The well-known broadband active noise control (BANC) system using an FIR filter usually works well when the primary and reference noise signals are periodic in nature. This paper investigates the mean convergence of weight errors of the BANC system in the presence of multiple harmonic excitation. Difference equations governing the mean convergence of the system are derived and discussed in detail. The obtained analytical results enrich our understanding of the BANC operated in an environment with multiple sinusoids. Extensive simulations are conducted to support the analytical findings.
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.
In real sound environment system, a specific signal shows various types of probability distribution, and the observation data are usually contaminated by a background noise of nonGaussian distribution type. Furthermore, there potentially exist various nonlinear correlations in addition to the liner correlation between input and output time series. Consequently, often the system input and output relationship in the actual phenomenon cannot be represented by a simple model using only the linear correlation and lower order statistics. In this study, complex sound environment systems difficult to analyze by using usual structural method is considered. By introducing an estimation method of the system parameters reflecting correlation information for conditional probability distribution under existence of the background noise, a prediction method of output response probability for sound environment systems is theoretically proposed in a suitable form for the additive property of energy variable and the evaluation in decibel scale. The effectiveness of the proposed method is experimentally confirmed by applying it to the observed data in the sound environment.
In a conventional narrowband active noise control system, each reference cosine wave has to be filtered by an estimate of the secondary-path. We call this part x-filtering block. The number of x-filtering blocks is equal to the number of targeted frequencies. The computational cost of the system due to the x-filtering operations may form a bottleneck in real system implementation. In this paper, we propose a new narrowband ANC system structure which requires only one xfiltering block regardless of q. All the cosine waves are combined as an input to a x-filtering block whose output is decomposed by an efficient bandpass filter bank into filtered cosine waves for the FXLMS that follows. As a result, the computaional cost of the system is considerably reduced. The new structure is further implanted in a recently developed ANC system that is capable of mitigating the frequency mismatch (FM). Simulations demonstrate that the new systems present robust performance very similar to that of their counterparts, but enjoy considerable advantages in system implementation.
In a typical conventional narrowband active noise control (ANC) system, each reference (cosine or sine) wave is filtered by an FIR secondary-path estimate called x-filtering block. The number of x-filtering blocks is twice of the number of targeted frequencies (q), which may pose a bottleneck in system implementation. In this paper, we propose new efficient and robust narrowband ANC systems. An IIR-type feedforward secondary-path compensator is newly introduced in front of the loudspeaker, whose inverse is an FIR minimum phase part of the secondary-path estimate. The remaining FIR nonminimum phase part is used as the x-filtering block whose length may be much shorter. To further reduce the complexity, we use a special bandpass filter bank to decrease the number of x-filtering blocks. As a result, the new systems only require, regardless of q, two (2) x-filtering blocks whose order may be significantly smaller than that of the secondary-path estimate. Modification to the new systems is also made to achieve robustness with respect to the frequency mismatch (FM) between the reference and primary signal frequencies. Extensive simulations reveal that the new systems and their modified versions work almost as well as the conventional system does, and are capable of mitigating the influence of the FM, while enjoy tremendous computational advantage.
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