Low-noise implementation technique for pipelined filters with crowded poles

Scattered look-ahead pipelining method can be efficiently used for high sample rate or low-power applications of digital recursive filters. Although the pipelined filters are guaranteed to be stable by this method, these filters suffer from large roundoff noise when the poles are crowded within some critical regions. To avoid this problem, a low-noise implementation technique is proposed. This method is based on the roundoff noise analysis of pipelined recursive filters and a constrained filter design approach using constrained Remez exchange algorithm. By the constrained filter design approach, the desired filter spectrum is satisfied while some of the pole angles are constrained to avoid pole crowding within critical regions. In addition, the constrained poles satisfy pipelining property without pole-zero cancellation, which leads to very hardware efficient design.