An adaptive quarter-wave tube that uses the sliding-Goertzel algorithm for estimation of phase

This paper describes an adaptive quarter wave tube used to attenuate a tone from the exhaust noise of a large diesel engine. A sliding-Goertzel algorithm was used to calculate the phase angle of the transfer function between a microphone in the adaptive quarter wave tube and in the main exhaust duct. The control system adjusted the length of the adaptive quarter wave tube until the phase angle was −90° and caused the sound pressure level at the cylinder firing frequency in the exhaust duct to be minimized. The system was able to adapt to changes in engine speed, exhaust gas temperature, and load applied to the engine. The results demonstrate that the sliding-Goertzel algorithm can be used effectively to estimate the phase angle in an adaptive–passive acoustic control system.