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On the complexity reduction of polyphase linear phase FIR filters with symmetric coefficient implementation

The multiple constant multiplication (MCM) implementation of polyphase decomposed finite impulse response (FIR) filters can be formulated as (1) one MCM block with all coefficients, (2) one MCM block for each subfilter, or (3) as a matrix MCM block. The coefficient symmetry of linear phase FIR filters, however, is not exploited in the later two formulations. In this paper, we investigate the MCM implementation of polyphase structures with coefficient symmetry, where each subfilter MCM block is synthesized separately. We show that by using the proposed implementation it is possible to reduce the number of adders compared with currently existing methods without increasing the storage elements. The proposed techniques can also be extended to the matrix MCM block implementation.