GRANULAR LIMIT-CYCLES OF L,-SCALED SECOND-ORDER ALL-PASS SECTIONS
Max Gerken · 1992
Digital Filters implemented by means of all-pass sections are useful in various applications. In this work the gran- ular limit-cycles of three second-order d-pass structures are in- vestigated. Two of them are well-known two-port wave digital all-pass filters and the third is a combination of a two-port adap- tor and a direct form structure. When implementing a complex conjugate pole pair, this third structure has the nice property of being optimally scaled in the L,-sense with no regard to the coefficient values. It is proved that the considered structures are free of granular limit-cycles for coefficients with absolute value lower than one half and two's-complement rounding. For coef- ficient values out of this range, the limit-cycle amplitudes are compared by means of measurements. The third structure is briefly compared to the other two with respect to round-off noise and forced-response stability.