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     

On an adaptive algorithm for IIR filters

The purpose of this communication is to discuss an IIR adaptive filter algorithm developed by Stearns [1], in terms of an example that appeared in a recent article [2]. The example concerns the approximation of a fixed second-order filter by a first-order adaptive filter, when subjected to a white noise input.     

Design of three-dimensional adaptive IIR notch filters

This paper investigates a realization of a three-dimensional (3-D) adaptive notch filter. The procedures are mainly divided into two parts: frequency-detecting and sinusoidal interference removal. The detections are based on adaptive line enhancer on infinite impulse response (IIR) lattice structure. In the interference removal part, a non-separable version of a 3-D notch filter is effectively applied. The magnitude response of a 3-D adaptive IIR notch filter is illustrated. At the end of the paper, the implementation of an IIR notch filter on a 3-D image is also conducted in order to show how to remove a sinusoidal interference superimposed on a 3-D image.     

Bias removal in equation-error adaptive IIR filters

In the equation-error formulation of adaptive IIR filters, the estimated parameters contain bias when there is noise in the desired response. A method that can eliminate this bias is investigated. The idea is to maintain a quadratic constraint on the feedback coefficients so that the noise contributes only a constant term to the mean-square error. This term does not affect minimization and thus the bias is eliminated. A quadratically constrained stochastic gradient search method is applied for optimization and convergence behavior, when the noise is white, is analyzed. Adaptation of the feedback FIR filter in second-order cascade form, useful for stability monitoring, is also considered. When the noise is nonwhite, the technique requires an adaptive whitening filter. Simulation results are included to demonstrate the bias removal capability of the method, corroborate the theoretical developments, and compare with existing techniques     

Analysis of gradient algorithms for TLS-based adaptive IIR filters

Steepest descent gradient algorithms for unbiased equation error adaptive infinite impulse response (IIR) filtering are analyzed collectively for both the total least squares and mixed least squares-total least squares framework. These algorithms have a monic normalization that allows for a direct filtering implementation. We show that the algorithms converge to the desired filter coefficient vector. We achieve the convergence result by analyzing the stability of the equilibrium points and demonstrate that only the desired solution is locally stable. Additionally, we describe a region of initialization under which the algorithm converges to the desired solution. We derive the results using interlacing relationships between the eigenvalues of the data correlation matrices and their respective Schur complements. Finally, we illustrate the performance of these new approaches through simulation.     

Rational sampling filter banks based on IIR filters

The problem of splitting the spectrum of a digital signal by using nonuniform infinite impulse response (IIR) filter banks is addressed. Near perfect reconstruction (NPR) is considered. The method uses the modulation of different IIR prototypes. The cancellation of the main aliasing components constrains the prototypes to be dependent on each other. By using this approach, linear-phase prototypes are needed, and noncausal filtering is required. Numerical examples of filter bank design are given, and the computational complexity is compared with the finite impulse response (FIR) case     

The gamma-filter-a new class of adaptive IIR filters withrestricted feedback

Generalized feedforward filters, a class of adaptive filters that combines attractive properties of finite impulse response (FIR) filters with some of the power of infinite impulse response (IIR) filters, are described. A particular case, the gamma filter, generalizes Widrow's adaptive transversal filter (adaline) to an infinite impulse response filter. Yet, the stability condition for the gamma filter is trivial, and LMS adaptation is of the same computational complexity as the conventional transversal filter structure. Preliminary results indicate that the gamma filter is more efficient than the adaptive transversal filter. The authors extend the Wiener-Kopf equation to the gamma filter and develop some analysis tools     

Design of IIR digital filters based on eigenvalue problem

This paper presents a new method for designing IIR digital filters with optimum magnitude response in the Chebyshev sense and different order numerator and denominator. The proposed procedure is based on the formulation of a generalized eigenvalue problem by using Remez exchange algorithm. Since there exist more than one eigenvalue in the general eigenvalue problem, we introduce a very simple selection rule for the eigenvalue to be sought for where the rational interpolation is performed if and only if the positive minimum eigenvalue is chosen. Therefore, the solution of the rational interpolation problem can be obtained by computing only one eigenvector corresponding to the positive minimum eigenvalue, and the optimal filter coefficients are easily obtained through a few iterations. The design algorithm proposed in this paper not only retains the speed inherent in the Remez exchange algorithm but also simplifies the interpolation step because it has been reduced to the computation of the positive minimum eigenvalue. Some properties of the filters such as lowpass filters, bandpass filters, and so on are discussed, and several design examples are presented to demonstrate the effectiveness of this method     

An adaptive IIR filter algorithm based on observers

The output error approach to adaptive IIR filtering is considered from a state observation perspective, and a new algorithm, termed the observer-based regressor filtering (OBRF) algorithm, is developed. The convergence requirements of the OBRF are established as a persistent excitation condition on the regressor and a strict positive reality (SPR) condition on an operator arising in the algorithm. Speed of convergence experiments show that the OBRF algorithm converges more quickly than the related output error algorithm for the hyperstable adaptive recursive filter (HARF), although the OBRF algorithm converges as quickly as typical equation error schemes. The OBRF is shown to compare favorably with equation error with respect to parameter bias in the presence of output measurement noise. Thus, OBRF is a compromise between the equation error and output error approaches. In addition, algorithm parameter selection to satisfy the SPR condition for OBRF is explored and compared with the related conditions for HARF     

New adaptive complex IIR filters and their application in OFDM systems

In this article, very low sensitivity variable complex filter (VCF) sections are developed. They have two important advantages: extremely low passband sensitivity and independent tuning of the bandwidth and the central frequency over a wide frequency range. The first advantage provides resistance to quantization effects, while the second one gives a better digital signal processing quality and extends the area of possible applications of the developed filters. Based on the proposed VCF sections an adaptive complex system is designed which demonstrates very fast convergence and low computational complexity. This system is applied for narrowband interference cancellation in multiband orthogonal frequency division multiplexing receivers and wideband noise cancellation in OFDM receivers. It is experimentally verified that a better signal-to-noise ratio and signal-to-interference ratio can be achieved using the proposed adaptive complex filtering scheme.     

Sufficient stability bounds for slowly varying direct-formrecursive linear filters and their applications in adaptive IIR filters

This article derives a sufficient time-varying bound on the maximum variation of the coefficients of an exponentially stable time-varying direct-form homogeneous linear recursive filter. The stability bound is less conservative than all previously derived bounds for time-varying IIR systems. The bound is then applied to control the step size of output-error adaptive IIR filters to achieve bounded-input bounded-output (BIBO) stability of the adaptive filter. Experimental results that demonstrate the good stability characteristics of the resulting algorithms are included. This article also contains comparisons with other competing output-error adaptive IIR filters. The results indicate that the stabilized method possesses better convergence behavior than other competing techniques     

A CONFIGURATION FOR REALIZATION OF THE MULTICHANNEL AND HIGH-ORDER IIR ADAPTIVE FILTERS

This paper develops a new hyperstable adaptive algorithm which can be used inthe multichannel ⅡR conflguration and/or the high-order ⅡR or zero-pole configuration for jointprocess estimation.     

Globally convergent blind source separation based on a multiuser kurtosis maximization criterion

We consider the problem of recovering blindly (i.e., without the use of training sequences) a number of independent and identically distributed source (user) signals that are transmitted simultaneously through a linear instantaneous mixing channel. The received signals are, hence, corrupted by interuser interference (IUI), and we can model them as the outputs of a linear multiple-input-multiple-output (MIMO) memoryless system. Assuming the transmitted signals to be mutually independent, i.i.d., and to share the same non-Gaussian distribution, a set of necessary and sufficient conditions for the perfect blind recovery (up to scalar phase ambiguities) of all the signals exists and involves the kurtosis as well as the covariance of the output signals. We focus on a straightforward blind constrained criterion stemming from these conditions. From this criterion, we derive an adaptive algorithm for blind source separation, which we call the multiuser kurtosis (MUK) algorithm. At each iteration, the algorithm combines a stochastic gradient update and a Gram-Schmidt orthogonalization procedure in order to satisfy the criterion's whiteness constraints. A performance analysis of its stationary points reveals that the MUK algorithm is free of any stable undesired local stationary points for any number of sources; hence, it is globally convergent to a setting that recovers them all.     

Design and discrete re-optimisation of all-pass based powersymmetric IIR filters

Tools are presented which enable the practitioner to efficiently design all-pass based, highly selective low-pass power symmetric-infinite impulse response (PS-IIR) filters which are well suited for sub-band decomposition in applications such as multirate acoustic echo cancellation (MAEC)     

Design of two-channel linear-phase QMF banks based on real IIR all-pass filters

The design of two-channel linear-phase quadrature mirror filter (QMF) banks constructed by real infinite impulse response (IIR) digital all-pass filters is considered. The design problem is appropriately formulated to result in a simple optimisation problem. Using a variant of Karmarkar's algorithm, the optimisation problem can be efficiently solved through a frequency sampling and iterative approximation method to find the real coefficients for the IIR digital all-pass filters. The resulting two-channel QMF banks possess an approximately linear phase response without magnitude distortion. The effectiveness of the proposed technique is achieved by forming an appropriate Chebyshev approximation of the desired phase response and then finding its solution from a linear subspace in a few iterations. Finally, several simulation examples are presented for illustration and comparison     

Derivation of an adaptive algorithm for IIR digital systems realized by power-wave digital filters

This paper presents a new efficient algorithm for adjusting the coefficients of an adaptive infinite impulse response power-wave digital filter in order to estimate the discrete-time signal y(k) as the recursively filtered version of the signalx(k). To do this, eight different prediction errors are defined which can be computed recursively with respect to model order and time, which leads to similar recursions as for the lattice algorithm [1], where autoregressive processes are considered. These recursions can be implemented as a digital filter which can be separated in ananalysis and asynthesis part, where the latter can be interpreted as a power-wave digital filter [2], [3], [13]. Hence, the stability of this adaptive network is always guaranteed [4]. Furthermore, it is shown that the proposed algorithm can be considered as an extension of the Levinson algorithm [7] for the efficient inversion of a special class of matrices.     

On fast FIR filters implemented as tail-canceling IIR filters

We have developed an algorithm based on synthetic division for deriving the transfer function that cancels the tail of a given arbitrary rational (IIR) transfer function after a desired number of time steps. Our method applies to transfer functions with repeated poles, whereas previous methods of tail-subtraction cannot. We use a parallel state-variable technique with periodic refreshing to induce finite memory in order to prevent accumulation of quantization error in cases where the given transfer function has unstable modes. We present two methods for designing linear-phase truncated IIR (TIIR) filters based on antiphase filters. We explore finite-register effects for unstable modes and provide bounds on the maximum TIIR filter length. In particular, we show that for unstable systems, the available dynamic range of the registers must be three times that of the data. Considerable computational savings over conventional FIR filters are attainable for a given specification of linear-phase filter. We provide examples of filter design. We show how to generate finite-length polynomial impulse responses using TIIR filters. We list some applications of TIIR filters, including uses in digital audio and an algorithm for efficiently implementing Kay's optimal high-resolution frequency estimator     

Design of IIR digital filters using complex allpass network based on eigenvalue problem

A new design method is presented for complementary IIR digital filters with given magnitude specifications based on the eigenvalue problem, which are composed of a single complex allpass section.<>     

Realization of IIR LDM digital filters

A method is presented of realizing an infinite impulse response (IIR) digital filter (DF) using linear delta modulation (LDM) as a simple analog/digital (A/D) converter. This method makes the realization of IIR digital filters much simpler than that of conventional ones because it does not require hardware multipliers or a pulse code modulation (PCM) A/D converter. Compared to the finite impulse response (FIR) LDMDF, this IIR LDMDF requires significantly less computation time