Application of modern control theory on performance analysis of generalized notch filters

Generalized notch filters have various applications in electrical and optical systems, which could also be interconnected with diverse systems. Both the transfer function and state space approaches can be used to formulate 2nd order notch filters and double notch filters to conduct performance analysis on a basis of classical control and modern control theories. Theoretical design of diverse types of notch filters is conducted, covering basic type, standard type, lowpass and highpass notch filters. In addition, root locus plots are introduced to track locations of system poles of notch filters for stability analysis and potential accurate pole placement. This approach can be expanded to notch filter analysis in other systems as well.