Spectrum estimation of non-uniformly sampled signals

A new method of spectrum estimation of nonuniformly sampled signals (sampling instants are randomly distributed) is proposed in this paper. It is assumed that the analysed signal carries most of its power at certain frequencies, i.e. the main components of the signal are periodic. The values of the frequencies are presumed to be unknown before the spectrum estimation starts. The signal is modelled as a linear combination of sinusoids with additive wideband noise. It is required that the power of the noise and of the signal harmonics which lie outside the area covered by the pre-selected frequency grid (for which the spectrum is estimated), is a small fraction of the total power of the signal. The spectrum is estimated by a recursive algorithm. The proposed procedure aims at two tasks: to determine frequencies which carry signal power and to obtain the amplitudes of the respective sinusoidal components. The method has been tested by simulation. It showed an important feature of estimating the signal spectrum above the Nyquist frequency (understood as half of the average sampling frequency)