All-pass based efficient and robust structures for finite precision implementation of digital filters

In this paper, a novel structure is derived for digital filters implemented with finite wordlength (FWL). Based on a realization of 1st order complex all-pass systems, we develop a structure for a real 2nd-order filter with complex conjugate poles, in which the transfer functions between the two states and the input signal are in a power-complementary pair. This property ensures that the state dynamics can be controlled easily such that no overflow occurs. In addition, a 2nd-order filter implemented using such a structure needs 7 multiplications and 7 additions for computing each output samples, which is more efficient than the existing optimal FWL structures. A procedure is given to extend such a structure to higher order filters and the corresponding expression for roundoff noise gain is derived. Simulations show that our proposed structure yields the excellent finite word length performance and outperforms the classical optimal structures in terms of reducing quantization errors.