A feedback canceller or an echo canceller is a system that eliminates, as much as possible, the output of a system from re-entering its input. In the case of an audio system having a microphone, an audio processing unit and a speaker (or any other audio transducer), it is known that the output signal can leave the speaker and come back to the input microphone by means of a physical acoustic path. This physical path where the output sound waves can propagate back to the input of the system is usually referred as “acoustic feedback path”.
The reentrant signal can be perceived as an echo if the feedback path delay is long and the gain is low. This is usually the case of telecommunication systems such as speakerphones. The system used to reduce such artifact is usually known as echo canceller.
If the feedback delay is shorter, but the loop gain is greater than one, it may cause a sustained oscillation. This is usually the case of hearing aids and amplified mic/headset pairs. It is perceived as a loud whistle, which forces the user to remove the apparatus from his/her ears. It can also be perceived as a ringing artifact if the oscillation gets attenuated. The system used to reduce such artifacts is usually known as feedback canceller.
Both echo canceller and feedback canceller are usually implemented as an adaptive system, whose goal is to match the system response of the acoustic feedback path. If the acoustic feedback path can be estimated, the feedback signal can also be estimated by supplying it with the output of the system.
When an acoustic feedback control system is stimulated with a sinusoidal signal from the environment in an adaptive digital filter, the adaptive algorithm will correlate the output of the filter with the feedback signal and with the stimulus signal itself. This will cause a degraded response to the feedback signal. This phenomenon is called “entrainment” as the feedback canceller gets entrained by the stimulus signal. It happens with signals that have high autocorrelation between samples, such as sinusoidal signals and other periodic signals.
The entrainment causes several effects upon the performance of the feedback canceller:                a. Entrainment degrades the estimate of the feedback signal, because its response gets distracted to the auto-correlated signal input. Therefore, the system has decreased feedback cancellation.        b. Entrainment causes attenuation of the input stimulus signal.        c. Entrainment increases the instability of the system. Once the periodic input stimulus is removed, the entrained system might immediately act as a feedback generator itself, which can cause sustained oscillation. This condition can get worse the longer the periodic input signal is allowed to stimulate the system, as the coefficients of some filter designs can grow indefinitely.        d. Entrainment degrades the response of a longer digital filter. Under entrainment, the longer the digital filter, the worse its response because the smaller coefficients at the tail of the filter are more sensitive to get mistuned by the entraining input signal.        
What is needed in the art is an improved system for avoiding or containing entrainment of digital filter designs. The system should be straightforward to implement in a variety of applications.