Showing papers on "Adaptive filter published in 1971"
TL;DR: In this paper, it is shown that modulo arithmetic may be used in the inverse filter to eliminate completely the possibility of instability, and a very simple automatic or adaptive equalisation system is presented.
Abstract: The limitations of present automatic and adaptive equalisers stem from the use of feedforward transversal filters. These drawbacks may be obviated by using a feedback transversal filter, the inverse filter, but this is only suitable for limited use since it can be an unstable circuit. It is shown that modulo arithmetic may be used in the inverse filter to eliminate completely the possibility of instability, and a very simple automatic or adaptive equalisation system is presented. Some interesting properties of the modulo inverse filter are included.
1,035 citations
TL;DR: In this article, a solution obtained by a direct approximation procedure in the z plane is presented, where the denominator of the transfer function turns out to be a Gaussian hypergeometric function, connected with the Legendre functions.
Abstract: A well-known limitation of the recursive digital filter, when compared to the nonrecursive filter, is its incapability of having a strictly linear phase characteristic; thus it may only approximate a constant group delay. For the analog filters the choice of the maximally flat criterion leads to the use of the Bessel polynomials. Yet digital approximations of these continuous filter functions are inadequate to yield the true maximally flat delay approximation of the recursive filters. Our purpose is to provide for the problem at hand a solution obtained by a direct approximation procedure in the z plane. The denominator of the transfer function turns out to be a Gaussian hypergeometric function, more particularly connected with the Legendre functions. The stability of the filters is discussed and some numerical results in regard to the amplitude and phase responses as well as the pole loci are given.
247 citations
TL;DR: In this paper, the authors compared the performance of several non-linear filters for the real-time estimation of the trajectory of a reentry vehicle from its radar observations, including iterative-sequential filters, single-stage iteration filters, and second-order filters.
Abstract: This paper compares the performance of several non-linear filters for the real-time estimation of the trajectory of a reentry vehicle from its radar observations. In particular, it examines the effect of using two different coordinate systems on the relative accuracy of an extended Kalman filter. Other filters considered are iterative-sequential filters, single-stage iteration filters, and second-order filters. It is shown that a range-direction-cosine extended Kalman filter that uses the measurement coordinate system has less bias and less rms error than a Cartesian extended Kalman filter that uses the Cartesian coordinate system. This is due to the fact that the observations are linear in the range-direction-cosine coordinate system, but nonlinear in the Cartesian coordinate system. It is further shown that the performance of the Cartesian iterative-sequential filter that successively relinearizes the observations around their latest estimates and that of a range-direction-cosine extended Kalman filter are equivalent to first order. The use of a single-stage iteration to reduce the dynamic nonlinearity improves the accuracy of all the filters, but the improvement is very small, indicating that the dynamic nonlinearity is less significant than the measurement nonlinearity in reentry vehicle tracking under the assumed data rates and measurement accuracies. The comparison amongst the nonlinear filters is carried out using ten sets of observations on two typical trajectories. The performance of the filters is judged by their capability to eliminate the initial bias in the position and velocity estimates.
210 citations
TL;DR: In this paper, a new class of selective non-recursive digital filters with a maximally flat frequency response in the passband and stopband is introduced, based on a special solution of the general Hermite polynomial interpolation and allows computation of the parameters of these filters in closed form.
Abstract: A new class of selective nonrecursive digital filters with a maximally flat frequency response in the passband and stopband is introduced. The proposed design method is based on a special solution of the general Hermite polynomial interpolation and allows computation of the parameters of these filters in closed form. Therefore it yields some advantage over numerical iterative methods. Design examples are given and an extension to the design of unsymmetrical bandpass systems is made.
205 citations
TL;DR: In this article, the authors proposed a planar digital filter with a finite and convergent sum of matrix-valued stages, where each stage can be separated with no error into the product of an m-length column vector multiplied into an n-length row vector, where m is the number of rows and n is the original filter array.
Abstract: A two-dimensional, or planar, digital filter can be described in terms of its planar response function, which is in the form of a matrix of weighting coefficients, or filter array. In many instances the dimensions of these matrices are so large that their implementation as ordinary planar convolutional filters becomes computationally inefficient. It is possible to expand the given coefficient matrix into a finite and convergent sum of matrix-valued stages. Each stage can be separated with no error into the product of an m-length column vector multiplied into an n-length row vector, where m is the number of rows and n is the number of columns of the original filter array. Substantial savings in computer storage and speed result if the given filter array can be represented with a tolerably small error by the first few stages of the expansion. Since each constituent stage consists of two vector-valued factors, further computational economies accrue if the one-dimensional sequences described by these vectors are in turn approximated by one-dimensional recursive filters. Two geophysical examples have been selected to illustrate how the present design techniques may be reduced to practice.
145 citations
TL;DR: In this article, five important tracking filters that are often candidates for implementation in systems that must track maneuvering vehicles are compared in terms of tracking accuracy and computer requirements for tactical applications.
Abstract: Five important tracking filters that are often candidates for implementation in systems that must track maneuvering vehicles are compared in terms of tracking accuracy and computer requirements for tactical applications. A rationale for selecting among these filters, which include a Kalman filter, a simplified Kalman filter, an ?-s filter, a Wiener filter, and a two-point extrapolator, is illustrated by two examples taken from the authors' recent experience.
137 citations
TL;DR: A recursive, fading memory filter for time-continuous and time-discrete systems is presented as a means for overcoming the destructive influence of model errors in Kalman filter applications that lead to the occurrence of divergence.
115 citations
TL;DR: In this paper, the use of the discrete Kalman filter as an equalizer for digital binary transmission in the presence of noise and intersymbol interference has been considered, and it has been shown that using the 6-tap KF yields a considerably smaller error probability than when a conventional transversal equalizer with 15 taps is used.
Abstract: Consideration is given to the use of the discrete Kalman filter as an equalizer for digital binary transmission in the presence of noise and intersymbol interference. When the channel is modeled as an n -tap transversal filter, the Kalman filter assumes a similar form with "feed forward and feedback." It is shown how the Kalman filter can be used to estimate both the tap weights and the binary signal. Computer results on a fixed 6-tap channel show that use of the 6-tap Kalman filter yields a considerably smaller error probability than when a conventional transversal equalizer with 15 taps is used. Limited computer studies on the same channel, assumed to be initially unknown, suggest that the Kalman filter is capable of converging rapidly in the adaptive mode. Though these results are very encouraging, much work remains in the study and optimization of performance in the adaptive mode.
109 citations
TL;DR: The motivation behind three design techniques that have been proposed are reviewed here, and the resulting designs are compared with respect to filter characteristics, ease of design, and methods of realization.
Abstract: Several new techniques for designing finite-duration impulse-response digital filters have become available in the past few years. The motivation behind three design techniques that have been proposed are reviewed here, and the resulting designs are compared with respect to filter characteristics, ease of design, and methods of realization. The design techniques to be discussed include window, frequency-sampling, and equiripple designs.
90 citations
84 citations
TL;DR: In this paper, the concept of the multipurpose active filter was introduced. But the Biquad topology offers unique flexibility compared to other active realizations, for example, switchable and adaptive filters are easily realized and different functions (e.g., bandpass and band-reject) are obtainable simultaneously from the same structure.
Abstract: While the electrical performance of the Biquad insures that active filter designs using this structure will be useful over a wide range of conditions, the Biquad topology offers unique flexibility compared to other active realizations. We now present the concept of the multipurpose active filter. For example, switchable and adaptive filters are easily realized and different functions (e.g., bandpass and band-reject) are obtainable simultaneously from the same structure.
TL;DR: Two classes of recursive digital filter of particular value for the processing of biological signals are described in some detail, applied to the recovery of an ECG waveform from wide- and narrowband contaminating noise.
Abstract: Digital filters achieve their frequency-selective properties by operating on the values of a sampled-data signal. After outlining an important design method for such filters, two classes of recursive digital filter of particular value for the processing of biological signals are described in some detail. These are applied to the recovery of an ECG waveform from wide- and narrowband contaminating noise.
TL;DR: In this paper the mean-square range-estimation error, the detection Signal-to-noise ratio (SNR), and the effects of sidelobes are expressed in terms of the impulse response of an arbitrary mismatched filter.
Abstract: In a multiple-target environment a radar signal processor often uses weighting filters that are not matched to the transmitted waveform. In this paper the mean-square range-estimation error, the detection Signal-to-noise ratio (SNR), and the effects of sidelobes are expressed in terms of the impulse response of an arbitrary mismatched filter. It is desired to find that impulse response that results in the minimum range-estimate variance subject to preassigned constraints on the side-lobes and the detection SNR. It is shown that for detecting the radar target and estimating its range, the form of the optimum filter is a modified transversal equalizer. If only detection is required, the optimum filter reduces to the transversal equalizer. Certain parameters upon which the solution depends can be found by solving a nonlinear programming problem. Numerical results are given for an interesting class of transmitted waveforms.
TL;DR: By a simple argument it is shown in this correspondence that any reasonable criterion of goodness will lead to an optimum filter that has this form.
Abstract: It has been observed by several authors that a number of different optimum receiving filters (corresponding to different criteria of goodness) for sampled-data transmission systems can be factored as a product of a matched filter and a periodic filter with the period equal to the sampling frequency. By a simple argument it is shown in this correspondence that any reasonable criterion of goodness will lead to an optimum filter that has this form.
TL;DR: In this article, an algorithm is derived for multichannel time series data processing, which maintains specified initial multiple filter constraints for known signal or noise sources while simultaneously adapting the filter to minimize the effect of the unknown noise field.
Abstract: An algorithm is derived for multichannel time‐series data processing, which maintains specified initial multiple filter constraints for known signal or noise sources while simultaneously adapting the filter to minimize the effect of the unknown noise field. Problems of implementing the technique such as convergence, determination of a starting filter, and comparison of results with conventional filters are discussed and illustrated with data from a vertical seismic array. The procedure is shown to be stable and obtains approximately 3–4 db gain in S/N improvement over conventional Wiener filtering in the band 1 to 3 hz.
TL;DR: A determination is made of the system performance degradation from matched-filter detection resulting from the use of a linear channel model that focuses attention on the critical filters in the communication link.
Abstract: The combined effects of filter distortion and the associated intersymbol interference on coherently detected biphase and quadriphase PSK signals are studied in white Gaussian noise. A determination is made of the system performance degradation from matched-filter detection resulting from the use of a linear channel model that focuses attention on the critical filters in the communication link. The critical filters that affect performance consist of transmission filters in the transmitter and/or transponder, receiver predetection filters, and data filters associated with the detector. Numerical results for adjacent symbol interference are given for detection using both integrate-and-dump filters as well as more general data filters, particularly an undumped 2-pole Butterworth data filter. The numerical results include symmetrical band limiting, broad-band filtering with a frequency offset, mismatched data filtering, cascaded filter chains, and the effects of pure phase distortion.
TL;DR: In this paper, the analysis and design of digital filter banks composed of equally spaced bandpass filters is discussed. And the results are extended to more general filter bank configurations, and it is shown that significant improvement in the composite filter bank response can be achieved by proper choice of the relative phases of the bandspass filters.
Abstract: A bank of bandpass filters is often used in performing short-time spectrum analysis of speech signals. This paper is concerned with the analysis and design of digital filter banks composed of equally spaced bandpass filters. It is shown that significant improvement in the composite filter bank response can be achieved by proper choice of the relative phases of the bandpass filters. The results are extended to more general filter bank configurations.
TL;DR: Bounds on the variance, valid for large signal-to-noise ratios, indicate that the new algorithm not only converges faster, but also has a smaller variance asymptotically than the present algorithm for moderate intersymbol interference and the same variance asyspymbol interference.
Abstract: Currently used adaptive equalizers for the minimization of mean-square error in digital communications commonly employ a fixed-step-size gradient-search procedure. The algorithm to be described here employs variable step sizes designed to minimize the error after a specified number of iterations. The resultant convergence rate provides considerable improvement over the fixed-step-size approach. Bounds on the variance, valid for large signal-to-noise ratios, indicate that the new algorithm not only converges faster, but also has a smaller variance asymptotically than the present algorithm for moderate intersymbol interference and the same variance asymptotically for large intersymbol interference. Computer simulation studies have verified these results.
Patent•
13 Sep 1971TL;DR: Adaptive linear transversal filter is trained with a periodic training sequence having period exactly equal to the number of variable parameters of the filter to be set in the training mode.
Abstract: Adaptive linear transversal filter is trained with a periodic training sequence having period exactly equal to the number of variable parameters of the filter to be set in the training mode. After training, tap coefficients may be cycled in a closed loop to a preferred position.
01 Apr 1971
TL;DR: It is shown that the Kalman-Bucy filter is constructible knowing precisely those covariances required to construct a Wiener filter, and no more, and that the filter is independent of the particular models of the processes generating these Covariances.
Abstract: The notion is exploded that to build a Kalman-Bucy filter, one needs to know the whole structure of the signal generating process. It is shown that the filter is constructible knowing precisely those covariances required to construct a Wiener filter, and no more, and that the filter is independent of the particular models of the processes generating these covariances. Performance of the Kalman-Bucy filter does depend on the models, however. Results are also obtained for the smoothing problem.
TL;DR: A recently developed method of filter synthesis is proposed, which does not require high accuracy working in a computer because it operates throughout with simple factors which are never multiplied into polynomials.
Abstract: A general classification of reactive ladder filters with real transmission zeros is given which is based on the extreme frequency behavior of port impedances and on types of design polynomials of the characteristic and effective transmission functions. It is shown that this classification provides an ordered algorithm for automatic realization of ladder structures which can be used to construct a logical development of appropriate computer programs. The bilinear frequency transformation is extended to all filter classes for a synthesis procedure entirely in the transformed plane. Accuracy limitations of this method are discussed and reasons for them are pointed out. A recently developed method of filter synthesis is proposed, which does not require high accuracy working in a computer because it operates throughout with simple factors which are never multiplied into polynomials. A design example of a through-supergroup filter is offered which demonstrates limitations of standard synthesis procedures.
TL;DR: In this article, the authors presented an approach for obtaining a linear time-varying recursive digital filter which will optimally simulate the behavior of an analog filter using generalized spline functions.
Abstract: A now approach is presented for obtaining a linear timevarying recursive digital filter which will optimally simulate the behavior of a linear time-varying analog filter The property of the best approximation of linear functionals by means of generalized spline functions is invoked in the derivation of the results In this approach, the optimal digital simulator is, viewed as a min-max estimator of the samples of the analog filter output based on the samples of its input These samples are not required to appear at uniformly spaced instants of time The assumption is made that the analog filter input belongs to a class \Omega_{a} of signals, each member of \Omega_{a} being generated by a known differential dynamical system \Lambda forced by some input whose energy is less than or equal to a constant \alpha^{2} By interpolating the samples of the analog filter input by a generalized spline associated with the differential operator pertaining to the system \Lambda , the structure of the optimal digital simulator is derived Error bounds are derived as functions of the maximum sampling subinterval length and the theory is illustrated by means of examples
TL;DR: It is concluded that, instead of restricting the spatial-filter recording to the linear region of the transfer characteristic of the photographic film, an optimum nonlinear spatial filter may be achieved.
Abstract: Generally, the synthesis of coherent spatial filters is restricted to the linear region of the transfer characteristic of a photographic film. However, a technique of synthesizing a nonlinear spatial filter such that the signal detection may be optimum will be described. In this paper, a generalized linear optimization technique is formulated. The application of this optimization technique toward a simple nonlinear spatial filter is demonstrated, and the extension of this optimization technique for a more complicated nonlinear spatial filter is also given. The signal detection by nonlinear optimum spatial filtering is analyzed. Finally, it is concluded that, instead of restricting the spatial-filter recording to the linear region of the transfer characteristic of the photographic film, an optimum nonlinear spatial filter may be achieved.
TL;DR: This paper illustrates by means of simple examples the application of stochastic approximation method as a single-channel adaptive processor under some conditions the expected value of its weight sequence converges to the corresponding Wiener optimum filter when the least-mean-square error criterion is used.
Abstract: One of the problems in signal processing is estimating the impulse response function of an unknown system. The well‐known Wiener filter theory has been a powerful method in attacking this problem. In comparison, the use of stochastic approximation method as an adaptive signal processor is relatively new. This adaptive scheme can often be described by a recursive equation in which the estimated impulse response parameters are adjusted according to the gradient of a predetermined error function. This paper illustrates by means of simple examples the application of stochastic approximation method as a single‐channel adaptive processor. Under some conditions the expected value of its weight sequence converges to the corresponding Wiener optimum filter when the least‐mean‐square error criterion is used.
01 Dec 1971
TL;DR: In this article, a recursive, minimum-variance linear filter and controller for systems in which white state-dependent noise appears in the system dynamics and measurements is derived, which is a generalization of the Kalman filter and possesses many of its desirable properties.
Abstract: A recursive, minimum-variance linear filter and controller is derived for systems in which white state-dependent noise appears in the system dynamics and measurements. The filter without control is a generalization of the Kalman filter and possesses many of its desirable properties. First, the discrete form of the filter is derived. By taking a formal limit, a continuous filter with convergence in distribution to an Ito representation is obtained. The concept of a perfect controller is given, showing the formal duality of the filter and controller with the stochastic controller derived by Wonham. Finally, some of the properties of the filter-controller system are illustrated through the use of a scalar example. It is shown that a filter-controller designed by neglecting the state-dependent noise can destabilize a dynamically stable system.
TL;DR: An experimental model of a coder for transmission of speech over a 9600-bits/s digital channel was built to demonstrate feasibility of an adaptive prediction-coding technique.
Abstract: An experimental model of a coder for transmission of speech over a 9600-bits/s digital channel was built to demonstrate feasibility of an adaptive prediction-coding technique. After analog-to-digital conversion of the speech input, the coder employs digital processing using a computer type organization. Resonances in the short-term speech spectrum are removed by a nonrecursive digital transmit filter and the resulting uncorrelated signal is coded by an 8000-bits/s direct feedback delta coder. The transmit filter parameters are adapted to the input spectrum by a least squares algorithm involving calculation of short term correlation coefficients of the sequence of input samples. These filter parameters are multiplexed with the delta coder output for transmission to the receiver. A recursive receive filter restores the original speech spectrum. A computer simulation of the voice digitizer was performed to determine the order of the digital filters and to optimize other parameters prior to the design of the experimental model. The results of the simulation and design considerations for the experimental model are described.
TL;DR: It is pointed out that as the computer made it possible to design more and more sophisticated and complicated filters, more numerical problems arose that necessitated new theoretical advances in the field.
Abstract: The role of the digital computer in various phases of electric filter design is summarized in this review paper. It is pointed out that as the computer made it possible to design more and more sophisticated and complicated filters, more numerical problems arose that necessitated new theoretical advances in the field. Brief descriptions of these new developments as well as assessments of the present situation are given for conventional passive, RC -active, and digital filters.
01 Dec 1971
TL;DR: In this paper, an adaptive decomposition filter is proposed to decompose a noisy composite signal of identical but unknown multiple wavelets overlapping in time, which can be applied to echoes and overlapping wavelets which might arise in radar, sonar, seismology, or electrophysiology.
Abstract: An algorithm is discussed which decomposes a noisy composite signal of identical but unknown multiple wavelets overlapping in time. The decomposition determines the number of wavelets present, their epochs, amplitudes and an estimate of the basic wavelet shape. The algorithm is an adaptive decomposition filter which is a combination of three separate filters. One is an adaptive cross-correlation filter which resolves the composite signal from noise by an iteration procedure; this is followed by a wavelet extraction filter which ferrets out the basic wavelet form, and last there appears an inverse filter which achieves decomposition of the composite signal in the time domain. The decomposition algorithm can be applied to echoes and overlapping wavelets which might arise in radar, sonar, seismology, or electrophysiology. The proposed theory has been thoroughly simulated and selected experimental results are presented to demonstrate the technique. These include decomposition of brain waves evoked by visual stimulation.
TL;DR: The equations for a recursive extended Kalman filter with exponential age-weighting of data and dynamics are derived and this technique offers promise in controlling the divergence problem that recursive filtering often encounters.
Abstract: The equations for a recursive extended Kalman filter with exponential age-weighting of data and dynamics are derived. A similar result is given for a second-order filter. It is seen that the filter equations are essentially of the same form as their unfaded counterparts. This technique offers promise in controlling the divergence problem that recursive filtering often encounters.
TL;DR: In this article, a design rule for digital filters minimizing their deadbands is derived by observing and comparing the widths, and thus the severity of the effect, of deadbands that occur in different realizations of the same filter.
Abstract: A design rule for digital filters minimizing their deadbands is derived here by observing and comparing the widths, and thus the severity of the effect, of deadbands that occur in different realizations of the same filter. It is asserted that, normally, the parallel realization is better than the direct realization. The caseade realization is comparable to the parallel realization, and would be better or worse depending on how the sections are cascaded.