Design of multiplierless elliptic IIR filters

A new straightforward design of a special class of elliptic IIR filters is presented. The major goal is the complexity reduction of the realized digital filter. The multiplier coefficients are implemented with a limited number of shift-and-add operations. This method is also called "multiplierless". Unlike classical design, closed-form relations are derived giving relationships between the filter specification and preferred multiplier coefficients. At least half of the coefficients can be implemented with the minimal number of shift-and-add operations without coefficient quantization. The second half of the coefficients can be optimized without any influence on the values of the first half of the coefficients. A high attenuation margin and low-sensitivity structures are used so that the specification is still fulfilled after quantization of the second half of the multiplier coefficients.