I have developed the hardware for an acoustic Active Noise Reduction module. The module accepts a microphone input which drives a DSP (ADAU1772 by Analog Devices), then drives a speaker. The idea is that the software in the DSP applies an inverse transfer function of the microphone and speaker combined, so as to present a 180 degree phase shifted sound out of the speaker, which cancels the input sound to the microphone. I have a basic profile that works, but it is limited in the fact that the phase of the mechanical system starts at 0 degrees out of phase at low frequencies and extends to about 360 degrees out of phase at 2kHz. To develop an inverse DSP transfer function would mean a phase lead filter or something along those lines where the phase lag is the most at low frequencies. I realize the mechanical system is not exactly minimum phase, so an exact solution is not needed. Given that I am not trying to go against causality, I am happy for the system to lag behind an acoustic cycle or 2, I just need a filter that provides 360 degrees phase lag at low frequencies and then very little phase lag at 2kHz. The aim is that this filter be implemented using a bi-quad IIR arrangement, or group of bi-quad IIRs within the Analog Devices Sigma Studio software environment, to be used on an ADAU1772 DSP.
Please let me know if you are interested.