There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Heart rate variability: standards of measurement, physiological interpretation and clinical use. Task Force of the European Society of Cardiology and the North American Society of Pacing and Electrophysiology.

Fundamentals Of Statistical Signal Processing

/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

The quintessential goal of sensor array signal processing is the estimation of parameters by fusing temporal and spatial information, captured via sampling a wavefield with a set of judiciously placed antenna sensors. The wavefield is assumed to be generated by a finite number of emitters, and contains information about signal parameters characterizing the emitters. A review of the area of array processing is given. The focus is on parameter estimation methods, and many relevant problems are only briefly mentioned. We emphasize the relatively more recent subspace-based methods in relation to beamforming. The article consists of background material and of the basic problem formulation. Then we introduce spectral-based algorithmic solutions to the signal parameter estimation problem. We contrast these suboptimal solutions to parametric methods. Techniques derived from maximum likelihood principles as well as geometric arguments are covered. Later, a number of more specialized research topics are briefly reviewed. Then, we look at a number of real-world problems for which sensor array processing methods have been applied. We also include an example with real experimental data involving closely spaced emitters and highly correlated signals, as well as a manufacturing application example.

Two decades of array signal processing research: the parametric approach

(1995). Fundamentals of Statistical Signal Processing: Estimation Theory. Technometrics: Vol. 37, No. 4, pp. 465-466.

/pdf/fundamentals-of-statistical-signal-processing-estimation-3001q9c4fj.pdf

Fundamentals of statistical signal processing: estimation theory

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

Modern Spectral Estimation: Theory and Application

A novel frequency estimator for a single complex sinusoid in complex white Gaussian noise is proposed. The estimator is more computationally efficient that the optimal maximum-likelihood estimator yet attains equally good performance at moderately high signal-to-noise ratios. The estimator is shown to be related to the linear prediction estimator. This relationship is used to reveal why the linear prediction estimator does not attain the Cramer-Rao bound even at high signal-to-noise ratios. >

Steven Kay

Papers

Fundamentals of statistical signal processing: estimation theory

Fundamentals Of Statistical Signal Processing

Spectrum analysis—A modern perspective

Modern Spectral Estimation: Theory and Application

A fast and accurate single frequency estimator

Steven Kay

Papers

Fundamentals of statistical signal processing: estimation theory

Fundamentals Of Statistical Signal Processing

Spectrum analysis&#8212;A modern perspective

Modern Spectral Estimation: Theory and Application

A fast and accurate single frequency estimator

Spectrum analysis—A modern perspective