A System Identification Based Approach for Design of IIR Digital Filters with Robust Stability

Design problem of infinite impulse response (IIR) filters is generally a non-linear optimization problem due to the presence of denominator polynomial. Additionally, the stability condition (position of poles) must be considered when optimizing the filter coefficients. Hence, an iterative optimization is usually required to solve the design problem for stable IIR filter. In this paper, we present a new method for the design of IIR filters without iterative optimization. We employ a system identification method for time series signal where the input signal and its ideal output signal are generated by a Gaussian stochastic process with a prescribed frequency characteristic. Then, based on Parseval’s theorem, we can obtain the IIR filter in the frequency domain. The advantage of the proposed method is to compute the IIR stable digital filters as a closed-form solution. That is, we can approximate the given frequency response and the constant group delay without using any iterative optimization. Also, we present a design method with specified maximum pole radius to achieve robust stability. Finally, design examples are presented to illustrate the effectiveness of the proposed method by designing a high-pass and low-pass IIR digital filter.