A system identification approach for design of IIR digital filters

In general, the problem of infinite impulse response (IIR) filters design has a non-linearity due to the presence of denominator polynomial; hence, an iterative optimization is usually needed to obtain the solution. In this paper, we independently generate several time series signals in stop-band, transition zone, and pass-band based on an algorithm which generates a Gaussian stochastic process with a prescribed frequency characteristic. After that, we synthesis the input signal and its ideal output signal, and can obtain the IIR filter by using system identification method from these signals. The advantage of the proposed method is that we can compute the IIR stable digital filters as a closed-form solution. We can approximate the given frequency response and the constant group delay without using iterative optimization. Finally, a design example is presented to illustrate the effectiveness of the proposed method by designing a high-pass IIR digital filter. As a result, we confirm the filter designed has a good magnitude response and an almost flat group delay.