Spectral estimation for random sampling using interpolation

Abstract In this paper, we initiate a theoretical investigation of spectral estimation of randomly sampled stochastic processes using interpolation. We develop a new method for spectral estimation of Poisson-sampled stochastic processes. Our method is based on exponential interpolation from the sampled process followed by resampling and usual discrete Fourier transform. We prove that this method — with appropriate corrections — is asymptotically unbiased and show how problems arising from aliasing in the resampling process can be overcome. We compare this method with other methods for spectral estimation of Poisson-sampled processes, and show that — in most cases — the new method is superior in accuracy and speed.

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