A state-space approach to adaptive RLS filtering

Adaptive filtering algorithms fall into four main groups: recursive least squares (RLS) algorithms and the corresponding fast versions; QR- and inverse QR-least squares algorithms; least squares lattice (LSL) and QR decomposition-based least squares lattice (QRD-LSL) algorithms; and gradient-based algorithms such as the least-mean square (LMS) algorithm. Our purpose in this article is to present yet another approach, for the sake of achieving two important goals. The first one is to show how several different variants of the recursive least-squares algorithm can be directly related to the widely studied Kalman filtering problem of estimation and control. Our second important goal is to present all the different versions of the RLS algorithm in computationally convenient square-root forms: a prearray of numbers has to be triangularized by a rotation, or a sequence of elementary rotations, in order to yield a postarray of numbers. The quantities needed to form the next prearray can then be read off from the entries of the postarray, and the procedure can be repeated; the explicit forms of the rotation matrices are not needed in most cases     

A new approach to subband adaptive filtering

Subband adaptive filtering has attracted much attention lately. In this paper, we propose a new structure and a new formulation for adapting the filter coefficients. This structure is based on polyphase decomposition of the filter to be adapted and is independent of the type of filter banks used in the subband decomposition. The new formulation yields improved convergence rate when the LMS algorithm is used for coefficient adaptation. As we increase the number of bands in the filter, the convergence rate increases and approaches the rate that can be obtained with a flat input spectrum. The computational complexity of the proposed scheme is nearly the same as that of the fullband approach. Simulation results are included to demonstrate the efficacy of the new approach     

A spatial filtering approach to robust adaptive beaming

The problem of controlling the superresolution in adaptive beamformers is treated. A straightforward method is presented that works for both narrowband and broadband arrays. The method is based on forming the blocking matrix in a general sidelobe canceller structure using a spatial FIR filter. The suppression of this spatial filter and the implicit noise of the leaky least-mean-square algorithm together determine the beamformer     

Optimal variable step size for the LMS/Newton algorithm withapplication to subband adaptive filtering

An efficient approach for the computation of the optimum convergence factor for the LMS (least mean square)/Newton algorithm applied to a transversal FIR structure is proposed. The approach leads to a variable step size algorithm that results in a dramatic reduction in convergence time. The algorithm is evaluated in system identification applications where two alternative implementations of the adaptive filter are considered: the conventional transversal FIR realization and adaptive filtering in subbands     

H/sub 2/ optimal linear robust sampled-data filtering design using polynomial approach

A new frequency domain approach to robust multi-input-multi-output (MIMO) linear filter design for sampled-data systems is presented. The system and noise models are assumed to be represented by polynomial forms that are not perfectly known except that they belong to a certain set. The optimal design guarantees that the error variance is kept below an upper bound that is minimized for all admissible uncertainties. The design problem is cast in the context of H/sub 2/ via the polynomial matrix representation of systems with norm bounded unstructured uncertainties. The sampled-data mix of continuous and discrete time systems is handled by means of a lifting technique; however, it does not increase the dimensionality or alter the computational cost of the solution. The setup adopted allows dealing with several filtering problems. A simple deconvolution example illustrates the procedure.     

麦克风阵列的协同自适应滤波语音增强方法

在麦克风阵列语音增强方法中,传统的广义旁瓣抵消器在处理存在显著脉冲噪声的语音信号时效果较差。为提高在脉冲噪声干扰下的语音信号增强效果,提出一种麦克风阵列的协同自适应滤波语音增强方法。该方法采用协同自适应滤波取代线性自适应滤波,基于NLMS算法导出了滤波器权值和协同因子的自适应更新算法。仿真实验结果表明,所提方法能有效地消除掉语音信号的脉冲噪声和高斯噪声,克服线性自适应滤波对非线性脉冲噪声的不敏感性,比广义旁瓣抵消器效果优越很多。     

An adaptive filtering approach to spectral estimation and SARimaging

We present an adaptive FIR filtering approach, which is referred to as the amplitude and phase estimation of a sinusoid (APES), for complex spectral estimation. We compare the APES algorithm with other FIR filtering approaches including the Welch (1967) and Capon (1969) methods. We also describe how to apply the FIR filtering approaches to target range signature estimation and synthetic aperture radar (SAR) imaging. We show via both numerical and experimental examples that the adaptive FIR filtering approaches such as Capon and APES can yield more accurate spectral estimates with much lower sidelobes and narrower spectral peaks than the FFT method, which is also a special case of the FIR filtering approach. We show that although the APES algorithm yields somewhat wider spectral peaks than the Capon method, the former gives more accurate overall spectral estimates and SAR images than the latter and the FFT method     

GSVD-based optimal filtering for single and multimicrophone speech enhancement

A generalized singular value decomposition (GSVD) based algorithm is proposed for enhancing multimicrophone speech signals degraded by additive colored noise. This GSVD-based multimicrophone algorithm can be considered to be an extension of the single-microphone signal subspace algorithms for enhancing noisy speech signals and amounts to a specific optimal filtering problem when the desired response signal cannot be observed. The optimal filter can be written as a function of the generalized singular vectors and singular values of a speech and noise data matrix. A number of symmetry properties are derived for the single-microphone and multimicrophone optimal filter, which are valid for the white noise case as well as for the colored noise case. In addition, the averaging step of some single-microphone signal subspace algorithms is examined, leading to the conclusion that this averaging operation is unnecessary and even suboptimal. For simple situations, where we consider localized sources and no multipath propagation, the GSVD-based optimal filtering technique exhibits the spatial directivity pattern of a beamformer. When comparing the noise reduction performance for realistic situations, simulations show that the GSVD-based optimal filtering technique has a better performance than standard fixed and adaptive beamforming techniques for all reverberation times and that it is more robust to deviations from the nominal situation, as, e.g., encountered in uncalibrated microphone arrays.     

Prefiltering approach for optimal polynomial prediction

A prefiltering approach for optimal prediction of polynomial signals is proposed. The new scheme enables the use of an arbitrary stable prefilter for which an optimal FIR postfilter is designed such that polynomial signals of given order are predicted unchanged. Additional degrees of freedom are used for noise suppression. The advantages of the approach are demonstrated with examples employing a first-order recursive prefilter     

A nonlinear operator-based speech feature analysis method withapplication to vocal fold pathology assessment

Traditional speech processing methods for laryngeal pathology assessment assume linear speech production with measures derived from an estimated glottal flow waveform. They normally require the speaker to achieve complete glottal closure, which for many vocal fold pathologies cannot be accomplished. To address this issue, a nonlinear signal processing approach is proposed which does not require direct glottal flow waveform estimation. This technique is motivated by earlier studies of airflow characterization for human speech production. The proposed nonlinear approach employs a differential Teager energy operator and the energy separation algorithm to obtain formant AM and FM modulations from filtered speech recordings. A new speech measure is proposed based on parameterization of the autocorrelation envelope of the AM response. This approach is shown to achieve impressive detection performance for a set of muscular tension dysphonias. Unlike flow characterization using numerical solutions of Navier-Stokes equations, this method is extremely computationally attractive, requiring only a small time window of speech samples. The new noninvasive method shows that a fast, effective digital speech processing technique can be developed for vocal fold pathology assessment without the need for direct glottal flow estimation or complete glottal closure by the speaker. The proposed method also confirms that alternative nonlinear methods can begin to address the limitations of previous linear approaches for speech pathology assessment     

Comb filtering of noisy speech using overlap-and-add approach

A new type of comb filter is presented to enhance speech based on an overlap-and-add approach. The filter taps are altered and smoothed according to the degree of periodicity in speech. Objective measures including the segmental SNR and cepstral distance are carried out for performance evaluation. Improvements in the SNR in the range 0-20 dB are observed     

A unified algebraic transformation approach for parallel recursiveand adaptive filtering and SVD algorithms

In this paper, a unified algebraic transformation approach is presented for designing parallel recursive and adaptive digital filters and singular value decomposition (SVD) algorithms. The approach is based on the explorations of some algebraic properties of the target algorithms' representations. Several typical modern digital signal processing examples are presented to illustrate the applications of the technique. They include the cascaded orthogonal recursive digital filter, the Givens rotation-based adaptive inverse QR algorithm for channel equalization, and the QR decomposition-based SVD algorithms. All three examples exhibit similar throughput constraints. There exist long feedback loops in the algorithms' signal flow graph representation, and the critical path is proportional to the size of the problem. Applying the proposed algebraic transformation techniques, parallel architectures are obtained for all three examples. For cascade orthogonal recursive filter, retiming transformation and orthogonal matrix decompositions (or pseudo-commutativity) are applied to obtain parallel filter architectures with critical path of five Givens rotations. For adaptive inverse QR algorithm, the commutativity and associativity of the matrix multiplications are applied to obtain parallel architectures with critical path of either four Givens rotations or three Givens rotations plus two multiply-add operations, whichever turns out to be larger. For SVD algorithms, retiming and associativity of the matrix multiplications are applied to derive parallel architectures with critical path of eight Givens rotations. The critical paths of all parallel architectures are independent of the problem size as compared with being proportional to the problem size in the original sequential algorithms. Parallelism is achieved at the expense of slight increase (or the same for the SVD case) in the algorithms' computational complexity     

A theory of adaptive filtering

This paper considers the adaptive signal extraction problem for time-discrete data when only very general a priori assumptions regarding the distributions of signal and noise are possible. Specifically, it is assumed that the noise is white, additive, and signal independent with mean zero and unknown variance and that the signal is band-limited. No stationarity assumptions are required. After a procedure is found under these conditions, the mean-square-error is derived asymptotically under narrower conditions-stationary Gaussian data with mean zero. Finally, a method of estimating the error variance from the data (without knowing the signal directly) is found.     

A STATISTICAL NOISE MODEL AND MATHEMATICAL MODEL OF SPECKLE PATTERN AND ADAPTIVE FILTERING APPROACH

A statistical noise model and a mathematical model for real speckle pattern are presented in this paper, and then, in view of the models, a new adaptive suboptimal image filtering approach is proposed. The proposed approach, with the local direction features of speckle pattern, combines the characteristics of optimal linear filter with non-linear filter and is an adaptive approximation to linear minimum mean square error filter. Experimental results show that the proposed approach has fairly good edge-preserved performance, compared with other present image filters, as well as much better filtering performance and robustness for speckle pattern.     

A signal processing framework based on dynamic neural networks withapplication to problems in adaptation, filtering, andclassification

We present a coherent neural net based framework for solving various signal processing problems. It relies on the assertion that time-lagged recurrent networks possess the necessary representational capabilities to act as universal approximators of nonlinear dynamical systems. This applies to system identification, time-series prediction, nonlinear filtering, adaptive filtering, and temporal pattern classification. We address the development of models of nonlinear dynamical systems, in the form of time-lagged recurrent neural nets, which can be used without further training. We employ a weight update procedure based on the extended Kalman filter (EKF). Against the tendency for a net to forget earlier learning as it processes new examples, we develop a technique called multistream training. We demonstrate our framework by applying it to 4 problems. First, we show that a single time-lagged recurrent net can be trained to produce excellent one-time-step predictions for two different time series and also to be robust to severe errors in the input sequence. Second, we model stably a complex system containing significant process noise. The remaining two problems are drawn from real-world automotive applications. One involves input-output modeling of the dynamic behavior of a catalyst-sensor system which is exposed to an operating engine's exhaust stream, the other the real-time and continuous detection of engine misfire     

A polynomial rooting approach to super-resolution array design

This paper is concerned with the design of super-resolution direction finding (DF) arrays that satisfy prespecified performance levels, such as detection-resolution thresholds and Cramer-Rao bounds on error variance. The sensor placement problem is formulated in the framework of subspace-based DF techniques and a novel polynomial rooting approach to the design problem, based on the new concept of the “sensor locator polynomial (SLP),” is proposed. This polynomial is constructed using the prespecified performance levels, and its roots yield the sensor locations of the desired array. The distinguishing feature of the proposed technique is that it hinges on the properties of the array manifold, which plays a central role in all subspace-based DF algorithms     

A scalable high-frequency noise model for bipolar transistors withapplication to optimal transistor sizing for low-noise amplifier design

Fully scalable, analytical HF noise parameter equations for bipolar transistors are presented and experimentally tested on high-speed Si and SiGe technologies. A technique for extracting the complete set of transistor noise parameters from Y parameter measurements only is developed and verified. Finally, the noise equations are coupled with scalable variants of the HICUM and SPICE-Gummel-Poon models and are employed in the design of tuned low noise amplifiers (LNA's) in the 1.9-, 2.4-,and 5.8-GHz bands     

A fast quasi-Newton adaptive filtering algorithm

The convergence rate of an adaptive system is closely related to its ability to track a time-varying optimum. Basic adaptive filtering algorithms give poor convergence performance when the input to the adaptive system is colored. More sophisticated algorithms which converge very rapidly regardless of the input spectrum algorithms typically require O(N²) computation, where N is the order of the adaptive filter, a significant disadvantage for real-time applications. Also, many of these algorithms behave poorly in finite-precision implementation. An adaptive filtering algorithm is introduced which employs a quasi-Newton approach to give rapid convergence even with colored inputs. The algorithm achieves an overall computational requirement of O(N) and appears to be quite robust in finite-precision implementations     

A pragmatic approach to adaptive antennas

This paper presents a novel approach for efficient computation of adaptive weights in phased-array antennas. The fundamental philosophical differences between adaptive antennas and adaptive signal-processing methodology are also delineated. This approach, unlike the conventional statistical techniques, eliminates the requirement for an interference covariance matrix, and represents a rethinking of the entire conventional approach to adaptive processing. This approach provides greater flexibility in solving a wider class of problems, at the expense of a slightly reduced number of degrees of freedom. It is important to note that the application of a deterministic approach to address stochastic problems with an ergodic structure can be seen in the works of Wiener (1949) and Kolmogorov (1939). This paper presents examples to illustrate the effectiveness and uniqueness of this new pragmatic approach