A Computationally Efficient Frequency-Domain Filtered-X LMS Algorithm for Virtual Microphone

The computational complexity of the virtual FXLMS algorithm is higher than that of the conventional FXLMS algorithm. The additional complexity comes from computation of three secondary path transfer functions (as opposed to one) and a transfer function between the physical and the virtual microphones. The order of these transfer functions may be very high in practical situations where the acoustic damping is low. The high computational complexity of the virtual FXLMS algorithm imposes issues like high power consumption, making it difficult to implement the algorithm in battery operated ANC devices such as active headsets. In addition, the operating sampling frequency of the algorithm is limited and this in turn restricts its operation to relatively low frequency applications. In this paper, a new virtual FXLMS algorithm is derived by implementing all of the secondary path transfer functions in the frequency domain. The algorithm is simulated using measured transfer functions in a duct with low acoustic damping. Implementation schemes are proposed for the new frequency-domain virtual FXLMS algorithm, citing its advantages for use as an efficient real-time active noise control algorithm.