Showing papers on "Kernel adaptive filter published in 1971"

New automatic equaliser employing modulo arithmetic

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.

Phase-Only Complex-Valued Spatial Filter*

Abstract: A new type of phase-only filter is described for wave-front construction, in which both the amplitude and phase information necessary to construct an arbitrary image over a limited field are encoded. It is shown that this phase-only filter can duplicate the performance of an ideal complex-valued spatial filter (a filter that controls both amplitude and phase transmittance). This phase-only filter controls the amplitude transmittance by the use of a modulated high-frequency phase carrier that diffracts a controlled amount of light into the image. This type of filter is particularly useful in the implementation of computational wave-front construction, because the maximum spatial frequency that must be plotted is associated with the image and not the carrier. The performance of the filter is examined both numerically and experimentally.

The Use of Linear Filtering as a Parameterization of Atmospheric Diffusion

Abstract: A simple linear filter is adapted for use in numerical models of the large-scale circulation to act in place of an explicit horizontal diffusion term in the equations. The filter can be shown to be ideally suited for this purpose in the sense that it can be made increasingly scale-dependent as the order of the filter is increased. The one-dimensional filter of order n is constructed from n three-point symmetrical operators and involves 2n/1 grid points. It is capable of eliminating two-grid-interval waves completely, yet allowing little or no damping of longer waves. In one space dimension, the use of the n = 1 order filter can be shown to be equivalent to the incorporation of a one-dimensional Fickian diffusion term in the differential equation. For any order n, the use of the one-dimensional filter is equivalent to the incorporation of a one-dimensional linear diffusion of order 2n. It is therefore apparent that as n increases, the ability of the filter to discriminate in its response to short-...

Multiple-constraint adaptive filtering

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.

Training adaptive linear filters

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.

The Kalman-Bucy Filter as a True Time-Varying Wiener Filter

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.

Adaptive signal processing through stochastic approximation

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.

Linear minimum-variance estimation and control in systems with state-dependent noise

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.

Nonlinear extensions of the fading memory filter

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.

Variational methods in adaptive filtering

Abstract: The practical implications of linear filter theory have long been recognized. The reduction of this theory to practice has generally been a long and difficult process. Much of the difficulty centers around problems of proper modeling of system parameters and the prior statistics of the plant and measurement noise and initial states. It is possible to pose various adaptive filter algorithms which, in effect, cause the filter to learn the system model as the system operates in real time. A very attractive feature of this approach is that it may be possible to reduce the time required to implement acceptable system design by reducing the time necessary for process modeling.