Permuted difference coefficient realization of FIR digital filters

A new realization for FIR digital filters, using permuted difference coefficients, is proposed in this paper. Its coefficients are obtained as the difference between the successive values of the original coefficients reordered in a sequence with falling magnitude. The proposed realization can hold desirable properties in FIR filters, such as an exactly linear phase characteristic and stable implementation, and is effectively applied to a wide range filter response. Quantization error analysis shows that the internal data word lengths must be somewhat increased to maintain the same roundoff noise as in a direct form realization. Computational complexity becomes about 23 percent and 18 percent for 99th- and 299th-order filters, taking the excess data word lengths into account, compared with the direct form.