Increasing the speed and saving multipliers in block parallel digital filters by a linear transformation

The linear transformation of flow graph matrices of block parallel digital filters can be applied to increase the speed of operation and to reduce the number of multipliers. To this aim we introduce a convenient matrix representation of block parallel digital filters and explain the transformation. As an example a second order block parallel filter with arbitrary block length L is generated which has the same high speed as an equivalent block-state space filter, but a multiplier complexity linear in block length L instead of square. For L=3 the number of multipliers is reduced by 32% compared with the block-state space filter and for L=6 by 26% compared with the structure proposed by Parhi