A Class of Deterministic Sensing Matrices and Their Application in Harmonic Detection

TL;DR

This paper introduces a new class of deterministic Fourier-based sensing matrices that improve sparse recovery performance and enable hardware-friendly harmonic detection from under-sampled data.

Contribution

It presents a novel deterministic sensing matrix construction with proven properties, facilitating harmonic detection without random sampling.

Findings

Deterministic matrices outperform random partial Fourier matrices in sparse recovery.

The proposed method accurately estimates harmonic frequencies and amplitudes from under-sampled data.

The approach is effective even in noisy environments.

Abstract

In this paper, a class of deterministic sensing matrices are constructed by selecting rows from Fourier matrices. These matrices have better performance in sparse recovery than random partial Fourier matrices. The coherence and restricted isometry property of these matrices are given to evaluate their capacity as compressive sensing matrices. In general, compressed sensing requires random sampling in data acquisition, which is difficult to implement in hardware. By using these sensing matrices in harmonic detection, a deterministic sampling method is provided. The frequencies and amplitudes of the harmonic components are estimated from under-sampled data. The simulations show that this under-sampled method is feasible and valid in noisy environments.