Deconvolution of Non-Minimum Phase FIR Systems Using Adaptive Filtering

We address, in this paper, the problem of estimating the input sequence of a known, non-minimum phase, FIR system, when a large number of its roots are located near or on the unit circle. This issue cannot be solved by conventional methods known to date. Recently, algorithms based on spectral factorization are considered as possible solutions of inversing nonminimum phase systems but, these techniques cannot prohibit the instability of the systems whose roots are located on the unit circle. We propose an alternative method based on adaptive filtering resulted from a new point of view of the deconvolution problem that avoids inversing the system. The LMS adaptive filter is used to meet our objective while faster implementation than optimization-based techniques, be it gradient based or genetic, is achieved. Moreover, the technique is validated by experimental results, in simulated cases, which are mainly focused on large sequence of signals in noisy conditions.