Causality study on a feedforward active noise control headset with different noise coming directions in free field

A systematic analysis is proposed to predict the performance of a typical feedforward single channel ANC headset in terms of the delay, especially the non-causal delay caused by different noise coming directions. First, the performance of a non-causal feedforward system for a band-limited noise is analyzed by using a simplified pure delay model, where it is found that the noise reduction bandwidth is narrowed and the maximum noise reduction is decreased with the increase of the non-causal delay. Second, a systematic method is developed, which can be used to predict the system performance with measured primary and secondary path transfer functions in most practical sound fields and to study the effects of the control filter length and the path delay on the performance. Then, the causality of a typical feedforward active noise control headset with the primary source at 0° and 90° positions in an anechoic chamber is analyzed, and the performance for the two locations predicted by the systematic analysis is shown in good agreements with the experiment results. Finally, an experiment of a typical feedforward active noise control headset in a reverberation chamber is carried out, which shows the validity of the proposed systematic analysis for other more practical sound fields.