Second-order Infinite Impulse Response Notch Research Articles

A robust feedforward hybrid active noise control system with online secondary‐path modelling

In this study, a robust feedforward hybrid active noise control (ANC) system with online secondary-path modelling (SPM) is proposed that is capable of not only effectively suppressing the broadband and narrowband noise components but also tracking the secondary path (SP) variations. An finite impulse response online SPM subsystem as well as an efficient decoupling filter are included in the proposed feedforward hybrid ANC (HANC) system. The decoupling filter is a parallel-form bandpass filter bank that consists of multiple bandpass filters that are derived from the second-order infinite impulse response notch filters. It takes the residual noise as its input and separates the broadband component from the narrowband component, with the former used as not only a desired signal for the SPM but also as an error signal for updating the broadband sub-controller, whereas the latter adapted simultaneously to scale the auxiliary white Gaussian noise and to update the narrowband sub-controller. Extensive simulations are conducted with both the synthetic and real SPs as well as the synthetic and real noise signals that are generated by a large-scale factory cutting machine (strand-cutter) to demonstrate the advantages and effectiveness of the proposed feedforward HANC system. Comparisons are also demonstrated with the original HANC system as well as its directly extended version with an online SPM subsystem.

Closed-form unbiased frequency estimation of a noisy sinusoid using notch filters

In this note, the problem of the frequency estimation of a sinusoid embedded in white noise is considered. The approach used herein is the minimization of the sample variance of the output of constrained notch filters fed by the noisy sinusoid. In particular, this note focuses on closed-form expressions of the frequency estimate, which can be obtained using notch filters having an all-zeros finite-impulse response (FIR) structure. The results presented in this note are as follows: 1) it is shown that the FIR notch filters obtained from standard second-order infinite-impulse response (IIR) filters are inadequate; 2) a new second-order IIR notch filter is proposed, which provides an unbiased estimate of the frequency; 3) the FIR filter obtained from the new IIR filter provides a closed-form unbiased frequency estimate; and 4) the closed-form frequency estimate obtained using the new FIR notch filter asymptotically converges toward the Pisarenko harmonic decomposition estimator and the Yule-Walker estimator.

An adaptive on-line sensor for roll eccentricity measurement and control

This paper is concerned with the problem of roll eccentricity compensation in steel strip rolling mills. A new roll eccentricity sensor is proposed for the task of retrieving the desired reference signal from the available roll force measurement. The sensor implements a modified comb filter structure which can be arranged in either tunable or adaptive form. The comb filter structure consists of a number of second-order infinite impulse response notch filter modules. Error surface analysis is carried out for the adaptive comb filter. Results from this analysis confirms that convergence is guaranteed provided that the initial frequency estimate is selected within the unimodal region. Such a condition is easily satisfied in practice since the fundamental frequency is related to the roll speed. Simulation results based on typical experimental data clearly indicate that the proposed sensor is appropriate and offers distinct advantages over other methods. The final roll eccentricity compensator is based on this new sensor and the functional units making up the complete compensation system are discussed in some detail within the paper.

Tunable/adaptive second-order IIR notch filter

ABSTRACT A modified second-order infinite impulse response (IIR) notch filter with constrained poles and zeros is presented to eliminate or retrieve sinusoids embedded in a broadband signal. Such a filter is ideally suited to either parallel or cascaded implementation. Two classes of problems are considered. The first is where the sinusoidal frequencies are known a priori. For this case a straightforward design procedure based on a set of design characteristic graphs is used to select tunable notch filter parameters. An interesting property of the notch filter model is that it can be converted to a line enhancer by interchanging the position of the poles and zeros. The second type of problem arises when the sinusoidal frequencies are unknown and possibly varying with time. This means that an adaptive solution is required and an important consideration is the parameter estimation accuracy. For this purpose, the paper derives the Cramer–Rao lower bound for the adaptive cascaded notch filter using a frequenc...