ELIMINATION OF LIMIT-CYCLES IN DIRECT FORM DIGITAL-FILTERS USING ERROR FEEDBACK

The elimination of zero-input limit cycles in direct form filter secti ons using either a rounding or a magnitude truncation fixed-point quan tizer is considered. The well-known criterion of Chang is reformulated for second-order filter sections in a more practical form using the b ilinear transformation. This enables graphical interpretation and quan titative analysis of the possible error feedback solutions for differe nt pole locations. The synthesis of limit-cycle-free error feedback fo r second-order filter sections is addressed in detail and several solu tions are proposed. The error feedback coefficients are constrained to power-of-two values or to symmetric values so that the implementation is efficient, e.g. with signal processors. Different limit-cycle-free solutions are discussed with design examples and their round-off nois e properties are compared. The absence of limit cycles is related to t he round-off noise properties of the filter section. The main conclusi on of the paper is that when the EF coefficients are appropriately cho sen, low round-off noise and the absence of limit cycles can always be accomplished at the same time. A particularly close correlation betwe en limit cycles and round-off noise is demonstrated with a rounding qu antizer: a limit-cycle-free implementation always guarantees low round -off noise. For most complex conjugate pole locations the converse rel ation also holds, i.e. low round-off noise implies the absence of limi t cycles.