A multi-input multi-output adaptive FIR filter with guaranteed convergence for feedforward ANC system

In this paper, a multi-input multi-output adaptive FIR filter with guaranteed convergence is designed for application in feedforward active noise control system. First, the existence of multi-input multi-output FIR filter for secondary path equalization is discussed. Second, update equation of this FIR filter is derived according to the LMS algorithm. Next, we derive an upper bound on the step size of the update equation which can ensure the convergence of the mean of the coefficients of this adaptive FIR filter. Based on this upper bound, step size can be chosen such that this adaptive FIR filter can achieve the fastest convergence. A feedforward multiple points active noise control system is then constructed by adopting our proposed step size. Simulation results show that our system can remove the effect of secondary paths and achieve superb low-frequency noise reduction