Digital signal resampling is required in many digital signal and image processing applications. Among the digital convolution based signal resampling methods, sinc-interpolation is theoretically the best one since it does not distort the signal defined by its samples. Discrete sinc-interpolation is most frequently implemented by the 'signal spectrum zero padding method.' However, this method is very inefficient and inflexible. Sinc-interpolation badly suffers also from boundary effects. In the paper, a flexible and computationally efficient methods for boundary effects free discrete sinc-interpolation are presented in two modifications: frame (global) sinc-interpolation in DCT domain and sinc-interpolation in sliding widow (local). In sliding window interpolation, interpolation kernel is a windowed sinc-function. Windowed sinc-interpolation offers options not available with other interpolation methods: interpolation with simultaneous local adaptive signal denoising and adaptive interpolation with super resolution. The methods outperform other existing discrete signal interpolation methods in terms of the interpolation accuracy and flexibility of the interpolation kernel design. Their computational complexity is O[log(Size of the frame)] per output sample for frame interpolation and O(Window Size) per output sample for sliding window interpolation.