The problem of digital signal and image resampling with discrete sinc interpolation is addressed. Discrete sinc interpolation is theoretically the best one among the digital convolution-based signal resampling methods because it does not distort the signal as defined by its samples and is completely reversible. However, sinc interpolation is frequently not considered in applications because it suffers from boundary effects, tends to produce signal oscillations at the image edges, and has relatively high computational complexity when irregular signal resampling is required. A solution that enables the elimination of these limitations of the discrete sinc interpolation is suggested. Two flexible and computationally efficient algorithms for boundary effects free and adaptive discrete sinc interpolation are presented: frame-wise (global) sinc interpolation in the discrete cosine transform (DCT) domain and local adaptive sinc interpolation in the DCT domain of a sliding window. The latter offers options not available with other interpolation methods: interpolation with simultaneous signal restoration/enhancement and adaptive interpolation with super resolution.