Stability-Guaranteed Odd-Order Notch-Width System Design Employing Unity-Bounded Function

It is well known that guaranteeing the stability of a recursive digital filter is the most important issue in the filter design process. The main objective of this paper is to present a new unity-bounded function for designing stable recursive digital filters. As an application example, this paper applies the new unity-bounded function to the design of odd-order recursive notch filters with controllable notch width, while the notch frequency is fixed. Notch filters with various notch widths are designed, and stability triangles are used to verify the stability of the designed odd-order notch filters using the proposed unity-bounded function.