Fourier-autoregressive spectral estimation

The Fourier-Autoregressive spectral estimator allows one to perform autoregressive spectral estimation on a narrowband basis as opposed to the conventional broadband approach. This capability is particularly valuable when the desired time series is a narrowband process, which is embedded in broadband observation noise. To generate the narrowband time series, the original data is passed through a bank of bandpass filters which is conveniently implemented by an FFT. It is shown that for a sinusoidal process in white noise, a tradeoff may be effected between the narrowband signal-to-noise ratio, which is principally responsible for spectral resolution, and the useable data record length.