Methods for sample rate conversion are provided that use a polynomial interpolator with minimax stopband attenuation. A method for sample rate conversion of an input signal is provided that uses a time-varying polyphase filter having a discrete polyphase index m. Another method for sample rate conversion of an input signal is provided that uses a time-varying polyphase filter having a continuous polyphase index τ. In these methods, an output time index is mapped to an input sample index and the polyphase index, the polynomial coefficients of a polyphase filter are computed using the polyphase index, and the polyphase filter is applied to an input sample at the input sample index to generate the output sample at the output time index.