On the Solution of the Recurrent Equation Used for the FIR-Filter Implementation

V.V. Myasnikov (Russia)


Signal processing, recursive filtering, fast algorithms


The algorithm used for approximation of the 1-D finite impulse response (FIR) of the linear filter by the recurrent equation is proposed. The recurrent equation is used for the recursive implementation of the FIR-filtering of the signal. The proposed algorithm gives the direct quasi-optimal solution of the approximation task with the mean-square criteria. Namely, it gives the recurrent equation parameters, which include the order of the recurrent equation, its coefficients and its starting values. Algorithm uses the covariance function of the FIR for estimation of the recurrent equation coefficients. The starting values of the recurrent equation are calculated as the solution of the linear equation system. Experimental results of the proposed algorithm are given. They show the dependence of the deviation between the optimal solution and the solution obtained via the proposed algorithm on the impulse response length. Presented results cause the conculsions, formed as the propositions. They show the optimal behaviors of the solution obtained via the proposed algorithm.

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