Inverse filtering in a single or in multiple channels arises as a problem in a number of applications in the areas of communications, active control, sound reproduction and virtual acoustic imaging. In the single-channel case, when the plant C(z) sought to be inverted has zeros outside the unit circle in the z-plane, an approximation to the inverse 1/C(z) can be realized with an FIR filter if an appropriate amount of modeling delay is introduced to the system. But the closer the zeros of C(z) are to unit circle (either inside or outside it), the longer the FIR inverse has to be, typically several tens of times longer than the plant. An off-line implementation utilizing a variant of the backward-in-time filtering technique usually associated with zero-phase FIR filtering is presented. This forms the basis on which a single-channel mixed phase plant can be inverted with an IIR filter of order roughly double than that of C(z), thus decimating the processing time required for the inverse filtering computation.
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