Showing papers on "Adaptive filter published in 1977"

A new phase unwrapping algorithm

Abstract: A new phase unwrapping algorithm is proposed that combines the information contained in both the phase derivative and the principal value of the phase into an adaptive numerical integration scheme. This new algorithm has proven itself to be very reliable and it can be easily incorporated in standard homomorphic signal processors.

Adaptive noise canceling applied to sinusoidal interferences

Abstract: This paper investigates a new method for eliminating sinusoidal or other periodic interference corrupting a signal. This task is typically accomplished by explicitly measuring the frequency of the interference and implementing a notch filter at that frequency. The method proposed herein uses an adaptive filter to eliminate the interference. The procedure is called adaptive noise canceling and is applicable when an auxiliary reference input is available containing the interference alone. The reference input is filtered in such a way that it closely matches the interfering sinusoid, and is then subtracted from the primary input leaving the signal alone. The results of this research show that when a sum of sinusoids is applied to an adaptive filter, the filter converges to a dynamic solution in which the weights of the filter are time varying. This time-varying solution implements a tunable notch filter, with a notch located at each of the reference frequencies. When used in noise-canceling applications, this adaptive notch filter provides a simple alternative to other methods of tracking and eliminating sinusoidal interferences.

A continuously-adaptive filter implemented as a lattice structure

Abstract: This paper is concerned with the use of adaptive, linear, non-recursive digital filters. Filters of this type are generally implemented in tapped-delay-line form and have been widely used in linear prediction filtering, spectral estimation and noise cancelling applications. Recently, an alternative implementation, called the lattice structure, has been proposed for fixed-coefficient recursive and non-recursive digital filters. The purpose of this paper is to present a class of adaptive algorithms suitable for use with the lattice structure, and to compare these algorithms with the conventional tapped-delay-line implementation. It is suggested that the successive orthogonalization offered by the lattice may provide convergence advantages not obtainable with tapped-delay-line methods.

Minimum norm recursive digital filters that are free of overflow limit cycles

Abstract: In recursive digital filters, the norm of the system matrix is an important design parameter with respect to overflow behavior. Filter realizations that minimize this norm are shown to be free of autonomous overflow limit cycles. Overflow-stable filters of any order, without any constraints on pole locations within the unit circle, can be realized by parallel-cascade structures of minimum norm systems. Minimum norm realizations require the minimum number of delay elements but, in general, more than the minimum number of multiplications and additions.

Tests of stability of multidimensional filters

Abstract: Novel stability criteria are established, for multidimensional digital and analog filters with rational transfer functions. The criteria generalize and simplify the stability test for two-dimensional digital filters developed by Huang [4], and significantly simplify the corresponding tests of stability of arbitrary multidimensional filters established by Anderson and Jury [6].

Online digital filters for biological signals: some fast designs for a small computer.

Abstract: After reviewing the design of a class of lowpass recursive digital filters having integer multiplier and linear phase characteristics, the possibilities for extending the class to include high pass, bandpass, and bandstop (‘notch’) filters are described. Experience with a PDP 11 computer has shown that these filters may be programmed simply using machine code, and that online operation at sampling rates up to about 8 kHz is possible. The practical application of such filters is illustrated by using a notch desgin to remove mains-frequency interference from an e.c.g. waveform.

The time-sequenced adaptive filter

Abstract: A new form of adaptive filter is proposed which is especially suited for the estimation of a class of nonstationary signals. This new filter, called the time-sequenced adaptive filter, is an extension of the least mean-square error (LMS) adaptive filter. Both the LMS and timesequenced adaptive filters are digital filters composed of a tapped delay line and adjustable weights, whose impulse response is controlled by an adaptive algorithm. For stationary stochastic inputs the mean-square error, which is the expected value of the squared difference between the filter output and an externally supplied "desired response," is a quadratic function of the weights--a paraboloid with a single fixed minimum point which can be sought by gradient techniques, such as the LMS algorithm. For nonstationary inputs however the minimum point, curvature, and orientation of the error surface could be changing over time. The time-sequenced adaptive filter is applicable to the estimation of that subset of nonstationary signals having a recurring (but not necessarily periodic) statistical character, e.g., recurring pulses in noise. In this case there are a finite number of different paraboloidal error surfaces, also recurring in time. The time-sequenced adaptive filter uses multiple sets of adjustable weights. At each point in time, one and only one set of weights is selected to form the filter output and to be adapted using the LMS algorithm. The index of the set of weights chosen is synchronized with the recurring statistical character of the filter input so that each set of weights is associated with a single error surface. After many adaptations of each set of weights, the minimum point of each error surface is reached resulting in an optimal time-varying filter. For this procedure, some a priori knowledge of the filter input is required to synchronize the selection of the set of weights with the recurring statistics of the filter input. For pulse-type signals, this a priori knowledge could be the location of the pulses in time; for signals with periodic statistics, knowledge of the period is sufficient. Possible applications of the time-sequenced adaptive filter include electrocardiogram enhancement and electric load prediction.

A self-tuning filter for fixed-lag smoothing

Abstract: The problem of estimating a discrete-time stochastic signal which is corrupted by additive white measurement noise is discussed. How the stationary solution to the fixed-lag smoothing problem can be obtained is shown. The first step is to construct an innovation model for the process. It is then shown how the fixed-lag smoother can be determined from the polynomials in the transfer function of the innovation model. In many applications, the signal model and the characteristics of the noise process are unknown. It is shown that it is possible to derive an algorithm which on-line finds the optimal fixed-lag smoother, a self-tuning smoother. The self-tuning smoother consists of two parts: an on-line estimation of the parameters in the one-step ahead predictor of the measured signal, and a computation of the smoother coefficients by simple manipulation of the predictor parameters. The smoother has good transient, as well as good asymptotic, properties.

Adaptive Filtering: An Integrated Autoregressive/Moving Average Filter for Time Series Forecasting

Abstract: This paper extends the applicability of a heuristic filtering technique, adaptive filtering, by dealing with a number of practical considerations in time series forecasting. These are problems that have been raised by other researchers examining this technique and by practitioners using it for time series analysis. These modifications make adaptive filtering much more comparable to the Box-Jenkins methodology for autoregressive/moving average processes. A specific application of adaptive filtering is provided.

Video bandwidth reduction system using a two-dimensional transformation, and an adaptive filter with error correction

Abstract: A reduction in bandwidth of two-dimensional video data is obtained by the two-dimensional transformation of the video data by means of one of a class of fast transformations followed by the elimination of certain non-significant transform coefficients prior to the transmission of the transform data. The lower-order transform coefficients or "zonal coefficients" which are usually significant in size, are always transmitted. Prior to transmission, parity bits are added to the zonal coefficients to allow error detection. An adaptive filter eliminates from the higher-order transform coefficients, those non-significant transform coefficients of magnitude less than a threshold level, which level is adjusted in response to the amount of data in the buffer memory awaiting transmission so as to transmit the most significant transform coefficients from a succession of two-dimensional data vectors. At the receiving end of the communication link the array of transform coefficients is reconstituted from the received data. The non-zonal coefficients, eliminated prior to transmission, are replaced by zeros in the reconstituted array. Transmission errors occurring in the zonal coefficients, are detected by parity checks and the erroneous zonal coefficients are replaced by the like transform coefficients from the previously received zonal coefficients corresponding to the prior scan of the same portion of the two-dimensional video data. An approximation to the original video data is obtained by the application of the inverse two-dimensional transformation to the reconstituted array of transform coefficients.

A generalized |ω|-filter for 3-D reconstruction

Abstract: The 3-D reconstruction of a density function is based on a direct convolution algorithm developed first by Ramachandran and Lakshiminarayanan. Their method adopts a particular choice of weighting function or filter which is called here an |ω|-filter. In some cases this choice of filter had an undesirable oscillatory response. To remedy this problem Shepp and Logan found a weighting function which produced a better reconstruction of a head section. The filter functions of Ramachandran and Lakshminarayanan and Shepp and Logan are only two of many choices for an |ω|-filter. Shepp and Logan's filter was the best for the early tomographic machines. Their filter function provided both a damped response to the cut-off frequency and a low sensitivity to noise. For the new tomographic machines, however, it is desirable to find filters that are not sensitive to counting noise, sample size and sample spacing as the previous filters. Here a study and generalization is made of the previous |ω|-filters. It extends the important filters of Ramachandran and Lakshiminarayanan, and Shepp and Logan to a class of generalized |ω|-filters. A generalized |ω|-filter can be chosen to have both good accuracy and a flexibility to cope with noise. A detailed comparison is made among the different possible filter shapes with respect to their responses to simulated data and noise. Finally in this paper it is demonstrated that a substantial reduction in the x-ray exposure time can be accomplished by choosing the appropriate generalized |ω|-filter.

Stabilization of certain two-dimensional recursive digital filters

Abstract: A possible extension of a well-known stabilization technique for one-dimensional recursive digital filters to the two-dimensional case was proposed by Shanks via a conjecture, stating that the planar least squares inverse of a two-dimensional filter polynomial is minimum phase and hence stable. In the present work, the conjecture has been verified first for a class of polynomials which are linear in one variable and quadratic in the other and then extended to a class of polynomials of higher degrees in the same variables. Though the conjecture is known to be false, in general, some conditions under which the conjecture is valid are explored.

Design of two-dimensional recursive filters by interpolation

Abstract: A technique for rotating the frequency responses of separable filters is developed. In this technique transfer functions having rational powers of z are introduced and realized by input/output signal array interpolations. Several applications of this technique to designing two-dimensional recursive filters are presented. Two- and multidimensional manipulations are performed by a series of one-dimensional manipulations.

Envelope-constrained filters--II: Adaptive structures

Abstract: Companion work on the design of envelope-constrained filters is extended and shown to provide an easily implementable adaptive filter with a structure quite similar to that of other adaptive filters based on least-squares techniques. Behavior of the new filter in noise is examined, and a variety of other extensions are discussed. An application to TV channel equalization is explored in some detail.

On parasitic oscillations in digital filters under looped conditions

Abstract: If a filter is used in multiplex telephone equipment, it actually operates in a loop due to the presence of two-wire/four-wire terminating equipment. Due to this, the power fed back into the filter input can, under adverse conditions, nearly equal the power leaving the output. This can be a cause for parasitic oscillations in case of digital filters. If properly designed, however, wave digital filters and nonrecursive digital filters remain stable.

Optimum edge detection filter

Abstract: Edge detection and enhancement are required in a number of important image processing applications. In this paper we consider the problem of optimizing spatial frequency domain filters for detecting a class of edges in images. The filter is optimum in that it produces maximum energy in the vicinity of the location of the edge for a given spatial resolution I and the bandwidth Ω. We show that the filter transfer function can be specified in terms of the prolate spheroidal wavefunctions for a given space–bandwidth product IΩ. Further we show that for values of IΩ less than 2, the optimal filter represents the Laplacian operator in image space followed by a low pass filter with a cutoff frequency Ω.

Multipliers for residue-number-arithmetic digital filters

Abstract: A recently proposed residue-number-arithmetic digital filter offers major cost and speed advantages over binary-arithmetic digital filters, but suffers one major drawback. The filter coefficients must be constant, since the lack of a fast method of multiplication by a fraction in residue arithmetic requires the coefficients to be realised by a fixed table look-up read-only memory. Two multipliers are proposed which realise a completely general fractional multiply and are suitable for digital-filtering applications.

Limit cycles in a two-dimensional first-order digital filter

Abstract: Limit cycles in a two-dimensional first-order digital filter are analyzed. Sufficient conditions for the nonexistence and sufficient and necessary conditions for the existence of limit cycles in the filter are derived. The limit cycles are of the two-dimensional degenerate type. Periods and an upper bound on the magnitudes of the limit cycles are also presented.

Adaptive Detection of Signals in Impulsive Noise Environments

Abstract: A detector structure and an adaptive algorithm are proposed for the reception of signals in noise backgrounds possessing broad-tailed probability distributions typical of impulsive noise. The adaptive detector combines the best features of linear matched filtering and hard-limiting receiver structures resulting in a small-signal SNR performance which is an improvement over either of these detectors alone. Furthermore, the adaptive detector is relatively easy to implement and is shown to provide efficient and robust performance for a wide range of underlying noise distributions.

Arrangement for simultaneous two-way data transmission over two-wire circuits

Abstract: An arrangement for simultaneous two-way data transmission of data signals with a given symbol frequency over two-wire circuits of a type found in telephone networks or of a comparable type. The arrangement comprises an echo canceler with an adaptive filter for producing from transmit channel signals approximated echo signals which are differentially combined with receive channel signals for forming substantially echo-free residual signals. A special type of code conversion is employed in the transmit channel, whereby p-level data symbols are converted into modified p-level data symbols which are thereafter converted into (2p-1)-level data symbols. The echo canceler comprises a digital adaptive filter to which the modified p-level data symbols and the residual signals with a sampling frequency equal to the symbol frequency are supplied. These measures result in a transmission signal having favorable spectral properties, a simple inverse code conversion and an echo canceler which combines simplicity of implementation with favorable convergence properties.

An adaptive recursive filter.

Abstract: : An adaptive recursive digital filter is presented in which feedback and feedforward gains are adjusted adaptively to minimize a least square performance function on a sliding window averaging process. A two-dimensional version of the adaptive filter is developed and its performance compared with the optimal Wiener filter. The filter is shown to be effective in separating three diagonal trajectory streaks from a background of correlated noise added to white noise. Although the recursive adaptive filter approaches the optimal Wiener filter in performance, it does not require a priori statistical knowledge as does the Wiener filter to which it is compared. The results indicate that the recursive adaptive filter learns the statistics and adapts. (Author)

Digital Control of High Performance Aircraft Using Adaptive Estimation Techniques

Abstract: Since the early 1960's, a rapid advance in signal processing, including filtering and estimation techniques, has been evident. In contrast, applied feedback control, particularly for aircraft, is currently based on technology available prior to 1960, i. e., primarily either constant gain feedback or at most a standard gain-scheduling. In this paper, an adaptive signal processing algorithm is joined with gain-scheduling to produce an effective scheme for controlling the dynamics of high performance aircraft. A technique is presented for a reduced-order model (the longitudinal dynamics) of a high performance short-takeoff-and-landing (STOL) aircraft. The actual controller views the nonlinear behavior of the aircraft as being equivalent to a randomly switching sequence of linear models taken from a preliminary piecewise-linear fit of the system nonlinearities. The adaptive nature of the estimator is necessary to select the proper sequence of linear models along the flight trajectory. From the analysis of the reduced-order model the nonlinear behavior has been found to be well approximated by assuming an effective switching of the linear models at random times, the durations of which reflect the motion of the aircraft in response to pilot commands.

Principles and Applications of Adaptive Filters: A Tutorial Review,

Abstract: : This report reviews the characteristics of a class of adaptive filters useful in signal processing and other applications where the properties of the signal are unknown or variable with time. The basic element of these filters is the adpative linear combiner, which weights (adjusts the gain of) and sums a set of input signals to form a single output signal. The weighting process is governed by a recursive algorithm that seeks to minimize the mean square of the difference between the combiner's output and a 'desired response' (training signal). It is shown that for statistically stationary inputs the mean-square difference is a quadratic function of the weight values, allowing the minimum to be sought by gradient estimation and other similar techniques. Expressions are given that define the relationship between rate of adaptation and deviation from optimal performance due to noise in the gradient estimation process for the Widrow-Hoff LMS algorithm. Methods of deriving the inputs to the combiner are described, including the use of a tapped delay line to form an adaptive transversal filter. Experimental results obtained by computer simulation are presented that show the ability of the adaptive transversal filter to model an unknown network or physical system; to reduce or eliminate intersymbol interference in multipath communication channels; to reduce or eliminate periodic interference in electrocardiography and broadband interference in the sidelobes of an antenna array; and to separate periodic and broadband signals and detect very low level periodic signals. (Author)

Two-dimensional wave digital filters using doubly terminated two-variable LC-ladder configurations

Abstract: This paper proposes a method of obtaining a two-dimensional wave digital filter of the recursive type from a doubly terminated LC-ladder network in two variables by replacing each series or shunt arm element of the ladder by its equivalent digital two-port. A number of realizations of the wave digital two-ports, which are canonic in multipliers, have been obtained. An example of a circularly symmetric low-pass two-dimensional digital filter is considered using these realizations. The sensitivity of this filter with respect to the multiplier coefficient changes due to finite word length is compared with that of the direct realization. It is found that the wave digital filter appears to be a more desirable form of implementation than the conventional cascade form.

Covariance-invariant digital filtering

Abstract: When discretizing continuous-time filters, one is often interested in preserving a property termed covariance-invariance. Techniques are outlined for synthesizing discrete-time filters which are covariance-invariant with corresponding continuous-time filters. The synthesis techniques involve straightforward matrix decompositions or polynomial root-finding algorithms that can easily be programmed on a digital computer. Applications of the technique to digital filter synthesis are outlined, with example designs presented for covariance-invariant Butterworth and Chebyshev digital filters. Based on the frequency response of these designs it is argued that the method of covariance-invariance is superior to the methods of impulse-invariance and bilinear-z as a response matching design technique for the synthesis of digital filters. This superiority is especially apparent at sampling rates that are marginal with respect to filter critical frequencies. Moreover, the covariance-invariant designs are stably invertible solutions to a so-called spectral factorization problem. This property may be important in inverse filtering applications.

Echo cancellation on time-variant circuits

Abstract: Echo cancellation is rapidly becoming a viable alternative to the conventional method of echo suppression currently in use to curtail echoes on long-distance telephone circuits. Echo suppressors introduce a switched loss into the return speech path when echo is present, and are inherently incapable of sustaining reduction of echo during periods of double-talk-while both parties are talking simultaneously. Echo cancellers use an adaptive filter to model the echo path, and compute a replica of the echo component present in the return speech signal. Subtraction of the replica from the return speech signal leaves it devoid of echo, allowing only the speech from the other party to be passed. Lack of synchronism in some classes of carrier system give rise to cyclic time variation in the echo path, termed "phase-roll," which must be tracked by the adaptive filter. Established adaptive echo cancellers are ineffective on circuits exhibiting phase-roll rates in excess of 0.5 Hz. The nature of the phase-roll problem is examined and two solutions discussed; use of compensating frequency offsets and cancellers with high-speed convergence. A prototype capable of satisfactory performance with speech on circuits exhibiting phase-roll rates up to 1.8 Hz is described. Modifications are proposed whereby the performance attained on speech signals can be made to approach the observed 3.4 Hz phase-roll limit with random noise input.

Approximation of two-variable filter specifications in analog domain

Abstract: This paper describes a technique for approximating 2-variable filter specifications in the continuous or analog domain. It is shown that the design of 2-variable filter functions using this approach reduces to the problem of identifying a suitable 2-variable reactance function g(s_1,s_2) and the realization of a stable single-variable transfer function T(s) . Then T(g(s_1,s_2)) is the desired 2-variable stable transfer function which is guaranteed to have at least one realization whenever T(s) and g(s_1,s_2) are realizable. Applications of the theory developed in this paper are presented in the design of lumped-distributed filters and 2-dimensional digital filters.