Xampling: Compressed Sensing of Analog Signals

TL;DR

Xampling extends compressed sensing to analog signals by combining analog pre-processing with nonlinear algorithms for efficient low-rate sampling across various applications, emphasizing practical hardware considerations.

Contribution

The paper introduces a unified Xampling framework that generalizes compressed sensing for analog signals, integrating analog compression and subspace detection.

Findings

Applicable to multiband communications with unknown carriers

Effective for signals with finite rate of innovation

Addresses practical hardware constraints

Abstract

Xampling generalizes compressed sensing (CS) to reduced-rate sampling of analog signals. A unified framework is introduced for low rate sampling and processing of signals lying in a union of subspaces. Xampling consists of two main blocks: Analog compression that narrows down the input bandwidth prior to sampling with commercial devices followed by a nonlinear algorithm that detects the input subspace prior to conventional signal processing. A variety of analog CS applications are reviewed within the unified Xampling framework including a general filter-bank scheme for sparse shift-invariant spaces, periodic nonuniform sampling and modulated wideband conversion for multiband communications with unknown carrier frequencies, acquisition techniques for finite rate of innovation signals with applications to medical and radar imaging, and random demodulation of sparse harmonic tones. A hardware-oriented viewpoint is advocated throughout, addressing practical constraints and exemplifying hardware realizations where relevant. It will appear as a chapter in a book on "Compressed Sensing: Theory and Applications" edited by Yonina Eldar and Gitta Kutyniok.