Martin Morf

Bio: Martin Morf is an academic researcher from Stanford University. The author has contributed to research in topics: Matrix (mathematics) & Covariance. The author has an hindex of 32, co-authored 110 publications receiving 5565 citations.

New results in 2-D systems theory, part II: 2-D state-space models—Realization and the notions of controllability, observability, and minimality

Abstract: In this part, a comparison between the different state-space models is presented We discuss proper definitions of state, controllability and observability and their relations to minimality of 2-D systems We also present new circuit realizations and 2-D digital filter hardware implementation of 2-D transfer functions

Recursive least squares ladder estimation algorithms

Abstract: Recursive least squares ladder estimation algorithms have attracted much attention recently because of their excellent convergence behavior and fast parameter tracking capability, compared to gradient based algorithms. We present some recently developed square root normalized exact least squares ladder form algorithms that have fewer storage requirements, and lower computational requirements than the unnormalized ones. A Hilbert space approach to the derivations of magnitude normalized signal and gain recursions is presented. The normalized forms are expected to have even better numerical properties than the unnormalized versions. Other normalized forms, such as joint process estimators (e.g., "adaptive line enhancer") and ARMA (pole-zero) models, will also be presented. Applications of these algorithms to fast (or "zero") startup equalizers, adaptive noise- and echo cancellers, non-Gaussian event detectors, and inverse models for control problems are also mentioned.

Fast calculation of gain matrices for recursive estimation schemes

Abstract: A sequence of vectors {x(t)} with dimension N is given, such that x(t+1) is obtained from x(t) by introducing p new elements, deleting p old ones, and shifting the others in some fashion. The sequence of vectors $ is sought. This paper presents a method of calculating these vectors with proportional-to-Np operations and memory locations, in contrast to the conventional way which requires proportional-to-N 2 operations and memory locations. A non-symmetric case is also treated.

Inverses of Toeplitz Operators, Innovations, and Orthogonal Polynomials

Abstract: We describe several interconnections between the topics mentioned in the title. In particular, we show how some previously known formulas for inverting Toeplitz operators in both discrete- and cont...

Fundamentals of digital image processing

Abstract: 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.

Spectrum analysis—A modern perspective

Abstract: 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.

Spectral analysis of signals

Abstract: 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.