Efficient Sampling of Band-limited Signals from Sine Wave Crossings

TL;DR

This paper introduces an efficient method for reconstructing band-limited signals from sine wave crossings, enabling simpler A/D converters and spectral analysis with reduced power and complexity.

Contribution

It proposes a novel approach to signal reconstruction using sine crossings and a modified Lagrange interpolator, improving efficiency and enabling spectral analysis from crossing data.

Findings

Reconstruction method achieves linear complexity.

Enables spectral analysis from sine crossings.

Validated with numerical examples.

Abstract

This correspondence presents an efficient method for reconstructing a band-limited signal in the discrete domain from its crossings with a sine wave. The method makes it possible to design A/D converters that only deliver the crossing timings, which are then used to interpolate the input signal at arbitrary instants. Potentially, it may allow for reductions in power consumption and complexity in these converters. The reconstruction in the discrete domain is based on a recently-proposed modification of the Lagrange interpolator, which is readily implementable with linear complexity and efficiently, given that it re-uses known schemes for variable fractional-delay (VFD) filters. As a spin-off, the method allows one to perform spectral analysis from sine wave crossings with the complexity of the FFT. Finally, the results in the correspondence are validated in several numerical examples.