L2 Approximation Error Evaluation for the Inverse of Mixing-Phase Systems and Channel Equalization Applications

The inverse system approximation using the finite impulse responses (FIR) and the corresponding model-order determination are essential to a broad area of signal processing applications such as seismic data processing, communication equalization, acoustic echo cancelation, plant control, etc. To the best of our knowledge, there exists no explicit formulation of the exact mean-square approximation error for the truncated inverse filters. Therefore, in this paper, we derive the exact L₂ approximation error function with respect to the model orders for the truncated inverse filter using an FIR. Our newly derived L₂ approximation error evaluation can be employed for the communication or signal processing system design involving the inverse filtering in the future.