Signal reconstruction from recurrent samples in fractional Fourier domain and its application in multichannel SAR

Sampling plays a critical role in remote sensing and signal analysis. In conventional sampling theory, the signal is sampled at a uniform rate at a minimum of twice the signal bandwidth. However, in many multichannel systems such as analog-to-digital converters, synthetic aperture radar (SAR), and synthetic aperture sonar (SAS), it requires that multidimensional signals or digital images be reconstructed from their recurrent samples, and the signals may not be bandlimited in the traditional Fourier domain. In this paper, a reconstruction algorithm for two-dimensional (2D) recurrently sampled signals is proposed in the fractional Fourier domain. This algorithm can handle the situations where the signal is nonbandlimited, and it is extended to the case of undersampling, where the traditional reconstruction algorithms might fail. The algorithm is based on the nonuniform fractional spectrum, and a method to speed up the computation of the nonuniform fractional spectrum is introduced. Reconstruction from recurrent samples in the case of undersampling is illustrated using numerical examples, and an application to multichannel SAR imaging is included to illustrate these results.