Recently, it became possible to detect single motor units (MUs) noninvasively via the use of spatial filtering electrode arrays. With these arrays, weighted combinations of monopolar electrode signals recorded from the skin surface provide spatial selectivity of the underlying electrical activity. Common spatial filters include the bipolar electrode, the longitude double differentiating (LDD) filter and the normal double differentiating (NDD) filter. In general, the spatial filtering is implemented in hardware and the performance of the spatial filtering apparatus is measured by its common mode rejection ratio (CMRR). High precision hardware differential amplifiers are used to perform the channel weighting in order to achieve high CMRR. But, this hardware is expensive and all channel weightings must be predetermined. Hence, only a few spatially filtered channels are typically derived. In this project, a distinct software equalization filter was cascaded with each of the hardware monopolar signal conditioning circuits to achieve accurate weighting and high CMRR. The simplest technique we explored was to design an equalization filter by dividing the frequency response of a“reference" (or“ideal") channel by the measured frequency response of the channel being equalized, producing the desired equalization filter in the frequency domain (conventional technique). Simulation and experimental results showed that the conventional technique is very sensitive to broadband background noise, producing poor CMRR. Thus, a technique for signal denoising that is based on signal mixing was pursued and evaluated both in simulation and laboratory experiments. The purpose of the mixing technique is to eliminate the noise as much as possible prior to equalization filter design. The simulation results show that without software equalization, CMRR is only around 30 dB; with conventional technique CMRR is around 50~60 dB. By using mixing technique, CMRR can be around 70~80 dB.

<p>In many practical multi-channel active sound control (ASC) applications, such as active noise control (ANC), various constraints need to be satisfied, such as the robust stability constraint, noise amplification constraint, controller output power constraints, etc. One way to enforce these constraints is to add a regularization term to the Wiener filter formulation, which, by tuning only a single parameter, can over-satisfy many constraints and degrade the ANC performance. Another approach for non-adaptive ANC filter design that can produce better ANC performance is to directly solve the constrained optimization problem formulated based on the <em>H</em>₂/<em>H</em>_inf control framework. However, such a formulation does not result in a convex optimization problem and its practicality can be limited by the significant computation time required in the solving process. In this dissertation, the traditional <em>H</em>₂/<em>H</em>_inf formulation is convexified and a global minimum is guaranteed. It is then further reformulated into a cone programming formulation and simplified by exploiting the problem structure in its dual form to obtain a more numerically efficient and stable formulation. A warmstarting strategy is also proposed to further reduce the required iterations. Results show that, compared with the traditional methods, the proposed method is more reliable and the computation time can be reduced from the order of days to seconds. When the acoustic feedback path is not strong enough to cause instability, then only constraints that prevent noise amplification outside the desired noise control band are needed. A singular vector filtering method is proposed to maintain satisfactory noise control performance in the desired noise reduction bands while mitigating noise amplification.</p> <p><br></p> <p>The proposed convex conic formulation can be used for a wide range of ASC applications. For example, the improvement in numerical efficiency and stability makes it possible to apply the proposed method to adaptive ANC filter design. Results also show that compared with the conventional constrained adaptive ANC method (leaky FxLMS), the proposed method can achieve a faster convergence rate and better steady-state noise control performance. The proposed conic method can also be used to design the room equalization filter for sound field reproduction and the hear-through filter design for earphones.</p> <p><br></p> <p>Besides efficient filter design methods, efficient filter implementation methods are also developed to reduce real-time computations in implementing designed control filters. A polyphase-structure-based filter design and implementation method is developed for ANC systems that can reduce the computation load for high sampling rate real-time filter implementation but does not introduce an additional time delay. Results show that, compared with various traditional low sampling rate implementations, the proposed method can significantly improve the noise control performance. Compared with the non-polyphase high-sampling rate method, the real-time computations that increase with the sampling rate are improved from quadratically to linearly. Another efficient filter implementation method is to use the infinite impulse response (IIR) filter structure instead of the finite impulse response (FIR) filter structure. A stable IIR filter design approach that does not need the computation and relocation of poles is improved to be applicable in the ANC applications. The result demonstrated that the proposed method can achieve better fitting accuracy and noise control performance in high-order applications.</p>