Multiplierless signal processors using table look-ups and residue arithmetic

New algorithms for computing convolutions and other multiplicative intensive signal processing functions are presented. These algorithms use squaring operations and additions but not two-operand multiplications. The squared law algorithms presented are extensions of the quarter squared and the one-over eight squared algorithms, and they are more powerful and more hardware efficient than them. They are appropriate for modular and residue arithmetic and rely on ROM lookup tables for computing the squaring operations. Since the ROM performing the squaring operation is at the heart of the new techniques, the author presents some memory compression schemes for minimizing the size of such lookup table ROMs.<>