Circulant and skew-circulant matrices as new normal-form realization of IIR digital filters - Circuits and Systems, IEEE Transactions on

Normal-form fixed-point state-space realizations of IIR filters are known to be free from both overflow oscillations and roundoff limit cycles, provided magnitude truncation type of arithmetic is used together with two’s complement overflow features. The eigenvalues of the state transition matrix have low sensitivity. In this paper two new normal-form realizations are presented which utilize circulant and skew-circulant matrices as their state transition matrices. The advantage of these realizations is that the A -matrix has only N (rather than N 2 ) distinct elements, and is amenable to efficient memory-oriented implementation. The problem of scaling the internal signals in these structures is addressed and an approximate solution can be obtained through a numerical optimization method. Several numerical examples are included.