In this letter, an effective acoustic feedback cancellation algorithm is proposed based on the normalized sub-band adaptive filter (NSAF). To improve the confliction between fast convergence rate and low misalignment in the NSAF algorithm, a variable step size is designed to automatically vary according to the update state of the filter. The update state of the filter is adaptively detected via the normalized distance between the long term average and the short term average of the tap-weight vector. Simulation results demonstrate that the proposed algorithm has superior performance in terms of convergence rate and misalignment.

This paper is about a new efficient method for the implementation of a Block Proportionate Normalized Least Mean Square (BPNLMS++) adaptive filter using the Fermat Number Transform (FNT) and its inverse (IFNT). These transforms present advantages compared to Fast Fourier Transform (FFT) and the inverse (IFFT). An efficient state space method for implementing the FNT over rectangular windows is used in the cases where there is a large overlap between the consecutive input signals. This is called Generalized Sliding Fermat Number Transform (GSFNT) and is useful for reducing the computational complexity of finite ring convolvers and correlators. In this contribution, we propose, as a first objective, an efficient state algorithm with the purpose of reducing the complexity of IFNT. This algorithm, called Inverse Generalized Sliding Fermat Number Transform (IGSFNT), uses the technique of Generalized Sliding associated to matricial calculation in the Galois Field. The second objective is to realize an implementation of the BPNLMS++ adaptive filter using GSFNT and IGSFNT, which can significantly reduce the computation complexity of the filter implantation on digital signal processors.

Regularization plays a fundamental role in adaptive filtering. There are, very likely, many different ways to regularize an adaptive filter. In this letter, we propose one possible way to do it based on a condition that makes intuitively sense. From this condition, we show how to regularize the recursive least-squares (RLS) algorithm.

We present a new structure for parallel affine projection (AP) filters with different step-sizes. By observing their error signals, the proposed alternating AP (A-AP) filter selects one of the two AP filters and updates the weights of the selected filter for each iteration. As a result, the total computations required for the proposed structure is almost the same as that for a single AP filter. Experimental results show that the proposed alternating selection scheme extracts the best properties of each component filter, namely fast convergence and small steady-state error.

This paper is about an efficient implementation of adaptive filtering for echo cancelers. The first objective of this paper is to propose a simplified method of the flexible block Multi-Delay Filter (MDF) algorithm in the time-domain. Then, we will derive a new method for the step-size adaptation coefficient. The second objective is about the realization of a Block Proportionate Normalized Least Mean Squares (BPNLMS++) with the simplified MDF (SMDF) implementation. Using the new step-size method and the smaller block dimension proposed by SMDF, we achieve a faster convergence of the adaptive process with a limited computational cost. Then, an efficient implementation of the new procedure (SMDF-BPNLMS++) block filtering is proposed using Fermat Number Transform, which can significantly reduce the computation complexity of filter implantation on Digital Signal Processor.

A new class of least-squares algorithms is presented for adaptive filtering. The idea is to use a fixed set of directions and perform line search with one direction at a time in a cyclic fashion. These algorithms are called Euclidean Direction Search (EDS) algorithms. The fast version of this class is called the Fast-EDS or FEDS algorithm. It is shown to have O(N) computational complexity and a convergence rate comparable to that of the RLS algorithm. Computer simulations are presented to illustrate the performance of the new algorithm.

This paper describes the outline of the active noise control system and the adaptive signal processing used in the practical systems. Focus is on the adaptive signal processing and algorithms which are widely used in many applications. Some variations in the algorithms for improving the control effect and for reducing the amount of calculation are also shown. Additionally, the limitations and some design guide are shown with the results of the numerical simulations.

In this paper, a new set of difference equations is derived for transient analysis of the convergence of adaptive FIR filters using the Sign-Sign Algorithm with Gaussian reference input and additive Gaussian noise. The analysis is based on the assumption that the tap weights are jointly Gaussian distributed. Residual mean squared error after convergence and simpler approximate difference equations are further developed. Results of experiment exhibit good agreement between theoretically calculated convergence and that of simulation for a wide range of parameter values of adaptive filters.

This paper proposes a fast implementation technique for RLS adaptive filters. The technique has an adjustable parameter to trade the throughput and the rate of convergence of the filter according to the applications. The conventional methods for improving the throughput do not have this kind of adjustability so that the proposed technique will expand the area of applications for the RLS algorithm. We show that the improvement of the throughput can be easily achieved by rearranging the formula of the RLS algorithm and that there are no need for faster PEs for the improvement.

Event-related are the kind of signals that are time-related to a given event. In this work, we will study the effect of bias and overlapping noise on Fourier linear combiner (FLC)-based filters, and its implication on filtering event-related signals. We found that the bias alters the weights behaviour, and therefore the filter output, and we discuss solutions to the problem of spectral overlap.

In this paper stochastic aradient adaptive filters using the Sign or Sign-Sign Algorithm are analyzed based upon general assumptions on the reference signal, additive noise and particularly jointly distributed tap errors. A set of difference equations for calculating the convergence process of the mean and covariance of the tap errors is derived with integrals involving characteristic function and its derivative of the tap error distribution. Examples of echo canceller convergence with jointly Gaussian distributed tap errors show an excellent agreement between the empirical results and the theory.

In this letter, we introduce a predictor based least square (PLS) algorithm. By involving both order- and time-update recursions, the PLS algorithm is found to have a more stable performance compared with the stable version (Version II) of the RLS algorithm shown in Ref.[1]. Nevertheless, the computational requirement is about 50% of that of the RLS algorithm. As an application, the PLS algorithm can be applied to the fast Newton transversal filters (FNTF). The FNTF algorithms suffer from the numerical instability problem if the quantities used for extending the gain vector are computed by using the fast RLS algorithms. By combing the PLS and the FNTF algorithms, we obtain a much more stable performance and a simple algorithm formulation.

This paper presents a new structure for noise and echo cancelers based on a combined fast abaptive algorithm. The main purpose of the new structure is to detect both the double-talk and the unknown path change. This goal is accomplished by using two adaptive filters. A main adaptive filter Fn, adjusted only in the non-double-talk period by the normalized LMS algorithm, is used for providing the canceler output. An auxiliary adaptive filter Ff, adjusted by the fast RLS algorithm, is used for detecting the double-talk and obtaining a near optimum tap-weight vector for Fn in the initialization period and whenever the unknown path has a sudden or fast change. The proposed structure is examined through computer simulation on a noise cancellation problem. Good cancellation performance and stable operation are obtained when signal is a speech corrupted by a white noise, a colored noise and another speech signal. Simulation results also show that the proposed structure is capable of distinguishing the near-end signal from the noise path change and quickly tracking this change.

An adaptive joint-process IIR filter with generalized lattice structure is constructed. This filter can borrow both FIR and IIR features and simultaneously holds the well-known merits of lattice structure.

A new gradient type adaptive algorithm is proposed in this paper. It is formulated based on the least squares criteria while the conventional gradient algorithms are based on the least mean square criteria. The proposed algorithm has two variable parameters and by changing them we can adjust the characteristic of the algorithm from the RLS to the LMS depending on the environment. This capability of adjustment achieves the possibility of providing better solutions. However, not only it provides better solutions than the conventional algorithms under some conditions but also it provides a very interesting theoretical view point. It provides a unified view point of the adaptive algorithms including the conventional ones, i.e., the LMS or the RLS, as limited cases and it enables us to analyze the bounds for those algorithms.

This paper proposes a new combined fast algorithm for transversal adaptive filters. The fast transversal filter (FTF) algorithm and the normalized LMS (NLMS) are combined in the following way. In the initialization period, the FTF is used to obtain fast convergence. After converging, the algorithm is switched to the NLMS algorithm because the FTF cannot be used for a long time due to its numerical instability. Nonstationary environment, that is, time varying unknown system for instance, is classified into three categories: slow time varying, fast time varying and sudden time varying systems. The NLMS algorithm is applied to the first situation. In the latter two cases, however, the NLMS algorithm cannot provide a good performance. So, the FTF algorithm is selected. Switching between the two algorithms is automatically controlled by using the difference of the MSE sequence. If the difference exceeds a threshold, then the FTF is selected. Other wise, the NLMS is selected. Compared with the RLS algorithm, the proposed combined algorithm needs less computation, while maintaining the same performance. Furthermore, compared with the FTF algorithm, it provides numerically stable operation.

In case of the system identification problem, such as an echo canceller, estimated impulse response obtained by the frequency-domain adaptive filter based on the circular convolution has estimation error because the unknown system is based on the linear convolution in the time domain. In this correspondence, we consider a sufficient condition to reduce the estimation error.