Showing papers on "Adaptive filter published in 1974"

Rapid Convergence Rate in Adaptive Arrays

Abstract: In many applications, the practical usefulness of adaptive arrays is limited by their convergence rate. The adaptively controlled weights in these systems must change at a rate equal to or greater than the rate of change of the external noise field (e.g., due to scanning in a radar if step scan is not used). This convergence rate problem is most severe in adaptive systems with a large number of degrees of adaptivity and in situations where the eigenvalues of the noise covariance matrix are widely different. A direct method of adaptive weight computation, based on a sample covariance matrix of the noise field, has been found to provide very rapid convergence in all cases, i.e., independent of the eigenvalue distribution. A theory has been developed, based on earlier work by Goodman, which predicts the achievable convergence rate with this technique, and has been verified by simulation.

Derivation and evaluation of improved tracking filter for use in dense multitarget environments

Abstract: When tracking targets in dense environments, sensor reports originating from sources other than the target being tracked (i.e., from clutter, thermal false alarms, other targets) are occasionally incorrectly used in track updating. As a result tracking performance degrades, and the error covariance matrix calculated on-line by the usual types of tracking filters becomes extremely unreliable for estimating actual accuracies. This paper makes three contributions in this area. First, a new tracking filter is developed that incorporates, in an a posteriori statistical fashion, all data available from sensor reports located in the vicinity of the track, and that provides both optimal performance and reliable estimates of this performance when operating in dense environments. The optimality of and the performance equations for this filter are verified by analytical and simulation results. Second, several computationally efficient classes of suboptimal tracking filters based on the optimal filter developed in this paper and on an optimal filter of another class that appeared previously in the literature are developed. Third, using an extensive Monte Carlo simulation, the various optimal and suboptimal filters as well as the Kalman filter are compared, with regard to the differences between the on-line calculated and experimental covariances of each filter, and with regard to relative accuracies, computational requirements, and numbers of divergences or lost tracks each produces.

Design of digital notch filters

Abstract: It is shown that a second-order digital notch filter is uniquely characterized by two distinct parameters, the notch frequency and the 3-dB rejection bandwidth. As a result, such a filter can be realized using only two multipliers. Methods are outlined to design a notch filter for a prescribed notch frequency and a prescribed 3-dB rejection bandwidth, along with procedures for postdesign adjustment of these parameters. All two-multiplier, canonic and noncanonic, notch filter configurations are developed using the multiplier extraction approach. These networks are then compared with regard to the effect of internal multiplication roundoff errors. Results of computer simulation of the notch filter configurations are also included.

Interpolation, extrapolation, and reduction of computation speed in digital filters

Abstract: Any digital filter can be decomposed into two basic subsets, an extrapolator the output of which is sampled at a frequency depending only on the filter bandwidth and an interpolator delivering the filtered signal at the imposed output sampling rate. Redundancy in extrapolator and interpolator is removed by introducing half-band nonrecursive filtering elements for which definition, performance figures and efficient implementation are supplied. They reduce significantly the necessary computation and storage at the cost of a slight group delay increase. A formula is given for the amount of multiplications to be carried out every second in a filter; it depends on the filter bandwidth, signal to distortion ratio, and input-output sampling rate. The method is extended to recursive filters and a comparison is made with existing techniques of implementing digital filters for the needs in computation and storage hardware: a specific example of design underlines the reduction in computation speed achieved in practice through this method, which brings digital filters in a most favorable position for their competition against analog filters in many application fields.

An l p design technique for two-dimensional digital recursive filters

Abstract: In this paper a design technique for the two-dimensional filters is proposed. An optimization algorithm is developed to minimize the p-error criterion under the constraint that the resulting filter be stable. Design of one-dimensional filter may be considered as a special case to which the proposed algorithm is applicable. Several examples are solved to illustrate the technique.

Design of circularly symmetric two-dimensional recursive filters

Abstract: The digital filtering of two-dimensional signals offers the many advantages characteristic of digital computers, such as flexibility and accuracy. Applications exist in the processing of images and geophysical data. A technique is presented for designing stable two-dimensional recursive filters whose magnitude response is approximately circularly symmetric. This is achieved by cascading a number of elementary filters which are called rotated filters because they are designed by rotating one-dimensional continuous filters and using the two-dimensional z-transform to obtain the corresponding digital filter. Stability of these filters is considered in detail and the results obtained are stated in two corollaries. In particular it is proved that rotated filters are stable if the angle of rotation is between 270° and 360°. Finally, methods of analysis and design of the shape, circular symmetry, and cutoff frequency of two-dimensional recursive filters are discussed.

Some comparisons between fir and iir digital filters

Abstract: The purpose of this paper is to make comparisons between optimum, linear phase, finite impulse response (FIR) digital filters and infinite impulse response (IIR) digital filters which meet equivalent frequency domain specifications. The basis of comparison is, for the most part, the number of multiplications per sample required in the usual realizations of these filters — i.e., the cascade form for IIR filters, and the direct form for FIR filters. Comparisons are also made between group-delay equalized filters and linear phase FIR filters. Considerations dealing with finite word-length effects are discussed for both these filter types. A set of design charts is also presented for determining the minimum filter order required to meet given low-pass filter specifications for both digital and analog filters.

Stability of multidimensional digital filters

Abstract: Conditions are obtained for a digital filter in three or more variables to be stable, and computational techniques for checking the stability are examined.

A Kalman filter approach to the deconvolution of seismic signals

Abstract: It is common practice to model a reflection seismogram as a convolution of the reflectivity function of the earth and an energy waveform referred to as the seismic wavelet. The objective of the deconvolution technique described here is to extract the reflectivity function from the reflection seismogram. The most common approach to deconvolution has been the design of inverse filters based on Wiener filter theory. Some of the disadvantages of the inverse filter approach may be overcome by using a state variable representation of the earth’s reflectivity function and the seismic signal generating process. The problem is formulated in discrete state variable form to facilitate digital computer processing of digitized seismic signals. The discrete form of the Kalman filter is then used to generate an estimate of the reflectivity function. The principal advantages of this technique are its capability for handling continually time‐varying models, its adaptability to a large class of models, its suitability for ...

Sequentially Adaptive Prediction and Coding of Speech Signals

Abstract: A new method of speech digitization called residual encoding is introduced, and its application to the speech digitization problem is studied. The residual encoding system is a form of differential pulse code modulation which utilizes both an adaptive quantizer and an adaptive predictor. The residual encoder differs from previous systems in two ways. First, a sequential estimation method is used to continuously update the predictor coefficients, and second, the predictor coefficients are not transmitted, but are extracted from the estimate of the speech signal at both the transmitter and receiver. No form of pitch extraction is employed. The residual encoding system with a Kalman filter or a stochastic approximation algorithm for identifying the predictor coefficients has produced good quality speech at a data rate of 16 kbit/s.

Design of Digital Notch Filters

Abstract: It is shown that a second-order digital notch filter is uniquely characterized by two distinct parameters, the notch frequency and the 3-dB rejection bandwidth. As a result, such a filter can be realized using only two multipliers. Methods are outlined to design a notch filter for a prescribed notch frequency and a prescribed 3-dB rejection bandwidth, along with procedures for postdesign adjustment of these parameters. All two-multiplier, canonic and noncanonic, notch filter configurations are developed using the multiplier extraction approach. These networks are then compared with regard to the effect of internal multiplication roundoff errors. Results of computer simulation of the notch filter configurations are also included.

Some considerations in the design of multiband finite-impulse-response digital filters

Abstract: Although much has been learned about the relationships between design parameters for finite impulse-response (FIR) low-pass digital filters, very little is known about the relationships between the parameters of multiband filters. Thus given a set of design specifications for a multiband FIR filter (e.g., filter band edge frequencies and desired ripples in each of the bands) it is difficult to choose a set of modified parameters which will yield an acceptable filter using a standard FIR design algorithm. By an acceptable filter we mean one with monotonic behavior of the frequency response in the DON'T-CARE or transition regions between bands and one providing at least the desired attenuation (or ripple) in each of the bands. In this paper, we examine the theoretical and practical issues of designing multiband filters and present several strategies for choosing the input parameters for the McClellan et al. filter-design algorithm to yield reasonable filters which meet arbitrary specifications.

Digital filtering of the e.c.g.—a comparison of low-pass digital filters on a small computer

Abstract: Algorithms for moving average, recursive and “Fourier transform” low-pass linear digital filters are described, with reference being made to the methods of design. The characteristics, including frequency, phase and impulse responses, of four specific filters are discussed in detail. In addition, some of the practical problems of programming these filters are considered. Factors such as execution times are evaluated in concluding which designs are most appropriate for filtering electrocardiograms.

A class of bootstrap estimators and their relationship to the generalized two stage least squares estimators

Abstract: This paper deals with the identification of a process modeled by a stable, linear difference equation of known order. Its output is subject to additive observation noise that is identically and independently distributed with zero mean and a constant variance. On-line estimators in which the process parameters as well as the process outputs are estimated simultaneously in real time are considered. For improving the stability of such on-line algorithms, a simple adaptive filter for the reference model is proposed. Further, it is shown that inclusion of such a filter relates the resulting bootstrap algorithms to the more general forms of the two stage least squares estimators viz. the k -class, h -class and the double k -class estimators. Effectiveness of the filter in stabilizing the on-line algorithms is demonstrated by using data generated by a fourth-order model.

An Algorithm for High-Speed Digital Filters

Abstract: This paper describes an algorithm that is suitable for fast implementations of nonrecursive and recursive digital filters. High speed is realized at the expense of memory; however, the memory-speed tradeoff is flexible so that many hardware and software implementations are practical. When memory is not limited, the time required to compute a filter output value is independent of the order of the filter.

Improvement of overflow behaviour of 2nd-order digital filters by means of error feedback

Abstract: In digital filters, nonlinear phenomena caused by adder overflow can occur. Some of these phenomena that have been observed in a 2nd-order recursive digital filter are mentioned. A circuit is described in which the error produced by overflow is delayed and fed back into the filter. It is shown that this circuit improves the overflow behaviour.

Optimizing non-recursive digital filters to non-liner phase characteristics

Abstract: Various methods based on optimization have been used to design linear phase filters. One such method has been to use a general-purpose optimization program to minimize some error criterion, a function of the filter coefficients and of the error between the specified and achieved gain responses. However, if this were to be used with arbitrary phase designs, the error criterion would have to be formulated as a function that combines the gain and phase errors in a meaningful way. It is shaown here that this particular difficulty can be avoided by regarding the phase specification as a deviation from the linear phase and splitting the characteristic into real and imaginary components, rather than gain and phase, and optimizing separately.

Digital filters with maximally flat amplitude and delay characteristics

Abstract: An analytical solution is obtained for the transfer function of a digital filter which exhibits an optimum maximally flat amplitude characteristic and a maximally flat delay characteristic simultaneously. Explicit values for the multipliers are given for the direct realization in terms of the degree of the network and an arbitrary bandwidth scaling factor. Finally, it is concluded that this type of filter is useful in the area where the degree of a non-recursive filter becomes excessive to fulfil an amplitude requirement (e.g. narrow bandwidth) and where recursive filters designed solely on an amplitude basis are too dispersive.

Minimax design of recursive digital filters

Abstract: The application of two new algorithms for minimax optimization due to Charalambous and Bandler is investigated. The application is to the problem of finding the coefficients of a recursive digital filter to meet arbitrary specifications of the magnitude or the group delay characteristics. Unlike the original minimax algorithm due to Bandler and Charalambous in which a sequence of least p th optimizations as p tends to infinity is taken, the two new algorithms do not require the value of p to do this. Instead, a sequence of least p th optimization problems is constructed with finite values of p in the range 1 . A criterion is given under which the order of the filter can be increased by growing filter sections. A general computer program has been developed, based on the ideas presented.

An electrically-reprogrammable analog transversal filter

Abstract: A basic building block constructed with CCD and MNOS technologies will be described. The tap weights are analog and electrically reprogrammable to realize Fourier transformers, matched filters and correlators, and adaptive filters.

New adaptive-signal-processing concept

Abstract: A new device is proposed that combines a surface-wave memory with an acoustoelectric convolver to yield an adaptive real-time correlator and convolver. The principal difficulty in combining these devices is obtaining short intense electron bursts in a small gap between a piezoelectric and a semiconductor.

Additional canonic realizations of digital filters using the continued-fraction expansion

Abstract: Three new canonic realizations of a digital-filter transfer function using the continued-fraction-expansion techniques are derived.

Self-adaptive equalizer for multilevel data transmission according to correlation encoding

Abstract: A self-adaptive equalizer comprises a transversal filter wherein the attenuators are adjusted with reference to the output signals of the filter. For use in a multilevel data transmission system according to correlative encoding, a first filter removes the correlation encoding from the transversal filter outputs. Means is provided for producing binary signals representative of the signs of the first filter outputs. A second filter encodes the binary signals in accordance with the correlative encoding. The attenuators are adjusted in compliance with the respective products of the difference between one each of the second and transversal filter outputs and the signals derived from those taps of the delay line of the transversal filter to which the relevant attenuators are connected.

New adaptive algorithms in Liapunov synthesis

Abstract: The speeds of the adaptive response of Lyapunov-designed adaptive systems are related to some extent to the degree of stability of the system. A generalized quadratic Lyapunov function is constructed to allow several new adaptive algorithms to be synthesized. The new algorithms each improve the degree of stability over previously reported adaptive algorithms. A root-locus analysis substantiates the improvement in response speed. While the framework for this short paper is that of full-state model-reference adaptation, the synthesis is applicable to systems employing output measurement, such as reduced-order model-reference systems [5] or an adaptive observer [20].

Picture processing using one-dimensional implementations of discrete planar filters

Abstract: The problem of implementing a two-dimensional recursive filter as a one-dimensional recursive filter is examined. The results of the present paper show that the exact one-dimensional implementation of a planar recursive filter is a time-varying filter. However, planar filters may be approximated by one-dimensional time-invariant recursive filters. The frequency response, stability, and storage requirements of the approximate filters are derived and illustrated.

Optimum adaptive imaging through atmospheric turbulence

Abstract: Recent results for the atmospheric mode decomposition are applied to an idealized imaging problem in which the receiver has a priori knowledge of the channel impulse response and mode decomposition. It is shown that a channel-matched filter receiver is essentially optimum and, on the average, achieves diffraction-limited performance. Furthermore, when the transmitting aperture lies within a single isoplanatic patch, this system may be realized without a priori channel knowledge by transmitted reference techniques.

Digital notch filter design procedure

Abstract: An analytical procedure for designing a linear digital notch filter is presented. The resultant filter is sixth-order and is implemented by cascading three second-order filters so as to avoid instability which may arise from computer coefficient truncation. The procedure outlined is straightforward, requires only simple algebraic steps, and gives filter parameter selection criteria for reducing the effects of computer coefficient truncation. Notch filters have utility in situations where a desired signal is corrupted by an additive sinusoidal pickup. One thus must process the noisy signal so as to remove the sinusoid without significantly distorting the desired signal.

Reduction of roundoff noise in wave digital filters

Abstract: Roundoff noise generated by arithmetic operations in a digital-filter computational sequence is undesirable in that it serves to distort the true signal at the output Furthermore, coefficient wordlength is directly related to the generated noise It is shown that a minimization of the filter attenuation sensitivity, which is characteristic of wave digital filters, serves to reduce the noise Analytical results confirm this for both floating-point and fixed-point systems A simulation where the actual noise is measured produces results which demonstrate the superior performance of the wave digital filter over the standard z-transform filter

Linear, Nonlinear, and Adaptive Delta Modulation

Abstract: The paper treats linear and nonlinear methods that refine the delta modulation process. These methods improve the quality of the decoded signal at a given transmission rate. Two linear processes are analyzed. The first one matches the source signal to the coder for minimum weighted noise in the decoded signal. The second one influences the signal which is fed to the comparator; it shapes the spectrum of the quantization noise desirably. Two nonlinear methods used in the delta modulation process are discussed. The first achieves a best possible prediction of the future signal from past binary decisions and thus a reduction of the error signal. The methods of the second type make the coder adaptive to variations in the power level of the source signal. This results in a large dynamic range of the coding system. A comparison of the various methods is made and a coding system for speech signals, based on a suitable combination of these methods, is described.