Yegui Xiao

Analysis of Online Secondary-Path Modeling With Auxiliary Noise Scaled by Residual Noise Signal

Online secondary-path modeling of active noise control (ANC) systems may be effectively implemented by injecting an auxiliary white noise whose magnitude is scaled by a function of residual noise signal. In this paper, a filtered-X LMS (FXLMS) based narrowband ANC system is analyzed, whose online secondary-path modeling is based on the use of an auxiliary white noise scaled by one-sample-delayed residual noise signal. Difference equations governing the dynamics of the entire system and closed-form expressions for steady-state mean-square errors (MSE) as well as the residual noise power are derived and discussed in detail. Extensive simulations are conducted to confirm the validity of the analytical findings.

Stochastic Analysis of the FXLMS-Based Narrowband Active Noise Control System

Noise signals generated by rotating machines such as diesel engines, cutting machines, fans, etc., may be modeled as noisy sinusoidal signals which can be successfully suppressed by narrowband active noise control (ANC) systems. In this paper, statistical performance of such a conventional filtered-x LMS (FXLMS)-based narrowband ANC system is investigated in detail. First, difference equations governing the dynamics of the system are derived in terms of convergence of the mean and mean squared estimation errors for the discrete Fourier coefficients (DFCs) of the secondary source. Steady-state expressions for DFC estimation mean square error (MSE) as well as the residual noise power are then developed in closed forms. A stability bound for the FXLMS in the mean sense is also derived. Extensive simulations of various scenarios are performed to demonstrate the validity of the analytical findings.

A New Robust Narrowband Active Noise Control System in the Presence of Frequency Mismatch

Narrowband active noise control (ANC) systems have many real-life applications where the noise signals generated by rotating machines are modeled as sinusoidal signals in additive noise. However, when the timing signal sensor, such as a tachometer used to identify the signal frequencies, and the cosine wave generator contain errors, the frequencies of reference sinusoids fed to each ANC channel will then be different from the real primary noise signal frequencies. This difference is referred to as frequency mismatch (FM). In this paper, through extensive simulations, we first demonstrate that the performance capabilities of a conventional parallel form narrowband ANC system using the filtered-x LMS (FxLMS) algorithm degrades significantly even for an FM as small as 1 %. Convergence of the algorithm in the mean sense is also analytically investigated for a better understanding of its performance degradation. Next, we propose a new narrowband ANC system that successfully compensates for the performance degradations due to the FM. The amplitude/phase adjustment of reference sinusoids and the FM mitigations in the proposed system are performed simultaneously in a harmonic fashion such that the influence of the FM can be removed almost completely. Simulations as well as application to a real noise signal are provided to demonstrate the effectiveness of the proposed new system

A Variable Step-Size FXLMS Algorithm for Narrowband Active Noise Control

In this paper, a variable step-size filtered-x LMS (VSS-FXLMS) algorithm is proposed for a typical narrowband active noise control system. The new algorithm converges much faster than the conventional FXLMS algorithm does, and indicates a convergence rate quite similar to that of the filtered-x recursive least square (FXRLS) algorithm in stationary noise environments. It also considerably outperforms these two existing algorithms in nonstationary situations. The proposed algorithm requires some more computations as compared with the FXLMS algorithm; however, its computational complexity is significantly less than that of the FXRLS algorithm. Numerous simulations for stationary and nonstationary scenarios are conducted to demonstrate the superior performance of the proposed VSS-FXLMS algorithm as compared with the FXLMS and the FXRLS algorithms.

Properties of FXLMS-Based Narrowband Active Noise Control With Online Secondary-Path Modeling

Rotating machines such as diesel engines, cutting machines, fans, motors, etc., generate sinusoidal noise signals that may be effectively reduced by narrowband active noise control (ANC) systems. In this paper, a typical filtered-X LMS (FXLMS) based narrowband ANC system equipped with an online secondary-path modeling subsystem is analyzed in detail. First, difference equations governing the dynamics of the FXLMS algorithm for secondary source synthesis and the LMS algorithm for secondary-path estimation are derived in terms of convergence in both mean and mean square. Steady-state expressions for mean-square error (MSE) as well as the residual noise power are then developed in closed form. Extensive simulations are performed to demonstrate the validity of the analytical results.

A New Constructive Procedure for 2-D Coprime Realization in Fornasini–Marchesini Model

This paper presents a new constructive procedure for coprime realization of 2-D systems by means of the Fornasini-Marchesini second (FM-II) local state-space model. By exploiting the structural properties of an FM-II model realization, the proposed method can reduce the upper bound on the realization order for a large class of 2-D systems to about half of that obtained by the realization procedure given by the authors recently. It is also revealed that the new procedure is able to obtain minimal realizations for a much larger class of 2-D systems than the existing methods. Nontrivial examples are presented to illustrate the basic ideas and the effectiveness of the proposed method.

Tracking properties of a gradient-based second-order adaptive IIR notch filter with constrained poles and zeros

Gradient-type adaptive IIR notch filters have many attractive merits for various real-life applications since they require a small number of computations and yet demonstrate practical performance. However, it is generally quite difficult to assess their performance analytically. Their tracking properties, in particular, have not yet been investigated. In this paper, the tracking performance of a plain gradient (PG) algorithm is analyzed in detail for a second-order adaptive IIR notch filter with constrained poles and zeros, which takes a linear chirp signal as its input. First, two sets of difference equations for the frequency tracking error and mean square error (MSE) are established in the sense of convergence in the mean and convergence in the mean square, respectively. Closed-form expressions for the asymptotic tracking error and MSE are then derived from these difference equations. An optimum step-size parameter for the algorithm is also evaluated based on the minimization of the asymptotic tracking error or the tracking MSE. It is discovered that the asymptotic tracking error may be driven to zero for a positive chirp rate by selecting a proper step size, which is an interesting property for a real-valued adaptive filtering algorithm. Extensive simulations are performed to support the analytical findings.

A New Efficient Narrowband Active Noise Control System and its Performance Analysis

A new narrowband ANC system structure is proposed which requires only two reference signal filtering (x-filtering) blocks regardless of the number of targeted frequencies. The reference cosine or sine waves are combined, respectively, to form an input to an x-filtering block. The output of each x-filtering block is decomposed into filtered-x cosine or sine waves by a special bandpass filter bank. In this way, the computational cost of the system may be significantly reduced. Analysis of the new system is then provided and discussed in some detail. Analytical results reveal that the proposed system performs quite the same as its counterpart does while requiring considerably fewer multiplications. Modification to the proposed structure is also made to cope with the frequency mismatch (FM) in real-life applications. Extensive simulations are conducted to demonstrate the effectiveness of the proposed system and its modified version, and as well as to confirm the validity of analysis.

A new LMS-based Fourier analyzer in the presence of frequency mismatch and applications

The performance of the conventional least mean square (LMS) Fourier analyzer may degenerate significantly, if the signal frequencies given to the analyzer are different from the true signal frequencies. This difference is referred to as frequency mismatch (FM). We first analyze the performance of the conventional LMS Fourier analyzer for a single sinusoid in the presence of FM. We derive the dynamics and steady-state properties of this analyzer as well as the optimum step size parameter which minimizes the influence of the FM. Extensive simulations reveal the validity of the analytical results. Next, a new LMS-based Fourier analyzer is proposed which simultaneously estimates the discrete Fourier coefficients (DFCs) and accommodates the FM. This new analyzer can very well compensate for the performance degeneration due to the FM. Applications to estimation/detection of dual-tone multiple frequencies (DTMF) signals and analysis of real-life noise signals generated by a large-scale factory cutting machine are provided to demonstrate the excellent performance of our new Fourier analyzer.

Statistical performance of the memoryless nonlinear gradient algorithm for the constrained adaptive IIR notch filter

Gradient-type algorithms for the adaptive infinite-impulse response (IIR) notch filters are very attractive in terms of both performance and computational requirements for various real-life applications. This paper presents, in detail, a statistical analysis of the memoryless nonlinear gradient (MNG) algorithm applied to the well-known second-order adaptive IIR notch filter with constrained poles and zeros. This analysis is based on a proper use of Taylor series expansion and nonlinearization of output signals of the notch and gradient filters. Two difference equations are derived first for the convergence in the mean and mean square senses, respectively. Two closed-form expressions, one for the steady-state estimation bias and the other for the mean-square error, are then derived based on the difference equations, with the former valid for both fast and slow adaptations and the latter valid for slow adaptation only. A closed-form coarse stability bound for the step size parameter of the algorithm is also derived. Extensive simulations are performed to reveal the validity and limitations of the analytical findings. Comparisons between the MNG and the conventional plain gradient algorithm are also made.