Reconstruction of uniformly sampled signals from non-uniform short samples in fractional Fourier domain

Signal reconstruction from non-uniform samples, especially for non-stationary signals, is an important issue in the area of digital signal processing. As a type of signal processing tool, the fractional Fourier transform has been proved to be effective for solving problems in non-stationary signal processing. For non-stationary discrete-time signals, the reconstruction of uniformly sampled signals from non-uniform samples in the fractional Fourier domain is first derived in this study. Since only finite non-uniform samples are collected in practical applications, for preferable reconstruction, two types of symmetric extensions are considered in the reconstruction to overcome the discontinuity problem that exists in the periodisation of short non-stationary sequences, which is more critical than that of long sequences. In addition, the average signal-to-noise ratio is used to evaluate the performance of the reconstruction with two types of symmetric extensions. Simulations and two applications are given to verify the effectiveness of the proposed reconstruction method.