Dual non-negative rational symbols with arbitrary approximation order Original Research Article

We consider the construction of dual filters with a prescribed approximation order, that is with the ability to reproduce polynomials up to a certain degree. Specifically, we illustrate how to construct nonnegative duals when starting from a nonnegative primal filter. This construction produces filters with rational symbol, which can then be either implemented efficiently as recursive IIR filter or approximated by a Laurent polynomial.