Showing papers on "Adaptive filter published in 1969"

Adaptive filtering

Abstract: Applications of the Kalman filter in orbit determination problems have sometimes encountered a difficulty which has been referred to as divergence. The phenomenon is a growth in the residuals; the state and its estimate diverge. This problem can often be traced to insufficient accuracy in modeling the dynamics used in the filter. Although more accurate modeling is an obvious solution, it is often an impractical, and sometimes an impossible, one. Model errors are here approximated by a white, Gaussian noise input, and its covariance (Q) is determined so as to produce consistency between residuals and their statistics. In this way, realtime feedback is provided from the residuals to the filter gain. Onset of divergence produces an increase in the filter gain and the adaptive filter is able to continue tracking. This scheme has a probabilistic interpretation. Under certain conditions the estimate of Q produces the most probable finite sequence of residuals.

An adaptive receiver for digital signaling through channels with intersymbol interference

Abstract: A tutorial paper on an adaptive receiver that is suitable for high-speed digital signaling over slowly time-varying, band-limited channels which have impulse responses that are unknown at the receiver is presented. The receiver utilizes a steepest-descent technique for adjusting its parameters to existing channel conditions. A treatment of the speed of adaptation of the receiver is included.

Recursive algorithm for the calculation of the adaptive Kalman filter weighting coefficients

Abstract: The optimal discrete adaptive Kalman filter, as presented by Magill, necessitates the iterative calculation of a weighting coefficient for each value of the quantized parameter space. This correspondence proposes a new recursive algorithm for the calculation of the weighting coefficients and compares it to the weighting coefficient algorithm of Magill. When there are L elements in the a priori known parameter space, it is shown that the memory and computational savings include 1) L memory allocations, 2) L scalar additions per iteration, and 3) L scalar multiplications per iteration.

A step-by-step active-filter design

Abstract: This article presents, in a simplified manner, a design method for active filters intended for those who are not filter specialists. By following the described five-step approach, a circuit designer who has some knowledge of passive filters will (without having to learn a whole new technology) be able to design active filters just as easily as he now handles conventional passive filters. Starting with the filter specification, it is shown sequentially how to realize a network that meets the prescribed requirements. Configurations and element values are given for the low-pass (LP), bandpass (BP), high-pass (HP), all-pass (AP), and band-elimination (BE), second-order active filter building blocks.

Optimal linear filtering for linear systems with state-dependent noise

Abstract: The purpose of this paper is to determine the linear optimal filtering algorithm for a message generated by noisy observations of a linear dynamic system with state-dependent, stochastic disturbances. These disturbances can be considered as stochastic parameter variations. As a consequence of the state-dependent noiso the message process is non-Gaussian. Hence the filter obtained by solving the Wiener-Hopf equation is only the optimal linear operation on the data. The optimal filter is non-linear. Unfortunately the dynamical equations for optimal nonlinear filtering can only be solved approximately. We show that one approximation reduces to the linear optimal filter. As an application we determine the linear optimal filter for a second-order system. This example provides us with a comparison of the performance of the linear optimal filter with a filter designed neglecting the presence of the state-dependent disturbances.

A Class of Time-Varying Digital Filters

Abstract: Discrete-time signals and digital filters have become increasingly important in recent years with the rapid advance of technology in integrated digital circuitry and the increasing availability of digital computers. This paper is concerned with a class of linear time-varying digital filters and the response of such filters with stochastic input signal. It is shown that these filters possess a number of useful properties; the most important of which is the preservation of wide-sense stationarity of stochastic inputs. Such properties can facilitate considerably the analysis of systems incorporating these filters. It is shown that this class is the most general class of time-varying filters that preserve the wide-sense stationarity of the inputs. A subclass of these filters is shown to be periodic and hence can be implemented simply by using parallel connection of time-invariant filters and a rotating switch. The response of these filters to periodic inputs is analyzed.

The Design and Synthesis of a Class of Microwave Bandpass Linear Phase Filters

Abstract: This paper is concerned with the design procedure and synthesis of a class of microwave bandpass linear phase filters which simultaneously exhibit a maximally flat amplitude and delay response about band center. In the first part of the paper a systematic procedure is developed for the construction of a nonminimum phase transfer function which exhibits a maximally flat delay and maximally flat amplitude characteristic. In the second part, a synthesis procedure is presented for the realization of the general nth-ordered transfer function by a generalized interdigital network. To simplify the design and construction of this filter, typical characteristics for filters of degree n = 3,4,5,6,7 are graphically presented together with a tabular representation of the polynomials which are required to design the filter. Finally, the results of an experimental filter of degree 3 are incorporated to illustrate that this class of nonminimum phase filters may readily be constructed in practice.

Optimal adaptive filter realizations for sample stochastic processes with an unknown parameter

Abstract: Techniques are given for realizing optimal learning systems for filtering a sampled stochastic process in the presence of an unknown constant or time-varying parameter. It is shown how the nonlinear Bayes optimal (quadratic sense) adaptive filters can be directly realized for continuous parameter spaces by real-time analog systems. Examples are given for both constant and time-varying unknown parameters.

Optimum digital filters for signal to noise ratio enhancement

Abstract: Summary One of the main objectives of seismic digital processing is the improvement of the signal-to-noise ratio in the recorded data. Wiener filters have been successfully applied in this capacity, but alternate filtering devices also merit our attention. Two such systems are the matched filter and the output energy filter. The former is better known to geophysicists as the crosscorrelation filter, and has seen widespread use for the processing of vibratory source data, while the latter is. much less familiar in seismic work. The matched filter is designed such that ideally the presence of a given signal is indicated by a single large deflection in the output. The output energy filter ideally reveals the presence of such a signal by producing a longer burst of energy in the time interval where the signal occurs. The received seismic trace is assumed to be an additive mixture of signal and noise. The shape of the signal must be known in order to design the matched filter, but only the autocorrelation function of this signal need be known to obtain the output energy filter. The derivation of these filters differs according to whether the noise is white or colored. In the former case the noise autocorrelation function consists of only a single spike at lag zero, while in the latter the shape of this noise autocorrelation function is arbitrary. We propose a novel version of the matched filter. Its memory function is given by the minimum-delay wavelet whose autocorrelation function is computed from selected gates of an actual seismic trace. For this reason explicit knowledge of the signal shape is not required for its design; nevertheless, its performance level is not much below that achievable with ordinary matched filters. We call this new filter the “mini-matched” filter. With digital computation in mind, the design criteria are formulated and optimized with time as a discrete variable. We illustrate the techniques with simple numerical examples, and discuss many of the interesting properties that these filters exhibit.

The Design of Optimal Convolutional Filters via Linear Programming

Abstract: Computational algorithms are given for the design of optimal, finite-length, convolutional filters with finite-length input sequences. Design techniques are developed for minimum-weighted-mean-square-error filters (MWMSE), for minimum-weighted-absolute-error filters (MWAE), and for filters which minimize the maximum output error (minimax). It is shown that the coefficients of the MWAE and minimax filters can be obtained by using standard linear programming methods. Next, the problem of developing a filter whose function is to "sharpen" a particular input waveform is considered. The filter input sequence is assumed to be derived from a Ricker wavelet of the velocity type and the desired output is the Dirac delta function. Convolutional filters are developed for this problem using each of the three performance criteria described above. The output sequences of each of the three optimal filters are discussed. It is shown that the minimax filter gives significantly better discrimination than can be obtained from either the MWAE or MWMSE filters.

General expression for the group delay of digital filters

Abstract: An expression for the group delay of a digital filter is derived in terms of the numerator and denominator polynomials of the transfer function H(z) The application of this expression to three cases is shown, and an important theorem relating to the exact realisability of linear phase digital filters is given

Discrete-time filtering apparatus

Abstract: In a discrete-time filter, sensitivity to coefficient variation is substantially reduced by using a unit delay interval, for the delay networks of the filter, which is not equal to the sampling interval. Furthermore, in realizing higher order filter systems, a plurality of such filters may be cascaded, each having a delay interval different from that of the other filters. The periods of repetition of the poles of the overall filter function are therefore different, resulting in improved filter performance.

A Timed-Shared Digital Filter Realization

Abstract: A special-purpose computer organization of a time-shared digital filter suitable for real-time applications is described. The computer is organized in functional modules so that the order of the filter, the coefficients of the filter, the programming form of the filter, and the multiplexing scheme for the filter are readily adaptable to system needs.

Digital notch filters

Abstract: The letter deals with the special class of digital filters that possess a prescribed notch frequency. The present techniques for synthetising such filters rest on the bilinear-transformation method, where the designer is required to synthetise a continuous s plane notch filter, prewarp it, and then apply the transformation. It is shown here that notch filters can be synthetised directly into the z−1 plane.

A nonlinear digital filter for industrial measurements

Abstract: A simple algorithm is presented for nonlinear filtering of a time series composed of a gaussian component, pulses and steps. The method used is a combination of simple statistical techniques. The main advantage is claimed to be a scheme for adaptation of the filter parameters.

Linear phase digital filter design

Abstract: The results of an investigation of linear phase digital filters are presented. It was determined that stable filters of this type are necessarily nonrecursive. The corresponding transfer function is presented in a general form in terms of basic z-plane pole and zero configurations. The design of digital filters of this form is accomplished by approximating a desired frequency function by one of four types of Fourier series. The types of series correspond to the forms of the z transfer function polynomial, which is either a mirror-image polynomial or a negative mirror-image polynomial, and either even or odd order.

Band selection filter with two active elements

Abstract: The invention relates to active band-selection filters with a band-selection transfer function of the second order. The filter contains resistances and lossy resonant circuits. A significant feature for filter circuits constructed in accordance with the invention is that they contain two active elements connected in such a way that the denominator of the transfer function has certain well-defined symmetry properties related to the circuit parameters of the two active elements and to the passive elements. In filters with these symmetry properties changes in the transfer function caused by variations in the active and passive filter elements are minimized and the manufacture of band-selection filter is simplified.

Adaptive filtering in satellite orbit estimation.

Abstract: Adaptive filter for estimating system noise inputs from actual residuals developed to control Kalman filter in satellite orbit estimation

Spatial filters for pattern detection and image enhancement

Abstract: A theory of spatial frequency domain filters is presented from the standpoint of leastsquare linear estimation. The general expression of this filter is obtained with few assumptions, thus allowing considerable flexibility in its application. Noise common to pictorial information usually can be described as a mutually exclusive process, whereas much of the available signal processing theory assumes additive noise. Types of pictorial noise discussed in this paper include the background of signal patterns, pattern obscurity, and image modulation due to the recording process. It is shown that the additive noise assumption is valid under certain conditions. The general filter is described in terms of spatial frequency estimates which are conveniently expanded for particular applications. A detection filter for determinative patterns is obtained and compared to the matched filter. A filter is derived to restore patterns degraded by noise and a linear distortion filter.

Improved self-tuning filter for low frequencies

Abstract: An improved method for introducing self-tuning features in an active filter for detection of weak signals in a noisy background is described. The filter, which works at low frequencies (100Hz-10kHz), is provided with facilities for search and tracking. During an experiment, the filter was able to detect a sinusoidal signal of 1mV r.m.s. in a 10kHz-bandwidth background noise of 3mV r.m.s.

Design and Performance of Optimum Power Series Filters

Abstract: A practical design procedure is formulated for the non-linear power series filters defined by Zadeh as An optimum set of values of Wgm(λ) based on the least mean square criterion is determined for filters with and without memory. The resulting filters turn out to be simple to construct. The performance of the filter is evaluated for some actual cases and the results compared with those obtained by Lubbock's filter. It is found that the proposed filter which is simpler than Lubbock's filter offers a performance almost as effective as the latter.

A Technique for Synthesizing Digital Filters

Abstract: In designing digital systems, one often faces the task of replacing a given analog filter by an equivalent digital filter. This paper proposes a method for synthesizing such digital filters in the time domain. It is assumed that the pulsed transfer function of the digital filter is a ratio of two rational polynomials. The coefficients are then determined by least-square fitting the digital filter to the analog filter's sampled input and output data. The resulting equations for computing the coefficients are linear. It is shown that the digital filter is essentially related to the analog filter, the sampling time, and the power spectrum of the signal being processed. If the signal is band-limited and the sampling frequency is sufficiently high, the digital filter can then be simply approximated by the Z transform of the analog filter multiplied by the sampling period.

Lowpass digital filters using least-squared-error design

Abstract: A method is presented of designing digital filters which give a least-squared-error fit to a polynomial expression. An example is given of a second-order digital-filter approximation to a first-order continuous filter.

A comparison of conventional and tracking filter systems for launch vehicle stabilization

Abstract: This paper extends a prior study on applications of an adaptive tracking filter to bending mode stabilization of large flexible boosters. The relative merits of fixed and tracking filters are evaluated for a variety of bending mode stabilization applications. The results motivated the design and evaluation of a tracking filter system for the Saturn V launch vehicle number 501. The principal conclusion is that better stability margins can be obtained using a tracking filter system instead of a conventional control system in certain gain stabilization applications. This improvement is accomplished at the expense of a substantial increase in system complexity, so that stability must be a critical problem in order to justify the use of a tracking filter.