Demystifying Band-Limited Extrapolation

Abstract

Extrapolation of band-limited signals gained scientific attention over the last 60 years. Thefamous methods: Gerchberg-Papoulis algorithm, Prolate spheroidal wave functions (PSWFs), andsinc interpolation—they all promise excellent results. But when it comes to their practical implementation,users may find themselves struggling with many unanswered questions. Especially PSWFsbecame viewed as mysterious. They are hard to compute and even harder to apply. In theory theypromise excellent extrapolation capabilities—something which is contrary to our intuition. This paradoxis resolved if we admit that the real-world data contain noise. In this paper we review the abovementionedmethods and try to provide a brief assessment of their capabilities by considering theeffects of noise and the length of signal observation.