A Novel Implementation for Narrow-Band FIR Digital Filters

In the cascade realization of fixed-point digital filters underdynamic range constraints, the output noise due to accumulation ofroundoff errors is highly dependent upon the order of the sections.For recursive filters it also depends on the pole—zero pairing that formsthe individual second-order sections. The output noise may vary overseveral orders of magnitude for different cascade realizations of high-order filters. Therefore an optimization procedure to fmd a good order-ing and pairing is very desirable.We propose a heuristic optimization procedure for finding a "nearoptimal" solution. The procedure is completely automatic and doesnot require any knowledgeable judgment. The number of functionevaluations required for a filter of N-cascaded sections is proportionalto N2. By using this procedure, "near optimal" solutions have beenfound for a 22nd-order recursive filter in 23 s, and for a 55th-ordernonrecursive filter in 37.5s, on an IBM 360-91 computer. Manuscript received May 14, 1974; revised December 30, 1974 andMarch 17, 1975. This work was supported by the Air Force Office ofScientific Research, United States Air Force, under Grant AF-AFOSR71-2101.The authors are with the Department of Electrical Engineering, Prince-ton University, Princeton, N.J. 08540.