On the Optimal Design of IIR Filter with its State-space Realization

The most widely used digital filters are finite impulse response (FIR) filters that are usually implemented with the transversal structures. For FIR filter, the output signal is a linear combination of filter coefficients that produces a quadratic function (mean-square-error) with a distinctive optimal operation point. FIR filter alternatively be realized for obtaining improvements in comparison of transversal filter structure for speed of convergence, computational complexity and finite word length properties. IIR filtering techniques exhibit reliable alternative for traditional FIR filtering. The principal advantage of IIR filters is lesser parameterization to achieve at par performance of FIR filters. In addition, the pole-zero structures ease their modeling in physical systems. On the other hand, the tradeoff for the attributes have few drawbacks inherent to IIR filtering with recursive structure such as filter stability, convergence to bias and/or local minima and for very slow convergence. This research paper proposes a new structure and realization of IIR filter. Special consideration is given to the issue of optimal state-space realization and newpole modulus based stability is derived.