Reducing the aliasing of nonlinear functions is an important problem in digital signal processing. The introduction of the Antiderivative Antialiasing (ADAA) method brought many benefits and is an active area of research. The current bottleneck in terms of aliasing reduction is the initial conversion from discrete- to continuous-time, which was previously done by linear interpolation. In this paper we derive PolyADAA, a method for computing the ADAA output when this conversion is done using higher order Lagrange interpolation. To obtain a viable solution, the nonlinear function is approximated using Chebyshev polynomials, which enable the ADAA integral to be computed. The paper provides numerical examples to show the effectiveness of the approach and discusses the advantages of the method.