Novel fast algorithm to design optimal eigen filters for transmission systems

The optimal finite impulse response (FIR) filter design has been very popular in science and engineering over many decades due to its guaranteed stability and wide variety of applications, especially for transmission systems. Designing eigen-filters is a common signal processing paradigm. Given a fixed filter length, the objective function is formulated in terms of passband and stop-band energies, and then the appropriate optimization technique is employed to determine the impulse response. In this paper, we would like to present a novel computationally-efficient optimal eigen-filter design scheme. Since the signal processing storage devices become less and less costly and more and more powerful, designing long FIR filters dynamically to address different channel conditions and modulations becomes crucial in modern telecommunication and signal processing applications. Computationally-efficient filter design schemes, which can be facilitated in real-time, are in high demand. Our proposed technology is based on fast eigen-decomposition. The computational complexity of our proposed new method is O(M²) compared to O(M³) of the conventional technique.