Pipelined Wave Digital Filter design for narrow-band sharp-transition digital filters

The finite word-length effects in most IIR digital filters can be improved by realizing the transfer function in terms of a cascade or parallel arrangement of second order filter sections instead of a direct-form realization. However, for narrow-band sharp-transition filters, we still have large roundoff noise problems even with second order sections. In this case, the WDF (Wave Digital Filter) can be a good solution. Although the WDFs can be pipelined by the cut-set localization procedure, the maximum sample rate cannot be increased by this technique due to the presence of the feedback loops in the WDFs. In this paper, a pipelined WDF design method for narrow-band sharp transition filters is proposed. The pipelining method is based on the DIFIR (Decomposed and Interpolated FIR) method, where an IIR filter with M-times wider transition bandwidth (compared with the original specification) is cascaded with log₂ M FIR filters which have very wide transition bandwidths. The new IIR filter produces much smaller noise. In addition, the new IIR transfer function satisfies the pipelining property which can be used in high speed or low power applications