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

Statistics for Spatial Data.

System Identification I

A method and an apparatus to analyze two measured signals that are modeled as containing desired and undesired portions such as noise, FM and AM modulation. Coefficients relate the two signals according to a model defined in accordance with the present invention. In one embodiment, a transformation is used to evaluate a ratio of the two measured signals in order to find appropriate coefficients. The measured signals are then fed into a signal scrubber which uses the coefficients to remove the unwanted portions. The signal scrubbing is performed in either the time domain or in the frequency domain. The method and apparatus are particularly advantageous to blood oximetry and pulserate measurements. In another embodiment, an estimate of the pulserate is obtained by applying a set of rules to a spectral transform of the scrubbed signal. In another embodiment, an estimate of the pulserate is obtained by transforming the scrubbed signal from a first spectral domain into a second spectral domain. The pulserate is found by identifying the largest spectral peak in the second spectral domain.

Signal processing apparatus and method

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Detection, Estimation, and Modulation Theory

From the Publisher:
Time-varying process identification (TVPI) is the latest chapter in the evolution of adaptive signal processing. In mobile communications systems, TVPI techniques facilitate adaptive noise reduction, echo cancellation, and predictive coding of signals. It also has applications in adaptive control

Identification of Time-Varying Processes

The problem of elimination of measurement noise and impulsive disturbances from autoregressive and autoregressive moving average signals is considered. It is shown that the task of simultaneous detection/tracking/restoration can be stated as a nonlinear filtering problem and solved using the theory of extended Kalman filter. Numerical tests carried out for real audio signals corrupted by both real and artificially generated disturbances confirm very good properties of the proposed algorithm.

Adaptive scheme for elimination of broadband noise and impulsive disturbances from AR and ARMA signals

This paper presents a new approach to rejection of complex-valued sinusoidal disturbances acting at the output of a discrete-time stable linear plant with unknown dynamics. It is assumed that the frequency of the sinusoidal disturbance is known, and that the output signal is contaminated with wideband measurement noise. The disturbance rejection control rule is first derived and analyzed for a nominal plant model, different from the true model. Then a special adaptation mechanism is added, which is capable of compensating modeling biases (errors in both magnitude and phase) so that, under Gaussian assumptions, the closed-loop system can converge in mean to the optimal solution.

A New Approach to Active Noise and Vibration Control—Part II: The Unknown Frequency Case

The paper presents results of local performance analysis of a generalized adaptive notch filter (GANF). GANFs are used for identification/tracking of quasi-periodically varying dynamic systems and can be considered an extension, to the system case, of classical adaptive notch filters. The tracking properties of the algorithm are studied analytically using a direct averaging approach and an approximating linear filter technique. Even though restricted to a single-frequency case, the presented analysis provides valuable insights into the tracking mechanisms of GANF, including the associated speed/accuracy tradeoffs, the achievable performance bounds, and tracking limitations. In addition, it allows one to formulate some useful rules of thumb for choosing design parameters.

Tracking analysis of a generalized adaptive notch filter

The parallel (multiple-model) schemes for identification of nonstationary stochastic systems are considered. First, the form of the optimal-local Bayesian predictor is derived under the assumptions that system coefficients vary according to the random walk model and that the Kalman-filter-based algorithms are used for identification purposes. A rational extension of this strategy, which can be applied to identification algorithms of any form, is discussed. Specific suggestions are made concerning the possible choice of adaptation gains of the competitive adaptive filters. Computer simulation results, confirming the good estimation robustness properties of the parallel identification schemes, are presented. It is shown that the proposed scheme can significantly decrease sensitivity of the identification algorithm to the rate of nonstationarity of the analyzed system or (alternatively) to the choice of design parameters such as adaptation gains and forgetting factors. >

http://ieeexplore.ieee.org/iel4/9/1840/00050350.pdf

Maciej Niedzwiecki

Papers

Identification of Time-Varying Processes

Adaptive scheme for elimination of broadband noise and impulsive disturbances from AR and ARMA signals

A New Approach to Active Noise and Vibration Control—Part II: The Unknown Frequency Case

Tracking analysis of a generalized adaptive notch filter

Identification of nonstationary stochastic systems using parallel estimation schemes