On the sensitivity of realizations of real coefficient digital filters using complex arithmetic

Previously, new structures using complex arithmetic were proposed for the implementation of real coefficient IIR digital filters. The quantization of the real-equivalent of a complex coefficient in these filters violates an assumption usually adopted in the analysis of coefficient sensitivity, i.e., quantization errors are uncorrelated to each other. In the present paper, a simple expression is derived to measure the L₂ sensitivity, of structures using complex arithmetic. Then, an explicit expression of the L₂ sensitivity is obtained for second-order digital filters with minimum norm