Fast Signal Interpolation Through Zero-padding and FFT/IFFT

Based on the sampling theorem, interpolation should be conducted by employing the sinc functions as the kernels. Inspired by the fact that the discrete Fourier transform (DFT) is sampled from the discrete time Fourier transform, a fast signal interpolation algorithm based on zero-padding and fast Fourier transform (FFT) and inverse FFT (IFFT) is presented. This algorithm gives a good approximate of the ideal interpolation, in spite of the windowing effect. The fundamental difference of this algorithm and the ideal sinc interpolation is unveiled, and shown to be deeply rooted in the connection of the sinc function and the Dirichlet function.