SYNTHESIS OF LOW-SENSITIVITY ORTHOGONAL DIGITAL-FILTERS

A novel method is proposed for the synthesis of low-sensitivity digita l filters meeting any prescribed transfer function. The method is base d on extracting an orthogonal matrix from the filter state matrix, res ulting in structures that need n Givens rotations and at most n + 1 mu ltipliers. Thus the proposed realization is canonic in the sense that it has the same degrees of freedom as the original transfer function. It is also shown that when the filter transfer function is a reciproca l reactant bounded function, it can be decomposed into allpass functio ns that need only Givens rotations for their realization. As the basic module in the realization is the Givens rotation, the CORDIC computat ion algorithm can be applied directly. This means considerable savings in computation time and complexity. It also results in structures tha t are less sensitive to the effects of finite word length. Illustrativ e examples, including the design and synthesis of linear phase selecti ve filters, are given to show the extremely low sensitivity with respe ct to finite word length of the resulting realizations when compared w ith other methods. (C) 1997 by John Wiley & Sons, Ltd.