Spectrum Estimation of Pseudo-random Nonuniformly Sampled Signals in the Fractional Fourier Transform Domain

The fast Fourier transform (FFT) and the fast fractional Fourier transform (FRFT) are used widely in signal processing for uniformly sampled signals. However, in many applications, nonuniform sampling is required in the frequency domain. And the theories and applications of nonuniformly sampled signals in the time and frequency domain have been studied and have a lot of advantages. In this paper, we intend to extend these theories to the fractional Fourier transform domain. First, introduce the digital spectrum (the discrete Fourier transform) of nonuniformly sampled signals. And then analyze the digital spectrum of nonuniformly sampled signals in the Fractional Fourier transform domain. Finally, present two examples and make simulations. The result shows that these theories are also effective in the fractional Fourier transform domain.