| As an environmental problem, acoustic noise pollution has garnered significant atten-tion worldwide. The traditional passive noise control techniques can effectively suppresshigh-frequency acoustic noises in a wide frequency band, and they have excellent high-frequency characteristics. However, they are ineffective or powerless in suppressing thosenoises with low frequency. In contrast with the passive noise control approaches, activenoise control (ANC) techniques have excellent low-frequency characteristic, which isideal for suppressing low-frequency harmonic acoustic noises. Harmonic acoustic noisesare usually generated by rotating machines and devices with reciprocating motion. Sincethe energy of harmonic acoustic noises concentrates at specific frequencies, they are akind of typical and common narrowband noises. In ANC field, the system used for atten-uating narrowband noises is the so-called narrowband ANC system. The developmentsof society and economy require more industrial, transportation, and other equipments.Such requirement directly results in a more serious noise pollution problem, which can-not be ignored. The narrowband ANC system has garnered significant attention for itseffectiveness in reducing low-frequency narrowband noises.To obtain insightful expressions that significantly enhance and enrich our understand-ing of the narrowband ANC system behavior, we have to execute in-depth and detailedanalysis on the performance of the system. On the other hand, in-depth and detailed anal-ysis will provide us theoretical foundation and guidance for further modifying the system.On the basis of statistical least mean square (LMS) theory, this dissertation investigatesperformances of narrowband ANC system based on the filtered - X LMS (FXLMS) algo-rithm in detail and in depth. The so-called performance analysis here means statistical orstochastic analysis of the system, that is, we statistically analyze the convergence and evensteady-state performance of the algorithm. The main contributions of this dissertation areconcluded in order as follows:(1) For a narrowband feedforward ANC system with online secondary-path modeling,system-self-excitation setup is an effective approach to be used to reduce the in?uenceof the auxiliary noise signal on the performance of the system. However, so far, themechanism that leads to a system's performance improvement using self-excitation is not clear, and the corresponding analytical and theoretical explanations are still missing.With such a system whose performance is improved by using self-excitation being tar-geted, we established the difference equations governing performance of the system interms of estimation errors of the control filter weights. After deriving the difference equa-tions through applying statistics and modern signal processing theories, we analyticallyinvestigated dynamics and steady-state performance of the system in detail and in depth.We finally provided theoretical proofs and explanations for the system's performance im-provement caused by self-excitation and figured out the key factors which in?uence suchperformance.(2) In a narrowband feedforward ANC system, the nonacoustic sensor or the referencesignal generator usually contains errors, which will result in frequencies of the referencesignal that are not identical to the frequencies of the primary noise. That is, frequencymismatch (FM) may exist between the reference signal and primary noise. If the FM,even it is very small, exists in the system, the narrowband noises being targeted couldnot be reduced effectively. With the consideration that there is no physical realization ofcomplex operations in real-life applications where multi-tone noise is usually contained,this dissertation provides statistical analysis of the narrowband feedforward ANC systemin presence of small FM as well as containing multi tones in the real and time domains.We preliminary investigated the in?uence of the FM on the performance of the narrow-band feedforward ANC system in the mean sense. Stability bounds and the relationshipsbetween such bounds and the FM were also provided.(3) When a feedback ANC system is used to cancel narrowband noise, there will beno FM since the reference signal is synthesized internally. The feedback ANC systemis of less robustness in comparison to the feedforward system. However, the feedbacksystem has been applied widely for its relatively simple control algorithm and compactstructure. The feedback structure equipped in a feedback ANC system makes it difficult toinvestigate the performance of the system. With the inspirations obtained from the aboveideas and analytical techniques applied to investigate the narrowband feedforward ANCsystems, this dissertation provides performance analysis of the feedback ANC system fornarrowband noises cancellation in depth from a new viewpoint. We developed the internalrelationships of discrete Fourier coefficients (DFCs) among signals in the system and con-sequently obtained the steady-state characteristics of the control filter weights. With such preliminary analytical results, we established the difference equations based on the con-trol filter weights themselves. Using statistics and modern signal processing theories, werecursively derived the difference equations, and then analytically investigated dynamicsof the feedback ANC system being targeted in detail.(4) To verify the effectiveness of self-excitation in improving the performance of thefeedforward narrowband ANC system, we designed a one-dimensional tube as the exper-imental system in this dissertation. Based on high-speed digital signal processor (DSP),the narrowband feedforward ANC system with self excitation was implemented and rep-resentative experiments of low-frequency narrowband noises cancellation in the tube wereconducted. Our experiments included single-tone and double-tone noise cancellation.The experimental results proofs the capability of the feedforward narrowband ANC sys-tem in suppressing narrowband noises, and it can be effectively promoted by using self-excitation.
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