Compressive Sensing of Linear Frequency Modulated Signals in Fractional Fourier Domains

Abstract

Compressive sensing is a new technique that allows sampling at very low rates compared to the Nyquist sampling rate, if the signal is sparse. Thus the signal should either be sparse in time domain or we should be able to determine any domain in which the signal is represented sparsely. In the reconstruction process, the signal is reconstructed by using linear projections of itself in an iterative way rather than using all samples of the signal. In this paper, multi-component linear frequency modulated (LFM) signals that are highly dense in time and frequency domains, are transformed into fractional Fourier domains in order to form sparse representations. Then, it is shown that by using compressive sensing in fractional Fourier domains, LFM signals can be represented almost by half of their lengths with high accuracy.