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arXiv · 2603.16242

Signal Recovery from Time and Frequency Samples

Mert Kayaalp·Oleg Szehr
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Abstract

We analyze signal recovery when samples are taken concomitantly from a signal and its Fourier transform. This two-sided sampling framework extends classical one-sided reconstruction and is particularly useful when measurements in either domain alone are insufficient because of sensing, storage, or bandwidth constraints. We formulate the resulting recovery problem in finite-dimensional spaces and reproducing kernel Hilbert spaces, and illustrate the infinite-dimensional setting in a Fourier-symmetric Sobolev space. Numerical experiments with sinc- and Hermite-based schemes indicate that, under a fixed sampling budget, two-sided sampling often yields better conditioned systems than one-sided approaches. A simplified spectrum-monitoring example further demonstrates improved reconstruction when limited time samples are supplemented with frequency-domain information.

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Mert Kayaalp, Oleg Szehr. 2026-03-17. Signal Recovery from Time and Frequency Samples. https://arxiv.org/abs/2603.16242

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