A narrowband active noise control system with reference synthesis

Abstract

Most active noise control (ANC) algorithms require a model of the secondary path (SP). If there are large changes in the SP, online SP modeling algorithms may not be able to follow the changes quickly enough to prevent divergence. In this work, the mirror-MFxLMS (MMFxLMS) is adapted to narrowband ANC, and the resulting algorithm is analyzed. The MMFxLMS is an algorithm similar to the MFxLMS and FxLMS but has online SP modeling; it is stable for any SP estimate and does not require auxiliary noise. In addition, a technique to alternate between MFxLMS and MMFxLMS is proposed, resulting in the M 3 FxLMS algorithm, which does not sacrifice performance and assures stability. However, the M 3 FxLMS requires a reference signal that is not available in feedback ANC.Feedback ANC is important in many practical cases, for instance, in ANC headphones. To solve this problem, a technique is proposed to synthesize a reference formed by a sum of sinusoids using measurements from the error sensor signal.This technique uses the fast Fourier transform to obtain estimates of the harmonic frequencies of the periodic noise components, and then refines and tracks these using a phase-locked loop (PLL). The resulting algorithm enables a stable ANC system, even under large and sudden changes in the SP. The proposed PLL is also new and has a lock-in range equal to the full band of the system. KEYWORDS active noise control (ANC), feedback, FxLMS, narrowband, PLL, stability INTRODUCTIONActive noise control (ANC) is a technique where waves (antinoise) with opposite phase to a noise signal are used to reduce the noise signal level. 1 In feedforward ANC, a signal called the reference signal is used to generate the antinoise signal, using additional information from a set of error sensors that indicates the residual noise level. In feedback ANC, the signal from a set of error sensors is used to generate the antinoise signal. In narrowband ANC, the noise to be canceled is assumed to be periodic or a sum of periodic signals. This paper addresses single-channel (one error sensor) narrowband feedback ANC, with applications, for instance, in ANC headphones.Most ANC algorithms require a secondary path (SP) model and can become unstable if that model is not sufficiently accurate. The SP model can be obtained before the start of noise canceling (offline) or during operation (online). If the SP changes significantly during noise cancelation, online SP modeling is required. However, even with online SP modeling, if there is a large and sudden change, the model may not be updated quickly enough and the algorithm may become unstable. To solve this problem, the authors have previously proposed the mirror-MFxLMS (MMFxLMS) algorithm. 2 1118

A survey on active noise control in the past decade—Part I: Linear systems

“…A novel mirror-FxLMS algorithm was proposed in [259], which is based on the algorithm in [245] and can guarantee stability without an auxiliary signal to online estimate secondary path. Such an algorithm can switch between the modified FxLMS (MoFxLMS) and mirror-modified FxLMS (MMoFxLMS) algorithms according to the absolute value of their weight coefficients 5 .…”

Frequency domain analysis of the mirror‐modified filtered‐x least mean squares algorithm with low ambient noise

“…First, a digital phase locked loop (PLL) is used to determine reference signal fundamental and harmonic in‐phase and quadrature components, namely the reference signals complex amplitudes . This PLL can be implemented using a noisy reference signal or even the error signal as in Reference 25. Then the signals are split into blocks of M samples.…”

“…For every instance of the LMS algorithm, (for instance ) replace it by the its frequency domain approximate equivalent (resulting in ). Note, that, for small step sizes, the LMS algorithm can be approximated by the Block LMS (BLMS) algorithm and that this can be implemented in the frequency domains as stated in Reference 25. The step sizes are calculated using the new signals.…”

“…21 Recently, improvements have been proposed for narrowband systems. 22,23 The authors have previously proposed the mirror-modified FxLMS (MMFxLMS) algorithm 24,25 for feedforward ANC, which is a variant of the FxLMS 10 and modified FxLMS (MFxLMS) 26 with online secondary path modeling that cannot diverge due to secondary path modeling errors. The MMFxLMS algorithm residual error is low, even though it may have incorrect secondary path models.…”

An analysis of the convergence condition for narrowband FxLMS

“…The noise produced by the transformer or the rotating machines such as engines, helicopters, motors, and so forth, can be considered as periodic and deterministic noises [1]. The narrowband active noise control (NANC) system equipped with the narrowband filteredx LMS (NFxLMS) algorithm is found to be effective in reducing such noises [2,3]. The stability analysis of the NFxLMS, which is mainly aimed at estimating the upper bound for the step size, that is μ max , can be performed in the time domain [4][5][6] or in the Z-domain [7][8][9][10][11].…”