A minimal parameter adaptive notch filter with constrained poles and zeros
01 Aug 1985-IEEE Transactions on Acoustics, Speech, and Signal Processing (IEEE)-Vol. 33, Iss: 4, pp 983-996
TL;DR: A new algorithm is presented for adaptive notch filtering and parametric spectral estimation of multiple narrow-band or sine wave signals in an additive broad-band process and uses a special constrained model of infinite impulse response with a minimal number of parameters.
Abstract: A new algorithm is presented for adaptive notch filtering and parametric spectral estimation of multiple narrow-band or sine wave signals in an additive broad-band process. The algorithm is of recursive prediction error (RPE) form and uses a special constrained model of infinite impulse response (IIR) with a minimal number of parameters. The convergent filter is characterized by highly narrow bandwidth and uniform notches of desired shape. For sufficiently large data sets, the variances of the sine wave frequency estimates are of the same order of magnitude as the Cramer-Rao bound. Results from simulations illustrate the performance of the algorithm under a wide range of conditions.
Citations
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Patent•
03 Apr 1997TL;DR: In this paper, a method and apparatus for analyzing two measured signals that are modeled as containing primary and secondary portions is presented, where coefficients relate the two signals according to a model defined in accordance with the present invention.
Abstract: The present invention involves method and apparatus for analyzing two measured signals that are modeled as containing primary and secondary portions. Coefficients relate the two signals according to a model defined in accordance with the present invention. In one embodiment, the present invention involves utilizing a transformation which evaluates a plurality of possible signal coefficients in order to find appropriate coefficients. Alternatively, the present invention involves using statistical functions or Fourier transform and windowing techniques to determine the coefficients relating to two measured signals. Use of this invention is described in particular detail with respect to blood oximetry measurements.
1,228 citations
Patent•
04 May 2004TL;DR: In this article, 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 are presented, and coefficients relate the two signals according to a model defined in accordance with the present invention.
Abstract: 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.
1,133 citations
TL;DR: A unified framework for the exact maximum likelihood estimation of the parameters of superimposed exponential signals in noise, encompassing both the time series and the array problems, is presented and the present formulation is used to interpret previous methods.
Abstract: A unified framework for the exact maximum likelihood estimation of the parameters of superimposed exponential signals in noise, encompassing both the time series and the array problems, is presented. An exact expression for the ML criterion is derived in terms of the linear prediction polynomial of the signal, and an iterative algorithm for the maximization of this criterion is presented. The algorithm is equally applicable in the case of signal coherence in the array problem. Simulation shows the estimator to be capable of providing more accurate frequency estimates than currently existing techniques. The algorithm is similar to those independently derived by Kumaresan et al. In addition to its practical value, the present formulation is used to interpret previous methods such as Prony's, Pisarenko's, and modifications thereof.
791 citations
TL;DR: In this article, an overview of several methods, filter structures, and recursive algorithms used in adaptive infinite-impulse response (IIR) filtering is presented, and several important issues associated with adaptive IIR filtering, including stability monitoring, the SPR condition, and convergence are addressed.
Abstract: An overview is presented of several methods, filter structures, and recursive algorithms used in adaptive infinite-impulse response (IIR) filtering. Both the equation-error and output-error formulations are described, although the focus is on the adaptive algorithms and properties of the output-error configuration. These parameter-update algorithms have the same generic form, and they are based on a prediction-error performance criterion. A direct-form implementation of the adaptive filters is emphasized, but alternative realizations such as the parallel and lattice forms are briefly discussed. Several important issues associated with adaptive IIR filtering, including stability monitoring, the SPR condition, and convergence, are addressed. >
644 citations
TL;DR: In this article, it is shown that vibration signals exhibit cyclostationarity if and only if the random speed fluctuation of the machine is periodic, stationary or cyclostatary.
409 citations
References
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24 Mar 1975
TL;DR: It is shown that in treating periodic interference the adaptive noise canceller acts as a notch filter with narrow bandwidth, infinite null, and the capability of tracking the exact frequency of the interference; in this case the canceller behaves as a linear, time-invariant system, with the adaptive filter converging on a dynamic rather than a static solution.
Abstract: This paper describes the concept of adaptive noise cancelling, an alternative method of estimating signals corrupted by additive noise or interference. The method uses a "primary" input containing the corrupted signal and a "reference" input containing noise correlated in some unknown way with the primary noise. The reference input is adaptively filtered and subtracted from the primary input to obtain the signal estimate. Adaptive filtering before subtraction allows the treatment of inputs that are deterministic or stochastic, stationary or time variable. Wiener solutions are developed to describe asymptotic adaptive performance and output signal-to-noise ratio for stationary stochastic inputs, including single and multiple reference inputs. These solutions show that when the reference input is free of signal and certain other conditions are met noise in the primary input can be essentiany eliminated without signal distortion. It is further shown that in treating periodic interference the adaptive noise canceller acts as a notch filter with narrow bandwidth, infinite null, and the capability of tracking the exact frequency of the interference; in this case the canceller behaves as a linear, time-invariant system, with the adaptive filter converging on a dynamic rather than a static solution. Experimental results are presented that illustrate the usefulness of the adaptive noise cancelling technique in a variety of practical applications. These applications include the cancelling of various forms of periodic interference in electrocardiography, the cancelling of periodic interference in speech signals, and the cancelling of broad-band interference in the side-lobes of an antenna array. In further experiments it is shown that a sine wave and Gaussian noise can be separated by using a reference input that is a delayed version of the primary input. Suggested applications include the elimination of tape hum or turntable rumble during the playback of recorded broad-band signals and the automatic detection of very-low-level periodic signals masked by broad-band noise.
4,165 citations
Book•
01 Jan 1975TL;DR: Feyman and Wing as discussed by the authors introduced the simplicity of the invariant imbedding method to tackle various problems of interest to engineers, physicists, applied mathematicians, and numerical analysts.
Abstract: sprightly style and is interesting from cover to cover. The comments, critiques, and summaries that accompany the chapters are very helpful in crystalizing the ideas and answering questions that may arise, particularly to the self-learner. The transparency in the presentation of the material in the book equips the reader to proceed quickly to a wealth of problems included at the end of each chapter. These problems ranging from elementary to research-level are very valuable in that a solid working knowledge of the invariant imbedding techniques is acquired as well as good insight in attacking problems in various applied areas. Furthermore, a useful selection of references is given at the end of each chapter. This book may not appeal to those mathematicians who are interested primarily in the sophistication of mathematical theory, because the authors have deliberately avoided all pseudo-sophistication in attaining transparency of exposition. Precisely for the same reason the majority of the intended readers who are applications-oriented and are eager to use the techniques quickly in their own fields will welcome and appreciate the efforts put into writing this book. From a purely mathematical point of view, some of the invariant imbedding results may be considered to be generalizations of the classical theory of first-order partial differential equations, and a part of the analysis of invariant imbedding is still at a somewhat heuristic stage despite successes in many computational applications. However, those who are concerned with mathematical rigor will find opportunities to explore the foundations of the invariant imbedding method. In conclusion, let me quote the following: "What is the best method to obtain the solution to a problem'? The answer is, any way that works." (Richard P. Feyman, Engineering and Science, March 1965, Vol. XXVIII, no. 6, p. 9.) In this well-written book, Bellman and Wing have indeed accomplished the task of introducing the simplicity of the invariant imbedding method to tackle various problems of interest to engineers, physicists, applied mathematicians, and numerical analysts.
3,249 citations
01 Nov 1981
TL;DR: In this paper, a summary of many of the new techniques developed in the last two decades for spectrum analysis of discrete time series is presented, including classical periodogram, classical Blackman-Tukey, autoregressive (maximum entropy), moving average, autotegressive-moving average, maximum likelihood, Prony, and Pisarenko methods.
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.
2,941 citations
TL;DR: It is shown how a deterministic differential equation can be associated with the algorithm and examples of applications of the results to problems in identification and adaptive control.
Abstract: Recursive algorithms where random observations enter are studied in a fairly general framework. An important feature is that the observations my depend on previous "outputs" of the algorithm. The considered class of algorithms contains, e.g., stochastic approximation algorithm, recursive identification algorithm, and algorithms for adaptive control of linear systems. It is shown how a deterministic differential equation can be associated with the algorithm. Problems like convergence with probability one, possible convergence points and asymptotic behavior of the algorithm can all be studied in terms of this differential equation. Theorems stating the precise relationships between the differential equation and the algorithm are given as well as examples of applications of the results to problems in identification and adaptive control.
1,370 citations
940 citations