Jean Jiang

Adaptive Volterra filters for active control of nonlinear noise processes

This paper presents a Volterra filtered-X least mean square (LMS) algorithm for feedforward active noise control. The research has demonstrated that linear active noise control (ANC) systems can be successfully applied to reduce the broadband noise and narrowband noise, specifically, such linear ANC systems are very efficient in reduction of low-frequency noise. However, in some situations, the noise that comes from a dynamic system may he a nonlinear and deterministic noise process rather than a stochastic, white, or tonal noise process, and the primary noise at the canceling point may exhibit nonlinear distortion. Furthermore, the secondary path estimate in the ANC system, which denotes the transfer function between the secondary source (secondary speaker) and the error microphone, may have nonminimum phase, and hence, the causality constraint is violated. If such situations exist, the linear ANC system will suffer performance degradation. An implementation of a Volterra filtered-X LMS (VFXLMS) algorithm based on a multichannel structure is described for feedforward active noise control. Numerical simulation results show that the developed algorithm achieves performance improvement over the standard filtered-X LMS algorithm for the following two situations: (1) the reference noise is a nonlinear noise process, and at the same time, the secondary path estimate is of nonminimum phase; (2) the primary path exhibits the nonlinear behavior. In addition, the developed VFXLMS algorithm can also be employed as an alternative in the case where the standard filtered-X LMS algorithm does not perform well.

Pole-Radius-Varying IIR Notch Filter With Transient Suppression

In this paper, a new IIR notch filter with transient suppression is proposed. The proposed algorithm utilizes a varying pole radius to significantly reduce the transient effect when eliminating a sinusoidal interference in signal enhancement. Based on a time-varying linear difference equation, the analytical solution to a sinusoidal interference is found. With a given tolerance of the transient disturbance, a scheme is derived to predict the duration of the transient response and to determine the damping parameter used for changing the pole radius. Computer simulations demonstrate that the developed pole-radius-varying IIR notch filter significantly outperforms the traditional IIR notch filter.

Adaptive second-order Volterra filtered-X RLS algorithms with sequential and partial updates for nonlinear active noise control

In this paper, we propose adaptive second-order Volterra filtered-X recursive least square (RLS) algorithms using sequential and partial updates for nonlinear active noise control. Recent research advancement has demonstrated that nonlinear active control is feasible for applications where the noise to be controlled may be a nonlinear and deterministic noise process such as chaotic noise rather than a stochastic, or white or tonal noise process, and both primary and secondary paths in an active noise control (ANC) system may exhibit a nonlinear behavior. To accommodate nonlinear active noise control, the standard second-order Volterra filtered-X recursive least square (VFXRLS) or least mean square (VFXLMS) algorithms are usually applied. The second-order VFXRLS algorithm offers fast convergence performance but suffers a huge computational burden. On the other hand, the standard second-order VFXLMS algorithm requires less computational complexity but behaves at a slow convergence rate. The proposed second-order VFXRLS algorithms with sequential and partial updates could significantly reduce the computational complexity required by the standard second-order VFXRLS algorithm with a compromised performance.

An adaptive technique for modeling second-order Volterra systems with sparse kernels

This paper proposes a simple technique for modeling second-order Volterra systems using an adaptive second-order Volterra delay filter (ASOVDF). The developed filter structure essentially extends an adaptive FIR delay filter to include linear and quadratic filter coefficients with an input assumed to be a zero-mean i.i.d. sequence with a symmetric distribution. The implementation of the ASOVDF is based on a stage-by-stage modeling process. At each stage, a dominant delay element is determined, the corresponding adaptive filter coefficient is incorporated to the adaptive filter coefficients from previous stages, and then these filter coefficients are adapted via the recursive least-squares algorithm. The ASOVDF requires few filter coefficients and has better performance and less computational complexity over the conventional adaptive second-order Volterra filter (ASOVF) in modeling second-order Volterra systems with sparse kernels.

Nonlinear active noise control using diagonal-channel LMS and RLS bilinear filters

This paper proposes an adaptive bilinear filter with a diagonal-channel structure for nonlinear active noise control. Based on the diagonal-channel structure, the diagonal-channel bilinear filtered-X least mean square (DBFXLMS) and recursive least square (DBFXRLS) algorithms are derived. In order to reduce the computational load for the DBFXRLS algorithm, the DBFXRLS algorithm with a sequential channel update (DBFXRLS-SEQ) is proposed. Computational complexity for each algorithm is examined. Computer simulations demonstrate the control performance improvement using the proposed algorithms.

An adaptive technique for determining a reduced model for a system

A reduced or sparse system model is discussed that will contain only the most significant components, as opposed to a complete finite impulse response (FIR) model which may not be very accurate with the requirement of only a few components. The technique presented uses an adaptive delay filter to provide the sparse model and compares it to the model obtained with the standard adaptive filter. >

Adaptive Harmonic IIR Notch Filters for Frequency Estimation and Tracking

In many signal processing applications, adaptive frequency estimation and tracking of noisy narrowband signals is often required in communications, radar, sonar, controls, biomedical signal processing, and the applications such as detection of a noisy sinusoidal signal and cancellation of periodic signals. In order to achieve the objective of frequency tracking and estimation, an adaptive finite impulse response (FIR) filter or an adaptive infinite impulse response (IIR) notch filter is generally applied. Although an adaptive FIR filter has the stability advantage over an adaptive IIR notch filter, it requires a larger number of filter coefficients. In practical situations, an adaptive IIR notch filter (Chicharo & Ng, 1990; Kwan & Martin, 1989; Nehorai, 1985) is preferred due to its less number of filter coefficients and hence less computational complexity. More importantly, a second-order adaptive pole/zero constrained IIR notch filter (Xiao et al, 2001; Zhou & Li, 2004) can effectively be applied to track a single sinusoidal signal. If a signal contains multiple frequency components, then we can estimate and track its frequencies using a higher-order adaptive IIR notch filter constructed by cascading second-order adaptive IIR notch filters (Kwan & Martin, 1989). To ensure the global minimum convergence, the filter algorithm must begin with initial conditions, which require prior knowledge of the signal frequencies. However, in many practical situations, a sinusoidal signal may be subjected to nonlinear effects (Tan & Jiang, 2009a, 2009b) in which possible harmonic frequency components are generated. For example, the signal acquired from a sensor may undergo saturation through an amplifier. In such an environment, we may want to estimate and track the signal’s fundamental frequency as well as any harmonic frequencies. Using a second-order adaptive IIR notch filter to estimate fundamental and harmonic frequencies is insufficient, since it only accommodates one frequency component. On the other hand, applying a higher-order IIR notch filter may not be effective due to adopting multiple adaptive filter coefficients and local minimum convergence of the adaptive algorithm. In addition, monitoring the global minimum using a grid search method requires a huge number of computations, and thus makes the notch filter impractical in real time processing. Therefore, in this chapter, we propose and investigate a novel adaptive harmonic IIR notch filter with a single adaptive coefficient to efficiently perform frequency estimation and tracking in a harmonic frequency environment.

Seismic phase detection and discrimination using adaptive filter coefficients

The authors present an approach to the detection and discrimination of seismic phases using multichannel data. When a seismic event (such as an earthquake or man-made explosion) occurs, the signal propagating from the source has several distinct phases which have varying propagation velocities and frequency content. By detecting and correctly identifying these phases one can estimate the distance between source and receiver. The detection algorithm considered consists of an adaptive correlation enhancer and a sliding window detector that make the detector insensitive to changes in the background noise level. The discrimination algorithm uses the adaptive correlation enhancers weights as input discriminants to a neural net.<<ETX>>

System modeling using a second-order Volterra delay filter

In this paper, we extend the linear delay filter, which is a technique for modeling sparse FIR systems, to a second-order Volterra delay filter to include the linear and quadratic filter coefficients for system modeling and identification. According to the error surface analysis, we propose two algorithms which are specially effective in modeling second-order Volterra systems with sparse system coefficients.

Complex system modeling using a complex delay filter

The adaptive delay filter is generalized to include complex coefficients with a complex input signal for complex system modeling. Based on the error surface analysis, two new algorithms to determine the determinant terms of an unknown complex system have been developed and successfully applied to identify complex FIR models. The techniques are especially effective for modeling sparse systems.<<ETX>>