Harmonic long-memory models

In this paper we address the modeling of long-memory signals with strong harmonic components. Current long-memory models, such as the fractional unit-pole model, fail to address the possibility of periodicities in the data. An example of harmonic long-memory signals is found in heart rate variability signals. We propose the harmonic fractional unit-pole model for modeling both the long-memory and harmonic components. The model is obtained by moving the fractional order pole on the unit circle away from zero frequency in a complex conjugate pair. The characteristics of the model, namely the power spectral density and the autocorrelation function are derived. A method is then given for the generation of harmonic long-memory signals. Finally the harmonic fractional unit-pole model is used to characterize heart rate variability signals