Stability-Ensured Highpass Variable Filter Utilizing Odd-Symmetric Transformation Function
Tian–Bo Deng · 2025
Differing from the conventional constant filter, a variable digital filter (VDF) has a great flexibility in terms of its frequency-response tunability for real-time tuning applications. The user can quickly tune filter’s frequency response whenever the frequency response needs to be changed. However, changing VDF’s coefficients may cause VDF’s instability. To ensure the stability, a smart technique is to do transformations on the VDF’s coefficients. Such transformations can assure that the VDF definitely fulfills the stability requirement. As a consequence, the transformed VDF is ensured to be stable. To carry out the transformations on VDF’s coefficients, it is necessary to employ a transformation function known as unity-bounded function that meets a specifically required condition. If it fulfills this condition, the transformation-based technique ensures the stability. This paper targets at revealing a novel unity-bounded function, which holds odd-symmetry. This odd-symmetric function is characterized by using a pair of parameters. By changing the parameter values, one can obtain a wide variety of functions, and all those functions definitely meet the requirement. This paper includes a variable high-pass filter (HPF) for illustrating the obtained stability. Computer simulations also verify the high design accuracy.