This paper proposes the design method of a function generator for use in a Digital-to-Analog converter for DVD-Audio. The impulse response of the function generator is a compactly supported sampling function of degree 2 that is expressed in the form of linear combination of quadratic piecewise polynomials function systems. To generate this impulse response, we design the convolution operator that can generate quadratic piecewise polynomials from the basis rectangular function. The function generator is constructed by combining a set of these convolution operators suitably. We further simplify the design of this function generator by making use of a two-scale relation of piecewise polynomials. This function generator can be realized in a small scale circuitry.