Spectral Analysis and Reconstruction for Periodic Nonuniformly Sampled Signals in Fractional Fourier Domain

Nonuniform sampling occurs in many applications due to imperfect timebase or random events. Periodic nonuniform sampling is a special type of nonuniform sampling. The properties and applications of periodic nonuniform sampling signals in traditional Fourier domain have been extensively studied, but so far none of the research papers covering the spectral analysis and reconstruction of periodic nonuniformly sampled signals in fractional Fourier domain have been published. This correspondence is to explore the spectral properties of periodic nonuniformly sampled signals associated with the fractional Fourier transform. First, based on the uniform fractional Fourier transform kernel, the general spectral representation of periodic nonuniformly sampled signals has been derived. Second, detailed analysis of periodic nonuniformly sampled chirp signals in the fractional Fourier domain have been performed. The results can be used to estimate the chirp rate and the sampling offsets. Finally, a more simple relationship between the discrete fractional spectrum of periodic nonuniformly sampled signals and the continuous spectrum has been obtained. Based on this relationship, the original continuous spectrum can be reconstructed from periodic nonuniformly sampled signals in fractional Fourier domain. In addition, the simulations are carried out to verify the correctness of the results.