Closed-loop performance of an active noise reduction (ANR) headset is limited by phase lag. Speaker dynamics, control hardware, and acoustic wave propagation from the control speaker to the error microphone all contribute to this phase lag. Understanding these sources of phase lag and their relative effects on performance allows for better design of an analog or digital ANR headset.

This thesis demonstrates that the three most significant sources of phase lag in a digital ANR headset are the dynamics of the control speaker's diaphragm, the anti-aliasing filter, and the smoothing filter. Additionally, it is demonstrated that the acoustic wave propagation from the control speaker to the error microphone is not a major contributor of phase lag. Based on these results, it was determined that attention should be focused on the anti-aliasing and smoothing filters when attempting to minimize phase lag and improve a digital ANR system's performance.

A design procedure was developed to calculate filter responses that contributed a minimal amount of phase lag to a headset. Using this minimal phase filter design procedure, a digital ANR headset was successfully built and tested. Initial testing revealed that the anti-aliasing filter was not as vital to performance as the smoothing filter. Further testing indicated that the anti-aliasing requirements could be effectively met through the use of only a smoothing filter. Therefore, in order to minimize the phase lag of a digital ANR headset, a smoothing filter may be utilized in the absence of an anti-aliasing filter for some applications.