Resolution of conventional Fourier, autoregressive, and special ARMA methods of spectrum analysis

The two-sinusoid frequency resolution of conventional Fourier, autoregressive (AR), and a special autoregressive-moving average (ARMA) power spectral density (PSD) estimators is considered in this paper. The conventional Fourier spectrum analysis methods have resolutions which are, on the average, roughly the reciprocal of the observation interval. However, for any particular case of two sinusoids of some initial phases, the resolution may be much greater or much less than the average resolution. The special ARMA PSD estimator can, in principle, perfectly resolve any two sinusoids if the autocorrelation function is perfectly known. The AR spectral estimate has a resolution which varies as a function of signal-to-noise ratio (SNR) from that of the conventional Fourier methods at low SNB to that of the special ARMA method of high SNR. A signal power estimation and a noise power cancellation technique is also presented.