Active noise cancellation in headphones by digital robust feedback control

Abstract

Active Noise Cancellation (ANC) may complement passive insulation of headphones by actively cancelling low frequency components of acoustical background noise. In systems with a single error microphone pointing towards the ear canal, a feedback controller performs the compensation task. We are focusing on fixed feedback controllers for broadband attenuation of arbitrary ambient noise. We use methods and optimization routines from control theory. In this discipline the key element is the so-called controller, which is in terms of signal processing a (digital) filter. The controller is designed by an optimization approach called the mixed-sensitivity H ∞ synthesis, which requires an accurate estimate of the secondary path between the cancelling loudspeaker and the error microphone, and the knowledge of the secondary path uncertainties as well as a specification of the closed-loop sensitivity. The advantage of this method is the convenient formulation of performance and uncertainty requirements in the frequency domain. We describe the design process and evaluate the controller, which is realized in state space form, within a real-time system. The real-time measurements show a good match with the expected behavior. They furthermore confirm the feasibility of broadband attenuation by fixed i.e. time invariant feedback controllers in a digital system. The novelty of this contribution comprises of the specific design process of a discrete robust feedback controller for broadband noise reduction (roughly 250 Hz) and the digital real-time system implementation.