FIR filters with sigma-delta modulation encoding

Two methods are presented for building FIR (finite impulse response) digital filters where either the impulse response or the input signal is encoded using sigma-delta modulation. For each method, both single-loop and two-stage sigma-delta modulation are used for encoding. These systems are operated at a sampling rate higher than the Nyquist rate of the signal, and their performance depends on the oversampling ratio. Except in the decoding circuit, these filters require no multiplication and hence can be built using simple hardware. An analysis of the systems is provided and examples for filters realized using these approaches are given.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>