One of the problems associated with adaptive FIR filters in the identification of systems with long impulse responses, is their excessive computational complexity. Recently a new kind of adaptive filters, based on three-level clipping of the input signal has been presented for reduction of their computational complexity. In this paper, a theoretical analysis of the steady-state misalignment of adaptive filter equipped with the LMS algorithm, based on three-level clipping, is presented and by using it the minimum mean square error is achieved. This analysis can be a basis in the design of the above mentioned filters with appropriate clipping levels and proper step-sizes for system identification applications.

Keywords: Adaptive Filter, Convergence Rate, Misalignment, Three-level Clipping, Weight Update

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