Minimal structures for symmetric FIR filters of arbitrary length

It is shown that, even in the very basic direct-form symmetric FIR (finite impulse response) filter structure, redundancy exists in terms of additive complexity. Methods for removing it are presented. A conventional direct-form implementation of an L-tap symmetric FIR filter requires L/2 or (L+1)/2 multiplications, L-1 additions, and L-1 delay units. The symmetry is exploited in such a way that the number of additions is significantly reduced, while the number of multiplications and the memory requirement remain the same. It is shown that the additive complexity can be reduced nearly to L/2. A complete solution is provided, for any L , to the derivation of the filter structure that requires the minimal number of additions, L/2 or (L+1)/2 multiplications, and L-1 delay units. Thus a new class of structures and algorithms for symmetric FIR filters is obtained