Quantization effects in high-speed pipelined recursive filters

An exploration is made of roundoff and quantization errors in pipelined high-speed recursive filters, implemented using look-ahead computation and a two's complement number system. These errors are theoretically estimated for a first-order recursive filter, for both decomposed and nondecomposed implementations. The maximum total roundoff error in decomposed scattered look-ahead filters is shown to be less than that in the nondecomposed scattered look-ahead filters. Further, the quantization error in decomposed filters is less when poles are closer to origin (as compared with nondecomposed ones). Experimental results are presented for a sixth-order Butterworth and a fourth-order Chebyshev low-pass filter. High speed can also be obtained by using redundant arithmetic in standard filter structures. These filters may suffer from reduced dynamic range and degraded finite word-length effects. Experimental results for such implementations are presented.