Design method of interpolation kernel using piecewise $\textit{n}$ th polynomials

Sampling rate conversion widely used in subband coding, A/D and D/A transitions etc. is an important techniques. Nyquist filters and the filter banks have been used far the sampling converter. However, they need many memories and, whenever the sampling rate is changed it is necessary to redesign filters. Then we propose design method of the new interpolation kernel. Design method of the new interpolation kernel is approximated each piecewise of lowpass filter by n th polynomials. The proposed kernel is not redesigned, whenever the sampling rate is changed. The proposed kernel is a continuous function, the sampling rate of the rational number can be converted.