Showing papers on "Adaptive filter published in 1985"

Adaptive Signal Processing

Abstract: GENERAL INTRODUCTION. Adaptive Systems. The Adaptive Linear Combiner. THEORY OF ADAPTATION WITH STATIONARY SIGNALS. Properties of the Quadratic Performance Surface. Searching the Performance Surface. Gradient Estimation and Its Effects on Adaptation. ADAPTIVE ALGORITHMS AND STRUCTURES. The LMS Algorithm. The Z-Transform in Adaptive Signal Processing. Other Adaptive Algorithms and Structures. Adaptive Lattice Filters. APPLICATIONS. Adaptive Modeling and System Identification. Inverse Adaptive Modeling, Deconvolution, and Equalization. Adaptive Control Systems. Adaptive Interference Cancelling. Introduction to Adaptive Arrays and Adaptive Beamforming. Analysis of Adaptive Beamformers.

Adaptive equalization

Abstract: Bandwidth-efficient data transmission over telephone and radio channels is made possible by the use of adaptive equalization to compensate for the time dispersion introduced by the channel Spurred by practical applications, a steady research effort over the last two decades has produced a rich body of literature in adaptive equalization and the related more general fields of reception of digital signals, adaptive filtering, and system identification. This tutorial paper gives an overview of the current state of the art in adaptive equalization. In the first part of the paper, the problem of intersymbol interference (ISI) and the basic concept of transversal equalizers are introduced followed by a simplified description of some practical adaptive equalizer structures and their properties. Related applications of adaptive filters and implementation approaches are discussed. Linear and nonlinear receiver structures, their steady-state performance and sensitivity to timing phase are presented in some depth in the next part. It is shown that a fractionally spaced equalizer can serve as the optimum receive filter for any receiver. Decision-feedback equalization, decision-aided ISI cancellation, and adaptive filtering for maximum-likelihood sequence estimation are presented in a common framework. The next two parts of the paper are devoted to a discussion of the convergence and steady-state properties of least mean-square (LMS) adaptation algorithms, including digital precision considerations, and three classes of rapidly converging adaptive equalization algorithms: namely, orthogonalized LMS, periodic or cyclic, and recursive least squares algorithms. An attempt is made throughout the paper to describe important principles and results in a heuristic manner, without formal proofs, using simple mathematical notation where possible.

A minimal parameter adaptive notch filter with constrained poles and zeros

Abstract: A new algorithm is presented for adaptive notch filtering and parametric spectral estimation of multiple narrow-band or sine wave signals in an additive broad-band process. The algorithm is of recursive prediction error (RPE) form and uses a special constrained model of infinite impulse response (IIR) with a minimal number of parameters. The convergent filter is characterized by highly narrow bandwidth and uniform notches of desired shape. For sufficiently large data sets, the variances of the sine wave frequency estimates are of the same order of magnitude as the Cramer-Rao bound. Results from simulations illustrate the performance of the algorithm under a wide range of conditions.

Generalized median filtering and related nonlinear filtering techniques

Abstract: We consider some generalizations of median filters which combine properties of both the linear and median filters. In particular, L filters and M filters are considered, motivated by robust estimators which are generalizations of the median as a location estimator. A related filter, which we call the modified trimmed mean (MTM) filter, is also described. The filters are evaluated for their performance on noisy signals containing sharp discontinuities or edges. It is shown that M filters can offer a more favorable combination of the running mean and median filters than can L filters, while MTM filters generally have better characteristics than M filters. We also show that an MTM filter is a data-dependent modification of L filters. The concept of double-window filtering is introduced as a refinement of MTM filtering. One representative set of filtered sequences of a test input using these filters are presented to illustrate the performance characterisics of these filters.

Second-order Volterra filtering and its application to nonlinear system identification

Abstract: Some recent results on the design and implementation of second-order Volterra filters are presented. The (second-order) Volterra filter is a nonlinear filter with the filter structure of (second-order) Volterra series. A simple minimum mean-square error solution for the Volterra filter is derived, based on the assumption that the filter input is Gaussian. Also, we propose an iterative factorization technique to design a subclass of the Volterra filters, which can alleviate the complexity of the filtering operations considerably. Furthermore, an adaptive algorithm for the Volterra filter is investigated along with its mean convergence and asymptotic excess mean-square error. Finally, the utility of the Volterra filter is demonstrated by utilizing it in studies of nonlinear drift oscillations of moored vessels subject to random sea waves.

New processing techniques based on the constant modulus adaptive algorithm

Abstract: This paper presents three extensions of the constant modulus algorithm (CMA) introduced in an earlier paper as a means of correcting degradations in constant enyelope waveforms. As originally formulated, the CMA employs an FIR filter with complex coefficients and accepts complex (quadrature) input data. In this paper, first a real input, real coefficient version of the algorithm is shown to perform arbitrarily close to the fully complex version. Secondly, the algorithm is extended for the enhancement of signals having a nonconstant but known envelope, as might arise in data signals with pulse shaping. Lastly, a multichannel version of CMA, wherein several observations are linearly combined, is presented for joint adaptation of multiple filters. This approach can be used, for example, as a means of spatial or polarization "beamsteering" to reject additive interferers and compensate for channel-induced polarization rotation.

Explicit formulas for lattice wave digital filters

Abstract: Explicit formulas are derived for designing lattice wave digital filters of the most common filter types, for Butterworth, Chebyshev, inverse Chebyshev, and Cauer parameter (elliptic) filter responses. Using these formulas a direct top down design method is obtained and most of the practical design problems can be solved without special knowledge of filter synthesis methods. Since the formulas are simple enough also in the case of elliptic filters, the design process is sufficiently simple to serve as basis in the first part (filter design from specs to algorithm) of silicon compilers or applied to high level programmable digital signal processors.

Adaptive filters for digital image noise smoothing: An evaluation*

Abstract: Six adaptive noise filtering algorithms were implemented and evaluated. There are (1) median filtering, (2) K-nearest neighbor averaging, (3) gradient inverse weighted smoothing, (4) sigma filtering, (5) Lee additive and multiplicative filtering, and (6) modified Wallis filtering. For the sake of comparison, the mean filter was also included. All algorithms were tested on noise corrupted copies of a composite image consisting of a uniform field, a bar pattern of periods increasing from 2 to 20 pixels, printed text, and a military tank sitting on desert terrain. In one test, uniformly distributed noise between gray levels of −32 and 32 was added to the composite image and filtered. In a second test, multiplicative Gaussian noise with mean 1.0 and standard deviation 0.25 was introduced, then filtered. A 7×7 pixel processing window was used in all six adaptive algorithms and the mean filter for both tests. An adaptive filter was used iteratively with varying window sizes to demonstrate the success of iterative adaptive smoothing. Filtering results were evaluated from statistics, examination of transects plotted from each filtered bar pattern, and from visual ranking by a group of observers.

Three-dimensional image processing using the concept of network resonance

Abstract: It is shown that simple algebraic methods may be used to design three-dimensional (3-D) recursive digital filters for two important applications: first, the selective enhancement of a two-dimensional (2-D) signal that is moving with time along a linear trajectory at known velocity and, second, the selective enhancement of 3-D spatially planar waves. The design techniques involve first-order 3-D networks in the continuous domain and proceed by analogy with an extension of the simple circuit theoretic concepts of resonance and Q factor. A 3-D spatial straight-line filter is designed in the frequency domain as a 3-D planar filter and, conversely, a 3-D spatially planar filter is designed in the frequency domain as a 3-D straight-line filter.

Filters for distortion-free two-band multirate filter banks

Abstract: In this paper, conditions are given for a two-band multi-rate filter bank to be alias free and to have a unity frequency response. It is shown that the class of quadrature mirror filters (QMF's) that satisfies these conditions is quite limited. A class of filters which does satisfy these conditions is given, and a simple procedure for designing filters from this class is presented with an example.

Digital Filters for Real-Time ECG Signal Processing Using Microprocessors

Abstract: Traditionally, analog circuits have been used for signal conditioning of electrocardiograms. As an alternative, algorithms implemented as programs on microprocessors can do similar filtering tasks. Also, digital filter algorithms can perform processes that are difficult or impossible using analog techniques. Presented here are a set of real-time digital filters each implemented as a subroutine. By calling these subroutines in an appropriate sequence, a user can cascade filters together to implement a desired filtering task on a single microprocessor. Included are an adaptive 60-Hz interference filter, two low-pass filters, a high-pass filter for eliminating dc offset in an ECG, an ECG data reduction algorithm, band-pass filters for use in QRS detection, and a derivative-based QRS detection algorithm. These filters achieve real-time speeds by requiring only integer arithmetic. They can be implemented on a diversity of available microprocessors.

Application of efficient linear FM matched filtering algorithms to synthetic aperture radar processing

Abstract: The applicability of two relatively new linear FM matched filtering algorithms to the processing of synthetic-aperture radar (SAR) data is examined and compared to the fast-convolution algorithm The algorithms, called basic spectral analysis and the step transform, use the properties of the linear FM signal to achieve some significant performance improvements The algorithms are evaluated on the basis of their ability to deal with problems peculiar to the SAR application, such as multilooking, range-cell migration, and variations in the FM rate of the input signal Computation rates are also derived as a function of resolution and target return signal aperture It is shown that no one algorithm is optimal for all cases The basic-spectral-analysis algorithm has the lowest computation rate at low resolutions, but has an output data rate which varies with the FM rate and cannot correct for nonlinear data shifts called range curvature The step transform has the most efficient computation rate at high resolutions It also has a constant output data rate and can correct for range curvature The fast-convolution algorithm has a lower computation rate than the step transform at low resolutions and can meet all of the SAR requirements mentioned All of the algorithms are able to perform multilook processing

Adaptive Optical Target Detection Using Correlated Images

Abstract: A method for target detection that achieves clutter rejection by the use of multiple observations of the same target scene is developed. Multiple scene observations can be obtained by processing separate frequency bands of the same target scene or by recursively processing sequential observations in time. Optimal detection algorithms are developed, based on the assumption that the image intensity can be modeled as a variable mean spatial Gaussian process. Several fast detection algorithms are derived which make use of the fact that the covariance matrices of many optical and infrared (IR) images can be accurately approximated by diagonal matrices. These algorithms provide efficient solutions to the problem of processing multiple correlated scenes or multiple sequential imaging. Computer simulations based on actual optical and IR image data were used for checking the theoretical results. The new detection algorithms achieved performance improvement in detection signal-to-noise ratio of up to 10 dB over conventional target correlation methods.

Full duplex speakerphone for radio and landline telephones

Abstract: A full duplex speakerphone employing adaptive filters and having application in radiotelephone systems. To cancel acoustic feedback echo of the receive signal, a representation of the receive signal generated via an A/D converter (601) and an adaptive filter (301) is subtracted by a summer (303) from the transmit signal generated by the speakerphone microphone (115). Adaptive filter receive signal representation coefficients employed in the receive signal adaptive filter (301) are modified when the receive signal is detected in a land party signal detector (225). Likewise, to cancel electronic echo of the transmit signal, a representation of the transmit signal generated via an A/D converter (605) and an adaptive filter (305) is subtracted from the receive signal by a summer (307). The adaptive filter transmit signal representation coefficients employed in the transmit signal adaptive filter (305) are modified when the transmit signal is detected.

Windowed fast transversal filters adaptive algorithms with normalization

Abstract: New fixed-order fast transversal filter (FTF) algorithms are introduced for several common windowed recursive-least-squares (RLS) adaptive-filtering criteria. O(N) operations per data point, where N is the filter order, are required by the new algorithms. These algorithms are characterized by two different time-variant scaling techniques that are applied to the internal quantities, leading to normalized and over-normalized FTF algorithms. It is this scaling that distinguishes the new algorithms from the multitude of fast-RLS-Kalman or fast-RLS-Kalman-type algorithms that have appeared in the literature for these same windowed RLS criteria, and which use no normalization or scaling of the internal algorithmic quantities. The overnormalized fast transversal filters have the lowest possible computational requirements for any of the considered windows. The normalized FTF algorithms are then introduced, at a modest increase in computational requirements, to significantly mitigate the numerical deficiencies inherent in all most-efficient RLS solutions, thus illustrating an interesting and important tradeoff between the growth rate of numerical errors and computational requirements for all fixed-order algorithms. Performance of the algorithms, as well as some illustrative tracking comparisons for the various windows, is verified via simulation.

Adaptive noise cancellation for a class of nonlinear, dynamic reference channels

Abstract: The computational complexity of nonlinear adaptive noise cancellation can be reduced by restricting the nonlinearity expected in the reference path to the noise canceler. The class of zero memory nonlinearities preceded by linear processors in the reference path is considered. Noniterative and iterative methods of system identification are applied to the determination of processor parameters in the noise canceler. The computational requirements of each of the algorithms are compared, and the iterative method is modified for improved convergence. Experimental results are presented for the modified iterative algorithm.

Stability analysis of fixed- point digital filters using computer generated Lyapunov functions- Part I: Direct form and coupled form filters

Abstract: We demonstrate the applicability of the constructive stability algorithm of Brayton and Tong in the stability analysis of fixed-point digital filters. In the present paper, we consider direct form and coupled form filters while in a companion paper we treat wave digital filters and lattice filters. We compare our results with existing ones which deal with either the global asymptotic stability of digital filters or with existence (resp., nonexistence) of limit cycles in digital filters. Several of the present results are new while some of the present results constitute improvements over existing results. In a few cases, the present results are more conservative than existing results. It is emphasized that whereas the existing results are obtained by several diverse methods, the present results are determined by one unified approach.

A class of low-noise computationally efficient recursive digital filters with applications to sampling rate alterations

Abstract: A new structure for multiband recursive digital filters is proposed. For meeting low-pass filter specifications, it uses fewer multiplications than conventional elliptic filter realizations. An approximation to the minimax solution is obtained numerically by minimizing the LP error norm. The analytic optimum for odd order low-pass filters of this new class turns out to be the elliptic filter itself, but in a new configuration. Analytic solution is also obtained for filters used in decimation/interpolation by a factor of 2. There are several realizations for this new structure, the choice of which depends on the location of poles and zeros. Some selected realizations always have low roundoff noise and small limit cycle bounds.

The tone capture properties of CMA-based interference suppressors

Abstract: An earlier paper introduced the constant modulus algorithm (CMA), an adaptive filtering technique for correcting multipath and interference-induced degradations in constant envelope waveforms such as FM and QPSK signals This algorithm exploits the fact that both multipath propagation and additive interference disrupt the constant envelope property of the received signal By sensing the received envelope variations, the adaptive algorithm can reset the coefficients of an FIR digital filter so as to remove the variations and, in the process, suppress the various interference components from the desired signal This paper examines a problem that arises when using CMA to suppress narrow-band interference If both the interferer and the signal have constant envelope and are spectrally nonoverlapping, then it is possible to find two different filter solutions, one which suppresses the interferer and another which "captures" the interferer and suppresses the desired signal This paper examines how "capture, can occur and how it may be prevented This problem is studied by characterizing the algorithm's behavior to an input consisting of only two sinusoids Assuming slow adaptation, the N-dimensional adaptive weight recursion is shown to compress into a two-by-two recursion in the tone output amplitudes This simplified recursion is then analyzed to determine what combinations of input amplitudes (signal-to-interference ratios) and filter initial conditions lead to "lock" and which lead to the capture of the interferer The results are then broadened to include multiple input tones and signals with nonzero bandwidth

On the design of digital filters as a sum of two all-pass filters

Abstract: The necessary and sufficient conditions are given for a digital filter transfer function to be implementable as a sum of two all-pass filters. The conditions are derived directly in the z -plane. The class of filters satisfying these conditions is shown to be wider than the class of filters obtained via the bilinear transformation from the corresponding conventional analog filters. An example shows that the given conditions enable us to design complementary filter pairs with different numerator and denominator orders directly using magnitude squared functions. These filters compare favorably with the corresponding classical filters.

Root properties and convergence rates of median filters

Abstract: Median filters are a special class of ranked order filters used for smoothing signals. Repeated application of the filter on a quantized signal of finite length ultimately results in a sequence, termed a root signal, which is invariant to additional passes of the median filter. In this paper, the theory is developed both for determining the cardinality of the root signal space of arbitrary window width filters applied to signals with any number of quantization levels and for counting or estimating the number of passes required to produce a root for binary signals.

An efficient algorithm for estimating noise covariances in distributed systems

Abstract: We present an efficient computational algorithm for estimating the noise covariance matrices of large linear discrete stochasticdynamic systems. Such systems arise typically by discretizing distributed-parameter systems, and their size renders computational efficiency a major consideration. Our adaptive filtering algorithm is based on the ideas of Belanger, and is algebraically equivalent to his algorithm. The earlier algorithm, however, has computational complexity proportional to p6, where p is the number of observations of the system state, while the new algorithm has complexity proportional to only p3. Furthermore, our formulation of noise covariance estimation as a secondary filter, analogous to state estimation as a primary filter, suggests several generalizations of the earlier algorithm. The performance of the proposed algorithm is demonstrated for a distributed system arising in numerical weather prediction.

Design of optimal Nyquist, partial response, Nth band, and nonuniform tap spacing FIR digital filters using linear programming techniques

Abstract: The design of a (FIR) finite-impulse-response digital filter with some of the coefficients constrained to zero is formulated as a linear programming (LP) problem and the Steiglitz's program [1] is modified and then used to design a class of constrained FIR digital filters. This class includes pulse shaping filters, N th band filters and nonuniform tap spacing filters, where some of the filter coefficients are constrained to zero. The advantage of the present approach, as compared to other methods, with regard to design speed and filter optimality and performance, are described, and illustrated by means of examples.

An Approximate Statistical Analysis of the Widrow LMS Algorithm with Application to Narrow-Band Interference Rejection

Abstract: The Widrow LMS algorithm is considered for the implementation of an adaptive prewhitening filter in a direct-sequence (DS) spread-spectrum receiver. Exact expressions for the steady-state tapweight covariance matrix and resulting average excess mean square error are developed for the real LMS algorithm when the input contains a random binary sequence (used to model a pseudonoise spreading sequence). It is shown here that the output samples of the adaptive filter possess approximately Gaussian statistics under the conditions of slow convergence and a large number of filter taps. Using this approximation, expressions for the resulting bit error rate (BER) when the adaptive algorithm is used to suppress a fading gone jammer are developed, and numerical results obtained from these expressions are compared to simulation results for the DS receiver.

Error models for stable hybrid adaptive systems

Abstract: This paper presents several stable adaptive algorithms for the control of hybrid and discrete systems in which the control parameters are adjusted at rates slower than those at which the systems operate. Continuous algorithms of an integral type, recently suggested in the literature [5] are also shown to belong to this class. From a practical standpoint, the infrequent adjustment of the control parameters makes for more robust adaptive control while from a theoretical point of view, the algorithms are attractive since they provide a unified framework for the design of continuous, hybrid, and discrete adaptive systems. Simulation results are included to indicate the type of responses that can be expected using the different algorithms.

Electronic noise-reducing system

Abstract: A method and apparatus for reducing noise from a near-field noise source sent together with signals from a far-field source. The method uses an adaptive shaping filter and a summer, in conjunction with a directional reference sensor and a primary sensor which have at least a common sensing element therebetween. The directional reference sensor situated between the near-field noise source and the far-field signal source, rejects the broad-band signal but accepts the broad-band noise and feeds this noise into a reference channel of the adaptive filter. The primary sensor accepts both the far-field signal and near-field noise with equally sensitivity. The primary sensor feeds into the primary channel of the adaptive filter. The adaptive filter system subtracts the noise in the reference channel from the signal-plus-noise in the primary channel, thus producing an output having a greatly improved signal-to-noise ratio.

Realization of Finite Impulse Response Filters Using Coefficients +1, 0, and -1

Abstract: New classes of nonrecursive linear digital filters are proposed as alternatives to conventional methods for digital signal processing devices. In fact, the traditional approach, where signal samples are represented by 8-15 bit words, can be very expensive to implement due to the complexity of multibit multipliers and adders. Filter structures consisting of a transversal filter with tap coefficients restricted to - 1, 0, or + 1 and cascaded with simple recursive sections are proposed. Using a mean square error criterion, dynamic programming methods to select optimum sets of coefficient values for the taps are presented and evaluated. It is shown that these structures lend themselves to very simple hardware implementations and offer a valid alternative to the conventional filtering approach. Designs for several example filters are presented, and their implementation complexity is examined.

Polynomial systems approach to optimal linear filtering and prediction

Abstract: The solution of the optimal linear estimation problem is considered, using a polynomial matrix description for the discrete system. The filter or predictor is given by the solution of two diophantine equations and is equivalent to the state equation form of the steady-state Kalman filter, or the transfer-function matrix form of the Wiener filter. The pole-zero properties of the optimal filter are more obvious in the polynomial representation, and new insights into the disturbance rejection properties of the filter are obtained. The plant or signal model can be stable or unstable, and allowance is made for both control and disturbance input subsystems, and white and coloured measurement noise (or an output disturbance subsystem). The model structure was determined by the needs of several industrial filtering problems. The polynomial form of filter may easily be included in a self-tuning algorithm, and a simple adaptive estimator is described.

Flexible design of computationaly efficient nearly perfect QMF filter banks

Abstract: This paper introduces a flexible design method of computationally efficient uniform filter bank where each filter channel is obtained by frequency translation of a prototype base-band filter. It is shown that the original signal decomposed by the analysis filter bank into N adjacent uniform subbands subsampled by N, can be reconstructed with negligible distortion. We give a practical implementation which allows an important reduction in computational complexity. It can be therefore applied to such signal processing tasks as speech coding or spectral parametrization of signals.