On the design of digital filters implemented with complex arithmetic

A topology for implementing a second-order digital recursive filter using complex arithmetic and having a transfer function with real coefficients is presented. The proposed structure is analyzed using state variables, separating the contributions into a real part and an imaginary part, and combining them at the output. The results give a low sensitivity and low roundoff noise digital filter topology. Accumulators are used to reduce the coefficient sensitivity of the filter structure. The input signal, although real, is applied to both the real and imaginary parts of the filter. It is shown that one of the realizations of the proposed filter could be a switched-capacitors one