Canonical coordinates and the geometry of inference, rate, andcapacity

Canonical correlations measure the cosines of principal angles between random vectors. These cosines multiplicatively decompose concentration ellipses for second-order filtering and additively decompose the information rate for the Gaussian channel. More over, they establish a geometrical connection between error covariance, error rate, information rate, and principal angles. There is a limit to how small these angles can be made, and this limit determines the channel capacity     

A VLSI design methodology for distributed arithmetic

Real-time signal processing requires fast computation of inner products. Distributed arithmetic is a method of inner product computation that uses table-lookup and addition in place of multiplication. Distributed arithmetic has previously been shown to produce novel and seemingly efficient architectures for a variety of signal processing computations; however the methods of design, analysis and comparison have been ad hoc. We propose a systematic method for synthesizing optimal VLSI architectures using distributed arithmetic.A partition of the inner product computation at the word and bit level produces a computation consisting of lookups and additions. We study two classes of algorithms to implement this computation, regular iterative algorithms and tree algorithms, each of which can be expressed in the form of a dependency graph. We use linear and nonlinear maps to assign computations to processors in space and time. Expressions are developed for the area, latency, period and arithmetic error for a particular partition and space/time map of the dependecy graph. We use these expressions to formulate a constrained optimization problem over a large class of architectures. We compare distributed arithmetic with more conventional methods for inner product computation and show how area, latency and period may be traded off while maintaining constant error.This work was supported by Ball Aerospace, Boulder, CO and by the Office of Naval Research, Electronics Branch, Arlington, VA under contract ONR 89-J-1070.     

A new subspace identification algorithm for high-resolution DOA estimation

In this paper, we propose a new direction of arrival (DOA) estimator for sensor-array processing. The estimator is based on a linear algebraic connection between the standard subspace model of the array correlation matrix and a special signal-plus-interference model, which we develop in this paper. The estimator we propose is a signal subspace scaled MUSIC algorithm, which we call SSMUSIC. It is not a subspace weighted MUSIC, because the scaling depends on the eigenstructure of the estimated signal subspace. SSMUSIC has the advantage of simultaneously estimating the DOA and the power of each source. We employ a second-order perturbation analysis of the estimator and derive stochastic representations for its bias and squared-error. We compare the new DOA estimator with the MUSIC estimator, based on these representations. Numerical results demonstrate the superior performance of SSMUSIC relative to MUSIC and the validity of the perturbation results.     

Wiener filters in canonical coordinates for transform coding,filtering, and quantizing

Canonical correlations are used to decompose the Wiener filter into a whitening transform coder, a canonical filter, and a coloring transform decoder. The outputs of the whitening transform coder are called canonical coordinates; these are the coordinates that are reduced in rank and quantized in our finite-precision version of the Gauss-Markov theorem. Canonical correlations are, in fact, cosines of the canonical, angles between a source vector and a measurement vector. They produce new formulas for error covariance, spectral flatness, and entropy     

A fault diagnosis system for the connected home

The connected home of the future, in which all consumer appliances in a home are networked together, is close to becoming the connected home of today. This article explores the role of fault diagnosis in such an environment and explains how agent technology may be applied. The article outlines the need for future standards that can maximize the benefit of a shared diagnostic system.     

Sleep quality in Lyme disease

Complaints of chronic fatigue as well as sleep disturbances are prevalent in Lyme disease. We compared polysomnographic measures of sleep in patients with documented Lyme disease with those of a group of age-matched normal control subjects. Eleven patients meeting Centers for Disease Control criteria for late Lyme disease with serologic confirmation by enzyme-linked immunosorbent assay and Western blot without a history of other medical or psychiatric illness and 10 age-matched control subjects were studied. Lyme disease patients and controls underwent 2 nights of polysomnography. Multiple sleep latency testing (MSLT) was performed in the patients. Sleep was staged by standard criteria, and continuity of sleep was assessed for each stage of frequency analysis of consecutive epochs. All patients studied reported sleep-related complaints, including difficulty initiating sleep (27%), frequent nocturnal awakenings (27%), excessive daytime somnolence (73%) and restless legs/nocturnal leg jerking (9%). Greater sleep latency, decreased sleep efficiency and a greater arousal index were noted in Lyme patients. The median length of uninterrupted occurrences of stage 2 and stage 4 non-rapid eye movement (NREM) sleep was less in Lyme patients (6.3 +/- 3.0 epochs in patients vs. 11.4 +/- 4.4 epochs in controls for stage 2, p < 0.01, and 4.3 +/- 4.4 epochs in patients vs. 11.2 +/- 6.3 epochs in controls for stage 4, p < 0.01), indicating greater sleep fragmentation. Mean sleep onset latency during the MSLT was normal (12.7 +/- 5.6 minutes). Three patients demonstrated alpha-wave intrusion into NREM sleep. These sleep abnormalities may contribute to the fatigue and sleep complaints common in this disease.