Variable digital filters having a recursive structure

Variable digital filters allow the frequency characteristics of a filter to be manipulated. Frequency transformations have been successfully used to obtain a variable filter from a nonrecursive prototype. However, this technique cannot be applied directly to filters having a recursive structure. A variation of this method is presented which allows variable filters to be obtained from both recursive and nonrecursive prototypes. This method has special advantages when the prototype has an equal number of poles and zeros (e.g., digital filters obtained by the bilinear transformation from an analog filter).