Fast Signal Interpolation Through Zero-padding and FFT/IFFT

TL;DR

This paper introduces a fast signal interpolation method using zero-padding and FFT/IFFT, providing an efficient approximation to ideal sinc interpolation based on the sampling theorem.

Contribution

The paper presents a novel fast interpolation algorithm leveraging FFT and zero-padding, connecting sinc functions with the Dirichlet function for improved efficiency.

Findings

The proposed method approximates ideal sinc interpolation effectively.

It reveals the fundamental link between sinc functions and the Dirichlet function.

The algorithm offers a computationally efficient alternative to traditional interpolation methods.

Abstract

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.