Optimal Synthesis of Second-Order State-Space Structures for Digital Filters
Date of Original Version
Sufficient conditions are derived for a second-order state-space digital filter with L2 scaling to be optimal with respect to output roundoff noise; and from these, a simple synthesis procedure is developed. Parallel-form designs produced by this method are equivalent to the block-optimal designs of Mullis and Roberts. The corresponding cascade-form designs are not equivalent, but they are shown, by example, to be quite close in performance. It is also shown that the coefficient sensitivities of this structure are closely related to its noise performance. Hence, the optimal design has low-coefficient sensitivity properties and any other low-sensitivity design is a good candidate for near-optimal noise performance. The uniform-grid structure of Rader and Gold is an interesting and useful case in point. © 1979 IEEE
IEEE Transactions on Circuits and Systems
Jackson, Leland B., Allen G. Lindgren, and Kim Young. "Optimal Synthesis of Second-Order State-Space Structures for Digital Filters." IEEE Transactions on Circuits and Systems 26, 3 (1979): 149-153. doi:10.1109/TCS.1979.1084623.