Aliasing in spectrum of nonuniformly sampled signals

Aliasing is a well known phenomenon in spectral analysis of sampled signal and it can be clearly described when the sampling interval remains constant. The situation is more complicated in nonuniform sampling that found its use in some kinds of measurements, such as those in radio-astronomy and biological sciences. In this paper we have derived the formula for power spectral density of nonuniformly randomly sampled sinusoid based on the uniform sampling approximation and Lomb-Scargle periodogram. The obtained results are analyzed with special attention to the aliasing effect. The detectability of a component beyond the Nyquist limit has been proven theoretically and also demonstrated on experimental data: the respiration signal derived from electrocardiogram and the heart rate signal in the condition referred to as cardiac aliasing.