In this paper we propose a method for implementation of sum-of-products using a shifted permuted difference coefficient method. Here we focus on implementation of FIR filters but the method is generally applicable to computation of sum-of-products. In this work we identify two fundamental blocks in the difference coefficient structure, a permutation network and an adder network. The former determine how the difference coefficients are selected while the latter computes the differences. We also propose that the differences are computed on odd, integer coefficients only. The proposed method is fast and yields filter implementations with low arithmetic complexity. This makes it a good candidate for being incorporated into the search for quantized coefficients in the synthesis of FIR filters.