The DXHS algorithm is equivalent to a passive internal model for sinusoidal signals

The DXHS algorithm was proposed as an active noise control method and is often referred to as an adaptive method. This paper shows that the DXHS algorithm is a dynamical system that is equivalent to a passive internal model for sinusoidal signals. It follows that the disturbance attenuation ability is a consequence of the internal model principle, although the DXHS algorithm is proposed based on the standard way of thinking for adaptive methods. Moreover, the closed-loop system stability is guaranteed for strictly passive secondary paths.