Use of transversal-recursive structures for efficient realization of low-noise digital filters with decimated output

For fixed-point realizations of narrow-band digital filters, the normal form is significantly less sensitive to roundoff error than either parallel or cascade direct forms. However, the normal form requires more multipliers. This disadvantage can be overcome in filters with decimated output by the use of nonminimal transversal-recursive structures derived from the normal form. These structures can reduce the required multiplication rates to values below those required for direct form realizations while, at the same time, further reducing round-off noise. In addition, these structures will not support overflow limit cycles and will either suppress or reduce the amplitude of roundoff limit cycles. These effects are illustrated with a numerical example of a sixth-order low-pass filter. The effects of multiplier coefficient quantization in these nonminimal structures are also illustrated in the numerical example.