Convergence performance of adaptive lattice filters with nonlinearparameter updates

The convergence properties of adaptive lattice filters with nonlinear parameter updates have been analysed. The theoretical expressions for the convergence rate and the asymptotic error variance of the PARCOR coefficient are derived. Using these expressions, the convergence performance in the absence of impulsive noise is investigated and compared with those of the linear-type and sign-type adaptive lattice filters. Furthermore, the mean parameter variation caused by an impulsive noise and the parameter recovery time are evaluated to comprehensively compare the convergence performances in the presence of impulsive noise     

Extended RLS lattice adaptive filters

This paper solves the problem of developing exact fast weighted RLS lattice adaptive filters for input signals induced by general orthonormal filter models. The resulting algorithm can be viewed as a counterpart of the extended fast fixed-order RLS adaptive filters previously derived.     

Cascade lattice IIR adaptive filters

The feedback lattice filter forms, including the two-multiplier form and the normalized form, are examined with respect to their relationships to the feedback direct form filter. Specifically, the transformation matrix between the lattice forms and the direct form is derived; parameter and state relationships between the lattice forms and the direct form are therefore obtained. An IIR filter structure-the cascade lattice IIR structure-is constructed. Based on this structure, three IIR adaptive filtering algorithms in the two-multiplier form can then be developed following the gradient approach, the Steiglitz-McBride approach and the hyperstability approach. Convergence of these algorithms is theoretically analyzed using either the ODE approach or the hyperstability theorem. These algorithms are then simplified into forms computationally as efficient as their corresponding direct form algorithms. Relationships of the simplified algorithms to the direct form algorithms are also studied, which disclose a consistency in algorithm structure regardless of the filter form. Three normalized lattice algorithms can also be derived from the two-multiplier lattice algorithms. Experimental results show much improved performance of the normalized lattice algorithms over the two-multiplier lattice algorithms and the direct form algorithms     

One-multiplier adaptive lattice algorithm for recursive filters

The formulation of one-multiplier lattice structures of the Gray-Markel type forinfinite impulse response filters is reviewed. Several special cases of this formulation — including the well-known Gray-Markel normalized lattice—are presented as scaled polynomial versions of the two-multiplier lattice. A new adaptive algorithm is presented for updating the parameters of one-multiplier lattice structured recursive filters. The LMS-based algorithm requires fewer computations than earlier reported algorithms [1]–[4].The research reported here was conducted with funds administered by the Naval Postgraduate School research council.     

New adaptive normalised lattice algorithm for recursive filters

A new adaptive algorithm is presented for updating the parameters of normalised lattice structured recursive filters. The normalised lattice can be represented in the form of CORDIC blocks by converting the reflection factors into trigonometric functions. The LMS based algorithm actually updates the arguments of these trigonometric functions, and requires fewer computations than an earlier reported algorithm     

Systolic architectures for adaptive multichannel least squares lattice filters

A family of systolic array architectures for adaptive multichannel least squares lattice (MLSL) filters is presented. These architectures are based on a recently developed algorithm that provides an efficient, numerically sound, and well-structured set of recursions for realizing MLSL filters. The algorithm is based on the recursive QR decomposition of the forward and backward error correlation matrices. Form input channels andp filter taps,O(pm ²) computations are required per time step. Numerous space-time tradeoffs are available in mapping the algorithm's recursions to systolic architectures, leading to the architectural family presented here.Los Alamos National Laboratory is operated by the University of California for the United States Department of Energy under contract W-7405-ENG-36.     

Performance of adaptive filters using combined lattice and transform techniques

A composite scheme combining lattice and transform techniques for implementation of adaptive filters is discussed. Results of the eigenvalue spreads and convergence time for simple correlation cancelers in combination with Walsh-Hadamard Transform (WHT) are reported.     

Convergence analysis of alias-free subband adaptive filters based on a frequency domain technique

Convergence analysis of alias-free subband adaptive filters (SADFs) is presented based on a frequency-domain technique where instead of analyzing the adaptive algorithms in the time-domain, the averaging method and the ordinary differential equation (ODE) method are applied to the frequency-domain expressions of the adaptive algorithms converted by the discrete Fourier transform. As an alias-free SADF algorithm, the SADF proposed by Pradhan and Reddy is known. In this paper, this technique is first applied to the Pradhan's SADF. The stability of the Pradhan's SADF is verified in the frequency domain, and a simple formula to evaluate the mean square error (MSE) of the algorithm is theoretically derived. By using a slight modification, the technique can be applied to the two-band delayless subband adaptive filter (DLSADF) with the Hadamard transform. The stability condition and the MSE of the DLSADF with the Hadamard transform are also obtained. Simulation results of both algorithms show the validity of the theoretical results.     

Convergence analysis of the adaptive lattice filter for a mixed Gaussian input sequence

The convergence performance of the adaptive lattice filter (ALF) using the stochastic gradient algorithm is measured by the convergence speed and estimated error variance of the PARCOR coefficient. The convergence properties of the ALF are analysed when the filter input has a Gaussian mixture distribution. First, theoretical expressions for the convergence rate and asymptotic error variance of the PARCOR coefficient are derived, and then the theoretical expressions are compared for single and mixed Gaussian input sequences. It is shown that the convergence performance of the ALF improves as the distribution of the input signal approaches a single Gaussian distribution.     

Adaptive lattice bilinear filters

Two fast least-squares lattice algorithms for adaptive nonlinear filters equipped with bilinear system models are presented. The lattice filter formulation transforms the nonlinear filtering problem into an equivalent multichannel linear filtering problem, thus using multichannel lattice filtering algorithms to solve the nonlinear filtering problem. The computational complexity of the algorithms is an order of magnitude smaller than that of previously available methods. The first of the two approaches is an equation error algorithm that uses the measured desired response signal directly to compute the adaptive filter outputs. This method is conceptually very simple, but results in biased system models in the presence of measurement noise. The second is an approximate least-squares output error solution; the past samples of the output of the adaptive system itself are used to produce the filter output at the current time. Results indicate that the output error algorithm is less sensitive to output measurement noise than the equation error method     

Convergence properties of an adaptive lattice filter exploitingnonlinear dynamics of a biochemical reaction system

An adaptive lattice filter (ALF) which computes the PARCOR coefficients through a cyclic enzyme system has recently been developed by the author. Using nonlinear dynamics of the cyclic enzyme system, the ALF becomes robust against impulsive noise, and the stability of the estimated AR model can be ensured. The convergence properties of the ALF are studied. First, a theoretical expression for the asymptotic error variance of the PARCOR coefficient is derived. Simulation results are presented, and the theoretical and simulated values show a very good match. Next, the convergence speed of the proposed ALF is compared with that of the simplified ALF. The step sizes are then determined by using the above theoretical expression such that both ALF's achieve the same error variance in steady states. The results show that the proposed ALF has excellent convergence properties than the simplified one     

Laguerre-domain adaptive filters

Using a tapped-delay-line as an adaptive fitter, the complexity of the filter increases with increasing correlation length of input and reference signal. The author seeks simple adaptive filter structures such that for a long correlation length only a minor complexity of the filter is needed. He considers adaptive mechanisms governed by an exponentially weighted squared-error criterion. Laguerre-domain adaptive filters are introduced, which lead to a tapped IIR-filter line. These filters contain a discount factor as a free variable, which makes it possible to set the memory and the number of adaptive coefficients independently. Convergence properties of the proposed adaptive filters are discussed     

A floating-point arithmetic error analysis of direct and indirectcoefficient updating techniques for adaptive lattice filters

The ways in which finite precision arithmetic effects can deleteriously manifest themselves in both the stochastic gradient and the recursive least squares adaptive lattice filters are discussed. closed form expressions are derived for the steady-state variance of the accumulated arithmetic error in a single adaptive lattice coefficient using a floating-point stochastic arithmetic error analysis. The analytical results show that the performance of adaptive lattice filters using a direct updating computational form is less sensitive to finite precision effects than that of adaptive lattice filters using an indirect updating computational form. In addition, a method for reducing the self-generated noise is presented. Experimental results obtained on a 32-b floating-point hardware implementation of the adaptive lattice filters and with computer simulations are included to verify the analytical results describing the effects of finite precision on adaptive lattice filters     

Multiplication-free adaptive digital filters

The authors update delta modulation digital filter weights using the LMS (least-mean-squares) and the SIGN algorithms to realize an adaptive digital filter without multiplication operations. It is shown that using the SIGN algorithm results in an adaptive filter that can be implemented using the simple up/down counting operations. Learning curves demonstrating convergence properties of the algorithms for a system identification problem are presented     

Stable quarter-plane 2-D lattice filters

The stability of the two-dimensional quarter-plane lattice filter developed by Parker and Kayran (1984) is not guaranteed. Their lattice filter is potentially unstable unless a number of conditions are satisfied. The validity of these conditions are difficult to test. Three different lattice filter structures which are structurally stable for all parameters are presented.<>     

Generalised lattice transformation for crystal filters

Crystal lattice filters are usually based on the transformation of a lowpass Brune section to a second-order lattice section. This letter describes a generalisation, which transforms n Brune sections simultaneously into a lattice of order 2n, and which offers advantages for high-order filters, or filters with complex transmission zeros.     

Sensitivity formulas for digital lattice filters

Formulas are given for the sensitivities of the transfer function with respect to the k-parameters in a digital lattice structure.     

Adaptive lattice filters for CDMA overlay

This paper presents the behavior of reflection coefficients of a stochastic gradient lattice (SGL) filter applied to a code division multiple-access overlay system. Analytic expressions for coefficients for a two-stage filter are derived in a Rayleigh fading channel with the presence of narrow-band interference and additive white Gaussian noise. It is shown that the coefficients of the lattice filter exhibit separate tracking and convergent properties, and that compared to an LMS filter, the lattice filter provides fast rate of convergence, while having good capability of narrow-hand interference suppression     

SIMPLIFIED LATTICE REALIZAT ION OF FIR DIGITAL FILTERS

This paper suggests a simplified lattice structure for implementing FIR digital filters,which halvesthe hardware requirements of a conventional lattice realization.The conversion algorithms between directrealizations and the simplified lattice forms are given.Furthermore,the algorithms for linear phase FIR fil-ters are simplified.The principal results are illustrated by a practical example.