Showing papers on "Adaptive filter published in 1979"

On the independence theory of equalizer convergence

Abstract: High-speed pulse amplitude modulated (pam) data transmission over telephone channels is only possible when adaptive equalization is used to mitigate the linear distortion found on the (initially unknown) channel. At the beginning of the equalization procedure, the tap weights are adjusted to minimize the inter symbol interference between pulses. The “stochastic gradient” algorithm is an iterative procedure commonly used for setting the coefficients in these and other adaptive filters, but a proper understanding of the convergence has never been obtained. It has been common analytical practice to invoke an assumption stating that a certain sequence of random vectors which direct the “hunting” of the equalizer are statistically independent. Everyone acknowledges this assumption to be far from true, just as everyone agrees that the final predictions made using it are in excellent agreement with experiments and simulations. We take the resolution of this question as our main problem When one begins to analyze the performance of the algorithm, one sees that the average mean-square error after the nth iteration requires knowing, as an intermediate step, the mathematical expectation of the product of a sequence of statistically dependent matrices. We transform the latter problem to a space of sufficiently high dimension where the required average may be obtained from a canonical equation V n+1 = A(α)V n + Here A(α) is a square matrix, depending on the “step-size” α of the original algorithm, and V n and F are vectors. The mean-square error is calculable from the solution V n .

Transient and convergent behavior of the adaptive line enhancer

Abstract: The adaptive line enhancer (ALE) was first described as a practical technique for separating the periodic from the broad-band components of an input signal and for detecting the presence of a sinusoid in white noise. Subsequent work has shown that this adaptive filtering structure is applicable to spectral estimation, predictive deconvolution, speech processing, interference rejection, and other applications which have historically used matrix inversion or Levinson's algorithm techniques. This paper uses an eigenvalue-eigenvector analysis of the expected ALE impulse response vector to demonstrate properties of the convergent filter and to quantify the convergence time and characteristics of the ALE. In particular the ALE's response to a sinusoid plus white noise input is derived and compared to a computer simulation of the ALE with such an input. The eigenvalue-eigenvector technique is then used to evaluate the ALE's performance as an adaptive prewhitener for autoregressive (AR) models with white observation noise. A method is demonstrated which prevents the problem of spectral estimation bias which usually accrues from the observation noise.

Optimal synthesis of second-order state-space structures for digital filters

Abstract: Sufficient conditions are derived for a second-order statespace digital filter with L_2 scaling to be optimal with respect to output roundoff noise; and from these, a simple synthesis procedure is developed. Parallel-form designs produced by this method are equivalent to the block-optimal designs of Mullis and Roberts. The corresponding cascadeform designs are not equivalent, but they are shown, by example, to be quite close in performance. It is also shown that the coefficient sensitivities of this structure are closely related to its noise performance. Hence, the optimal design has low-coefficient sensitivity properties, and any other low-sensitivity design is a good candidate for near-optimal noise performance. The uniform-grid structure of Rader and Gold is an interesting and useful case in point.

An Optimal Frequency Domain Filter for Edge Detection in Digital Pictures

Abstract: Edge detection and enhancement are widely used in image processing applications. In this paper we consider the problem of optimizing spatial frequency domain filters for detecting edges in digital pictures. The filter is optimum in that it produces maximum energy within a resolution interval of specified width in the vicinity of the edge. We show that, in the continuous case, the filter transfer function is specified in terms of the prolate spheroidal wave function. In the discrete case, the filter transfer function is specified in terms of the sampled values of the first-order prolate spheroidal wave function or in terms of the sampled values of an asymptotic approximation of the wave function. Both versions can be implemented via the fast Fourier transform (FFT). We show that the optimum filter is very effective for detecting blufred and noisy edges. Finally, we compare the performance of the optimum edge detection filter with other edge detection filters using a variety of input images.

A convergence proof for a hyperstable adaptive recursive filter (Corresp.)

Abstract: Hyperstability, a concept from nonlinear stability theory, is used to develop a real-time adaptive recursive filter useful in a nonstationary environment.

Optimum second order digital filter

Abstract: A second order digital filter utilizing six processor operations, two add instructions, two shift instructions and two store instructions. No multipliers are required. The filter is used as a digital filter in a servo loop having a Z transform of, G(Z)=4 (1-Z-1)+Z-2.

Roundoff noise and overflow in normal digital filters

Abstract: Minimum-norm realizations of fixed-point digital filters provide guaranteed immunity from autonomous overflow limit cycles. This paper presents an analysis of the relationship between dynamic range and roundoff noise for a class of minimum-norm realizations called "normal." For normal realizations, the eigenvectors of the system matrix form an orthogonal basis for the system state space. An explicit expression for minimum roundoff noise, under an 12 dynamic range constraint, is derived, and means for achieving this minimum are given. The simple expression for minimum roundoff noise permits easy determination, by trial and error, of optimal subfilter structures. Explicit expressions for the state-space parameters of optimal secondorder normal filters are given.

Second-order output statistics of the adaptive line enhancer

Abstract: The adaptive line enhancer (ALE) is an adaptive digital filter designed to suppress uncorrelated components of its input, while passing any narrow-band components with little attenuation. The purpose of this paper is to analyze the second-order output statistics of the ALE in steady-state operation, for input samples consisting of weak narrow-band signals in white Gaussian noise. The ALE output is shown to be the sum of two uncorrelated components, one arising from optimum finite-lag Wiener filtering of the narrow-band input components, and the other arising from the misadjustment error associated with the adaptation process. General expressions are given for the output auto-correlation function and power spectrum with arbitrary narrow-band input signals, and the case of a single sinusoid in white noise is worked out as an example. Finally, the significance of these results to practical applications of the ALE is mentioned.

Analysis of the frequency domain adaptive filter

Abstract: The purpose of this note is to demonstrate significant analytical simplifications for studying the behavior of adaptive filtering in the frequency domain as opposed to studying the behavior of adaptive filtering in the time domain. A closed form expression, for the single complex weight in the frequency domain adaptive filter, is presented which allows significant statistical analysis to be performed. The mean-square error of the filter is evaluated as a function of the algorithm step size and the signal and noise powers.

A new approach for the design of digital interpolating filters

Abstract: The paper presents a new class of interpolators characterized by the property that the mean power of their error sequence, as a function of frequency, approximates zero in the Chebyshev sense. The design method, which is based on some observation and newly found general properties, will be described in some detail. An example shows the special properties of these interpolators in comparison with former results. Measurements done with a practical implementation are presented as well. A design chart for these filters is provided.

Optimum Filter Design for a Single-Phase Solid-State UPS System

Abstract: A systematic design procedure for the output filter of a singlephase uninterruptible power supply (UPS) system is developed. The basic specifications for the UPS system are first established. Four different output filter configurations are then analyzed and compared for sinusoidal pulsewidth and single-pulse modulated inverter output (i.e., filter input) voltage. On the basis of the above comparison, ``optimum'' filters are selected for both modulation techniques. Using a minimization function for filter cost and size, a set of filter design parameters corresponding to each type of modulation are obtained on the per unit basis. The theoretical results are verified on an experimental breadboard utilizing a current commutated thyristor inverter. Finally, the overall filter design procedure is outlined and a design example is presented.

Statistical design of autoregressive-moving average digital filters

Abstract: Procedures are presented for the systematic design of digital filters that contain poles and zeros. The procedures are simple, fast, and effective. All of the important algorithms are of the Levinson-type. The first key idea in the paper is that one may begin a design by posing a linear prediction problem for a stochastic sequence. The second is that a high-order "whitening" filter may be constructed for this sequence and "inverted" to yield a high-order all-pole filter whose spectrum approximates the spectrum of the stochastic sequence. The third key idea is that the all-pole filter may be used to generate consistent unit-pulse and covariance sequences for use in the Mullis-Roberts algorithm. This algorithm is then used to obtain a low-order digital filter, with poles and zeros, that approximates the high-order all-pole filter. The results demonstrate that the Mullis-Roberts algorithm, together with the design philosophy of this paper, may be used with profit to reduce filter or stochastic model complexity and to design spectrum-matching digital filters.

Design of stable two‐dimensional analogue and digital filters with applications in image processing

Abstract: A method is proposed for the frequency domain design of linear two-dimensional analogue and digital filters with guaranteed stability. The technique used is based on the result that the numerator and the denominator of the input immittance of a two-variable network (which is passive and lossy) are strictly Hurwitz polynomials. One of these strictly Hurwitz polynomials is assigned to the denominator of a two-variable analogue transfer function and the network elements are then used as the variables of optimization thereby guaranteeing the stability of the analogue transfer function. The transfer function of the corresponding two-dimensional discrete (digital) filter is obtained from the analogue transfer function by the bilinear transformation. Examples illustrating the versatility of the technique in designing 2D digital filters of arbitrary order approximating a given magnitude and group delay response are presented. These filters are used to process a simple binary image. The results obtained demonstrate the importance of linear phase in image processing applications. The method presented here can be extended to the design of stable m-dimensional analogue and digital filters.

Predictive speech signal coding with reduced noise effects

Abstract: A predictive speech signal processor features an adaptive filter in a feedback network around the quantizer. The adaptive filter essentially combines the quantizing error signal, the formant related prediction parameter signals and the difference signal to concentrate the quantizing error noise in spectral peaks corresponding to the time-varying formant portions of the speech spectrum so that the quantizing noise is masked by the speech signal formants.

Adaptive structures for multiple-input noise cancelling applications

Abstract: This paper is concerned with problems in which the interference present in a primary signal is reduced using a sum of M linearly-filtered reference signals. These latter signals contain interference components which are correlated with that present in the primary. Examples occur in antenna array processing and in multiple-axis seismometer recordings of geophysical data. In the structures of interest, the linear filters are adaptive and employ a lattice configuration. Previous work in this area has been restricted to the case of a single reference signal. The multiple-reference case is shown to have unique characteristics which do not appear in the single-dimensional case. Examples illustrating this difference are presented.

Adaptive Clutter Filtering Using Autogressive Spectral Estimation

Abstract: A new adaptive filter to reject clutter is derived using autoregressive spectral analysis techniques. The adaptive filter performs open. Ioop processing, resulting in a shorter transient response, and is therefore suitable for radar waveforms containing only a small number of samples. A number of examples including application to ballistic missile defense are presented to demonstrate the performance capabilities of the new adaptive filter.

An adaptive approach to time‐series forecasting

Abstract: This paper extends the applicability of the Carbone-Longini adaptive estimation procedure (AEP) to time-series forecasting. Comparisons with adaptive filtering, the Box-Jenkins methodology, and multiple regression analysis as it applies to time-series analysis are provided. Specific time-series data examined by Box and Jenkins and Box and Tiao constitute the basis for these comparisons. The analysis of the results indicate the robustness and performance superiority of the simple distributive-lag forecast model coupled with the concept of adaptively “tracking” rather than “fitting” historical data.

The generation of adaptive law structures for globally convergent adaptive observers

Abstract: Observing the state of an unknown linear system by means of a parametrized representation of the standard Luenberger observer with an additional adaptive loop (adaptive observer) is considered. A general technique on how to construct suitable adaptive laws for this additional loop is presented and it is proven that these adaptive laws always result in global and arbitrarily fast convergence of the adaptive process. Because the adaptive laws can assume a variety of different structures, both structural and parametric degrees of freedom in the adaptive law (rather than the so far available parametric degrees alone) are obtained, which can be used in a future optimization of the adaptive observer performance.

Double talk detector for echo cancellers

Abstract: Three double talk detectors (DTD) are used in combination with an echo canceller having an adaptive filter and a center clipper. First and second double talk detectors are used in the presence of double talk to selectively freeze the adaptive filter correction loop and to disable the center clipper. The third double talk detector is used to detect the initial adaptive period of the echo canceller. Control of the adaptive filter and clipper is effectively transferred from the first to the second double talk detector upon termination of the initial adaptive period as determined by the third double talk detector. The third double talk detector also detects a false double talk condition (where the distant talker pauses in speech) and overrides the second double talk detector in order to maintain the clipper in an active state.

Charge-coupled device (CCD) adaptive discrete analog signal processing

Abstract: A CCD adaptive signal processor is described which uses a so-called `clipped-data' least mean square (LMS) error algorithm to optimize the selection of tap weights in a CCD filter. A detailed description of a 16-tap monolithic silicon CCD analog adaptive filter is also presented. The filter is comprised of a basic linear combiner formed with a nondestructively tapped CCD analog delay line and electrically reprogrammable MOS analog conductances as the tap weights. To demonstrate the feasibility of adaptive analog signal processing, a 2-tap weight CCD adaptive filter is described and experimental results presented.

Adaptive digital echo cancellation circuit

Abstract: The present invention discloses an adaptive digital echo cancellation circuit including a finite impulse response digital filter, wherein the digital filter coefficients are adapted by continuous updating to compensate for telephone subscriber line echo conditions to enable the digital filter to continuously simulate the instantaneous subscriber line echo. The continuous coefficient update is provided by a correlator which includes provision for introducing non-linearities into the PCM transmitted and received signals, in parallel with the speech path, to derive a simplified digital representation of the PCM speech, thereby reducing the signal processing hardware required by the correlator to derive the updated filter coefficients.

On GLR detection and estimation of unexpected inputs in linear discrete systems

Abstract: In this paper, we present a recursive generalized likelihood ratio (GLR) test algorithm for detecting sudden changes in linear discrete systems. We demonstrate the application of linear filtering techniques to obtain a recursive GLR algorithm so that the requirement for matrix inversions in the previously known GLR algorithms can be reduced or avoided. Furthermore, the GLR algorithm is extended to the case when the sudden change follows known linear dynamics. An adaptive filtering scheme which uses the input estimate to correct the state estimate is also presented for the time-varying input case.

Filter and system incorporating the filter for processing discrete samples of composite signals

Abstract: A system for processing discrete digitized samples representing composite signals utilizing a filter which eliminates a periodic signal component from the composite signal. The filter receives and stores consecutive digital sample representations of the composite signal and, for each received sample representation, provides a digital average representation of the values of a selected number of the received digital sample representations which define a zero average value of the periodic signal component. In one embodiment of the signal processing system, the filter is arranged in circuit with digital delays and digital signal combining and differencing circuits to form a digital color television signal dropout compensator, which is adaptable for use in NTSC, PAL, PAL-M, or other television standard systems. In a dropout compensator adapted for NTSC color television signals, the filter receives the digital composite television signal and eliminates the chrominance component therefrom, leaving only the luminance component at its output. A following digital subtractor is coupled to subtract the luminance component provided by the filter from the received digital composite television signal and provide the chrominance component at its output. The separated chrominance component is phase adjusted on consecutive television lines and recombined with the separated luminance component provided by the filter for substitution in the television signal in place of the dropout affected portion thereof. The dropout compensator also includes a digital delay of one horizontal line period through which the television signal components are passed to provide the delay necessary for substituting television signal information from a prior horizontal line.

Adaptive filter with tap coefficient leakage

Abstract: Adaptive filters are commonly used in echo cancelers and automatic equalizers. Usually adaptive filters include a tapped delay line and apparatus coupled to the delay line for producing a tap coefficient signal, whose sign and magnitude indicate the appropriate correction in adjusting the filter. However, in the presence of input signals having a partial frequency band spectrum, known filters tend to become unstable, e.g., tap coefficient signals blow up. The instant arrangement includes apparatus for weakly driving the tap coefficient signals to optimal values. As illustrated in a deceptively simple embodiment, a tap coefficient updating component is extended through a one's complement converter to a first input of a binary adder. A two's complement output of the adder is fed back to a second input of the adder. The sign of the adder output is also provided to a CARRY-IN input terminal of the adder. Functionally, a unit leak is introduced in the least significant bit of the adder output tap coefficient signal whenever the updating component and the tap coefficient signal are of opposite algebraic signs. Otherwise, no leak is introduced. Thereby the tap coefficient signal is weakly driven toward zero.

Self-adaptive Kalman filter

Abstract: It is shown how the refined instrumental variable (r.i.v.) method of recursive parameter estimation can be modified simply so that it functions as an optimal adaptive filter and state-estimation algorithm.

A sequential failure detection approach and the identification of failure parameters

Abstract: This paper is concerned with the problem of a failure diagnosis for a discrete-time system with parametric failure, in which the occurrence time and mode of parametric failure cannot be estimated in advance. The failure diagnosis system which is proposed consists of three parts : (i) a normal mode filter, (ii) a detector for anomaly states, and (iii) an adaptive extended Kalman filter. The normal mode filter is called the optimal Kalman filter and transports the information of its innovation sequence to the detector. The detector which is based on the SPRT approach detects anomaly states affected by the parametric failure. The adaptive extended Kalman filter estimates simultaneously system parameters and the states under the failure mode. The adaptive procedure is directed by increasing the calculated covariance on the basis of hypothesis tests for the estimation errors of unknown parameters. Numerical results for a simple plant model illustrate the effectiveness of the proposed failure diagnosis system.