FFT Interpolation from Nonuniform Samples Lying in a Regular Grid

TL;DR

This paper introduces a direct FFT-based interpolation method for periodic band-limited signals from nonuniform samples in a regular grid, improving efficiency and stability over existing techniques.

Contribution

It proposes a novel interpolation method exploiting erasure polynomial properties, offering significant improvements over prior burst error recovery techniques.

Findings

Method has comparable complexity to FFT

Numerically stable and efficient

Outperforms existing BER technique

Abstract

This paper presents a method to interpolate a periodic band-limited signal from its samples lying at nonuniform positions in a regular grid, which is based on the FFT and has the same complexity order as this last algorithm. This kind of interpolation is usually termed "the missing samples problem" in the literature, and there exists a wide variety of iterative and direct methods for its solution. The one presented in this paper is a direct method that exploits the properties of the so-called erasure polynomial, and it provides a significant improvement on the most efficient method in the literature, which seems to be the burst error recovery (BER) technique of Marvasti's et al. The numerical stability and complexity of the method are evaluated numerically and compared with the pseudo-inverse and BER solutions.