An overall optimization method for arbitrary sample rate converters based on integer rate SRC and lagrange interpolation

Combinations of integer ratio sample rate conversion and polynomial interpolators are widely used structures for arbitrary or asynchronous sample rate conversion (ASRC). However, since these two components are typically designed independently, the performance of the structure is not optimal with respect to a given error norm such as weighted least squares or Chebyshev norms. To overcome this drawback, we propose a design method for this class of ASRC filters that enables an optimization of the whole structure. For this reason, an analytical description of the continuous frequency response of the system, derived from a closed formula for the continuous frequency response of Lagrange interpolators, is introduced. Based on this model, we propose a design method that minimizes the error in the Chebyshev sense. ASRC filters designed according to this design procedure exhibit considerably reduced error norms compared to existing designs, whereas the improvement depends on several factors such as signal bandwidth, the prototype filter order, the integer interpolation ratio and the order of polynomial interpolation.