Design of robust IIR magnitude filters via semidefinite programming

In this paper we consider the design of lowpass infinite impulse response (IIR) magnitude filters which are robust against the implementation error. It is shown that the design problem can be cast as a quasiconvex problem with a set of linear matrix inequality (LMI) constraints and the autocorrelation sequences of the filter coefficients as the design variables. The relation between the norm error of autocorrelation sequences and that of filter coefficients is derived, and the issue of filter stability is addressed by deriving a lower bound on the distance from the pole to the unit circle. Simulation results show that our designed filter is immune from the errors caused by finite precision implementation. The method can also be used in similar highpass and bandpass IIR filter design.