On Design of IIR Cascaded-Resonator-Based Complex Filter Banks

This paper extends the research on cascaded-resonator (CR)-based filter banks introduced in previous studies. These IIR filter banks are online adaptive, making them highly suitable for spectral decomposition and signal analysis. The multiple-resonator-based structure offers an efficient design with low side lobes and high stopband attenuation. While earlier works focused on the fundamental structure and principles of these filter banks, the efficiency of their design was not thoroughly explored. In this study, thanks to the full periodicity of the frequency response, significant improvements in the modeling of the characteristic polynomial (the denominator of the transfer function) and preprocessing filters are introduced, resulting in an enhanced sparsity and a computational efficiency. Additionally, the previously employed linear programming algorithm for solving semi-infinite problems including a large number of linear constraints is replaced by more advanced quadratic programming (QP) or linear least-squares (LLS) optimization methods. These changes lead to a much faster and more powerful design process, even for filter banks with a larger number of resonator cascades and/or resonators per cascade. Furthermore, additional enhancements to the design methodology are proposed, further improving the robustness and applicability of the filters. These advancements enable the creation of highly efficient filter banks capable of handling complex and dynamic spectral analysis tasks in real time.