters

Time difference of arrivals (TDOAs) of emitter wavefronts to spatially distributed array of sensors can be used to determine the source location. In this paper, we suggest a new method of TDOA estimation for multiple unknown sources of ARMA type and additive noise that is correlated between the sensors. We first consider the appropriate model for non-integer delays, and then we derive a theoretical formula that needs only the receiver cross-spectra and the source poles for the TDOA determination. The poles are estimated by a least squares technique, and a sample correlation is applied to evaluate the receiver cross-spectra. Results from simulations illustrate the performance of the algorithm.

Estimation of time difference of arrivals for multiple ARMA sources by a pole decomposition method

We introduce an extension of the usual notion of an input/output map and for linear constant-parameter systems an extended transfer function, that has a (matrix) polynomial- or more generally a differential/difference operator inverse, containing as a submatrix Rosenbrock's system matrix. A new class of system equivalence - "maximally strict system equivalence" (m.s.s.e.) is introduced as a necessary and sufficient condition for two minimal systems to have the same transfer function. We give an outline of the extension of these results to non-minimal systems, where results are only known for state-space systems in this generality. In the conclusion we discuss the relation of the extended system matrix to other deterministic and stochastic problems.

Extended system matrices-Transfer functions and system equivalence

We present a fast and potentially numerically advantageous algorithm for finding canonical minimal state-space realizations from given multivariable transfer functions.

A fast projection method for canonical minimal realization

Recursive algorithms for the solution of linear least-squares estimation problems have been based mainly on state-space models. It has been know, however, that such algorithms exist for stationary time-series, using input-output descriptions (e.g., covariance matrices). We introduce a way of classifying stochastic processes in terms of their "distance" from stationarity that leads to a derivation of an efficient Levinson-type algorithm for arbitrary (nonstationary) processes. By adding structure to the covariance matrix, these general results specialize to state-space type estimation algorithms. In particular, the Chandrasekhar equations are shown to be the natural descendants of the Levinson algorithm.

Martin Morf

Papers

Fast Cholesky algorithms and adaptive feedback filters

Estimation of time difference of arrivals for multiple ARMA sources by a pole decomposition method

Extended system matrices-Transfer functions and system equivalence

A fast projection method for canonical minimal realization

Levinson- and chandrasekhar-type equations for a general discrete-time linear estimation problem