Design of linear phase IIR filters via weighted least-squares approximation

A new method for designing IIR digital filters with linear phase in the passband is proposed. This method is based on frequency-weighted least-square error optimization using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method. The gradient of the cost function with respect to the design parameters, required for the implementation of the BFGS method, is derived. The proposed method is started by obtaining an initial IIR filter design using model reduction of a linear phase FIR filter. Based on this initial design the cost function is minimized using the BFGS method. An example shows that the proposed method leads to very good filter designs.