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A novel Fourier transform estimation method using random sampling

This paper considers Fourier transform estimation of deterministic signals from a finite number of random samples. We refer to the recently reported methods by Masry facilitating significant acceleration of the convergence rates of the Fourier transform estimates with the growing number of samples. The acceleration does not start uniformly across all frequencies. It starts at DC and its close neighborhood. Then it spreads to higher frequencies once the average sampling rates significantly increase. In this paper we propose a modification of the signal sampling methods and appropriate to them data processing algorithms to allow moving away from zero the frequency about which the acceleration starts to practically any point in the frequency domain. We derive an expression of the mean-square error of the estimated spectrum as a measure of accuracy. Simulation results confirm the validity of the results presented in this paper.