A new multiplication scheme is proposed, for application to single multiplier CMOS based DSP processors, for the implementation of low-power digital FIR filters through the reduction of switching activity within the multiplier section of the filter. The scheme operates in conjunction with a transpose direct form FIR filter structure and a modified DSP processor architecture, through a significant reduction in power can be obtained by using algorithms to order the filter coefficients. This reduction is demonstrated using two basic examples, with different wordlengths and filter orders, achieving up to 63% reduction in switching activity.