Accurate spectral estimation from unequally spaced samples of exponentially damped sinusoidal signals

A method is presented to interpolate and extrapolate unequally spaced signals that are not bandlimited. This is achieved by utilizing the Gregory-Newton quadrature formula which circumvents aliasing without bandlimiting. With the Gregory-Newton quadrature formula, it is possible to compute the Fourier spectrum of the unequally spaced signals, which is not bandlimited. The effect of noise on the Gregory-Newton quadrature formula is observed. Specifically, the quality of interpolation, extrapolation, and the spectrum as a function of various signal-to-noise ratios is observed. This may be a useful technique for computing unaliased spectra of unequally spaced, damped sinusoidal signals having a signal-to-noise ratio greater than 20 dB.