This paper presents a tutorial review of lattice structures and their use for adaptive prediction of time series Lattice filters associated with stationary covariance sequences and their properties are discussed The least squares prediction problem is defined for the given data case, and it is shown that many of the currently used lattice methods are actually approximations to the stationary least squares solution The recently developed class of adaptive least squares lattice algorithms are described in detail, both in their unnormalized and normalized forms The performance of the adaptive least squares lattice algorithm is compared to that of some gradient adaptive methods Lattice forms for ARMA processes, for joint process estimation, and for the sliding-window covariance case are presented The use of lattice structures for efficient factorization of covariance matrices and solution of Toeplitz sets of equations is briefly discussed

Lattice filters for adaptive processing

Suppose we have two random variables X, Y with a known joint density function fx,y(.,.). Assume that in a particular experiment, the random variable Y can be measured and takes the value y. What can be said about the corresponding value, say x, of the unobservable variable X?

Lectures on Wiener and Kalman Filtering

This paper presents several methods for the identification of the impedance and reflection coefficient profile of a nonuniform, discrete transmission-line from its response to a given forcing function. This problem is the prototype for a wealth of one-dimensional inverse scattering problems arising in various fields. A unified, straightforward approach is presented, providing all known inversion procedures and some novel ones. The derivations readily follow from causality of signal propagation on the transmission-line. It is shown that a direct exploitation of the signal propagation model leads to recursive, computationally efficient and reliable inversion algorithms. In particular, the relationships between layer peeling (Schur type, difference equation) and layer-adjoining (Levinson type, integral equation) algorithms are clearly displayed.

Inverse scattering for discrete transmission—line models

This paper discusses a new set of differential methods for solving the inverse scattering problem associated to the propagation of waves in an inhomogeneous medium. By writing the medium equations in the form of a two-component system describing the interaction of rightward and leftward propagating waves, the causality of the propagation phenomena is exploited in order to identify the medium layer by layer. The recursive procedure that we obtain constitutes a continuous version of an algorithm first derived by Schur in order to test for the boundedness of functions analytic inside the unit circle. It recovers the local reflectivity function of the medium. Using similar ideas, some other differential methods can also be derived to reconstruct alternative parametrizations of the layered medium in terms of the local impedance or of the potential function.The differential inverse scattering methods turn out to be very efficient since, in some sense, they let the medium perform the inversion by itself and thus...

/pdf/differential-methods-in-inverse-scattering-qz06hq4arv.pdf

Differential methods in inverse scattering

A survey on the maximum entropy method and parameter spectral estimation

In this paper, we study the factorization and the representation of Fredholm operators belonging to the algebra R generated by inversion and composition of Toeplitz integral operators. The operators in R have the interesting property of being close to Toeplitz (in a sense quantifiable by an integer-valued index a) and, at the same time, of being dense in the space of arbitrary kernels. By using these properties, we derive a set of efficient algorithms (generalized fast-Cholesky and Levinson recursions) for the factorization and the inversion of arbitrary Fredholm operators. The computational burden of these algorithms depends on how close (as measured by the index a) these operators are to being Toeplitz. We also obtain several important representation theorems for the decomposition of operators in R in terms of sums of products of lower times upper triangular Toeplitz operators. These results can be used to approximate operators corresponding to noncausal and time-variant systems in terms of operators represent- ing causal and anticausal time-invariant systems, a property that has a large number of potential applications in signal processing problems.

The factorization and representation of operators in the algebra generated by

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

Toeplitz Operators

Author Tools

Chat about Author

Papers

The factorization and representation of operators in the algebra generated by