Multiplierless FIR filters with discrete-value sigma-delta encoded coefficients

The authors present an oversampled sigma-delta modulation based encoding scheme to reduce an FIR (finite impulse response) filter´s coefficient or input signal samples to values with only a few nonzero bits, eliminating the need for multiplications. This scheme realizes a substantial reduction in sample rate and additions over previous differential digital coding schemes by replacing the direct truncation within a sigma-delta modulator with a more sophisticated quantizing procedure which truncates to the next nearest canonic signed-digit code (number representable as sum of difference of a few powers-of-two). Computer simulations are used to demonstrate and verify the expected performance of this scheme, and comparisons are made with previously reported results. The proposed scheme offered a 64-times improvement in the sample rate required to implement the filter without increasing the hardware complexity